department of mathematics€¦ · 1 bmh-101 calculus-1 5 1 0 6 25 75 2 bmh-102 ... 5 bmh-205...

DEPARTMENT OF MATHEMATICS

Outlines of Tests, Syllabi and Courses of Reading

For

B. Sc. Honors School in Mathematics

(Semester I-VI) (3 Years)

(Under Credit Based Continuous Evaluation Grading System)

For

Batch 2019 & 2020

SRI GURU GRANTH SAHIB WORLD UNIVERSITY

FATEHGARH SAHIB (Established Under Punjab State Act 20/2008 and approved by UGC under Section 2(f) of UGC Act 1956)

(All Copyrights Reserved with the University)

Batch 2019 & 2020

Eligibility Criteria for Admission

A candidate must have passed 10+2 (having Mathematics as one of the major subjects) with at least

50 percent marks or an equivalent CGPA.

Admission Procedure: The admission will be made purely on merit basis of 10+2 examination.

OUTLINES OF TEST & DISTRIBUTION OF MARKS

1. Evaluation

a) There shall be Two Mid Term Examinations in each semester.

b) The internal assessment based on the continuous comprehensive evaluation in theory as

well as practical subject will carry a weightage 25% of the total marks allocated to the

paper.

c) End semester examination will carry a weightage of 75% of total marks.

d) Each theory paper examination shall be of 3 hours duration.

2. Format of Mid Semester Test (MST) Question Paper

a) The internal paper will carry 26 marks and will be of 1.5 hours duration.

b) The question paper will be divided into two sections (A and B).

c) Section A will be compulsory consisting of four short answer type questions of 2 marks

each.

d) Section B will consist of five questions of six marks each. Student will be required to

attempt any three questions form section B.

3. Marks Distribution for Internal Assessment based on Continuous Evaluation:

A) Theory Papers (Total Marks 100, Internal Assessment=25 Marks)

The 25 Marks will be awarded on the basis of following distribution:

a) First Mid Semester Test : 6.5 marks

b) Second Mid Semester Test : 6.5 marks

c) Seminar/ Assignment/ Quiz : 09 marks

d) Attendance : 03 marks

The marks for attendance will be allocated as under:

More than 90% : 03 marks

80.1% to 90% : 02 marks

75 to 80% : 01 marks

Note: For theory papers having total marks different than 100, the internal assessment marks

will be awarded on proportionate basis of above marks.

B) Practical Papers

(Total Marks= 50, External Marks= 37.5, Internal Marks= 12.5 Marks)

The 12.5 Marks for Internal Assessment will be awarded as follows:

a) Lab Performance during Semester : 6.5 marks

b) Practical Note Book : 03 marks

c) Attendance : 03 marks

The marks for attendance will be allocated as under:

More than 90% : 03 marks

80.1 to 90% : 02 marks

75 to 80% : 01 marks

Note: For practical papers having total marks different than 50, the internal assessment

marks will be awarded on proportionate basis of above marks.

4. Format of End Semester Theory Examination Paper

a) The end semester theory paper examination will carry 75 marks (In case the total marks

allocated to the paper are 100) and will be of 3 hours duration.

b) The question paper will be divided into three sections (A, B and C).

c) Section A will be compulsory consisting of nine short answer type questions (uniformly

set from the whole syllabus) of 03 marks each.

d) Section B will consist of four questions of 12 marks each from Part-I. The student will

be required to attempt any two questions.

e) Section C will consist of four of 12 marks each from Part-II. The student will be

required to attempt any two questions.

Semester -I

Sr.

No.

Course

Code

Course Title Contact Hours

L T P

Credits Max. Marks

Internal External

1 BMH-101 Calculus-1 5 1 0 6 25 75

2

BMH-102 Basic Algebra 5 1 0 6 25 75

3 BMH -103 Coordinate Geometry 5 1 0 6 25 75

4

BMH-104 Fundamentals of Computer

Science

5 1 0 6 25 75

5 BMH-105A Punjabi

(For students who have

studied Punjabi in Matric )

3 0 0 3 25 75

BMH-105B Elementary Punjabi

(For students who have not

studied Punjabi in Matric )

3 0 0 3 25 75

Credits: 27

Semester-II

Sr.

No.

Course

Code


L T P

Credits Max. Marks

Internal External

1 BMH-201 Calculus-II 5 1 0 6 25 75

2 BMH-202 Matrix Algebra 5 1 0 6 25 75

3 BMH-203 Analytical Solid Geometry 5 1 0 6 25 75

4 BMH-204 Discrete Mathematics - I 5 1 0 6 25 75

5 BMH-205 Communication Skills in

English

3 0 2 4 25 75

Credits: 28

Semester-III

Sr.

No.

Course Code Course Title Contact Hours

L T P

Credits Max. Marks

Internal External

1 BMH-301 Real Analysis 5 1 0 6 25 75

2 BMH-302 Ordinary Differential

Equations

5 1 0 6 25 75

3 BMH-303 Mathematical Methods 5 1 0 6 25 75

4 BMH-304 Programming in C 4 0 0 4 25 75

BMH-304L Programming in C Lab 0 0 4 2 12.5 37.5

5

BMH-305 Physics 4 0 0 4 25 75

BMH-305L Physics Lab 0 0 4 2 12.5 37.5

Credits: 30

Semester-IV

Sr.

No.

Course Code Course Title Contact Hours

L T P

Max. Marks

Credits Internal External

1 BMH-401 Basic Linear Algebra 5 1 0 6 25 75

2 BMH-402 Partial Differential

Equations

5 1 0 6 25 75

3 BMH-403 Numerical Methods 4 0 0 4 25 75

BMH-403L Numerical Methods

Lab

0 0 4 2 12.5 37.5

4 BMH-404 Chemistry 4 0 0 4 25 75

BMH-204L Chemistry Lab 0 0 4 2 12.5 37.5

5 BMH-405 Environment Science 5 1 0 6 25 75

Credits: 30

Semester-V

Sr.

No.

Course

Code


L T P

Credits Max. Marks

Internal External

1 BMH-501 Modern Algebra 5 1 0 6 25 75

2 BMH-502 Discrete Mathematics-II 5 1 0 6 25 75

3 BMH-503 Probability and Statistics 5 1 0 6 25 75

4 BMH-504 Operations Research 5 1 0 6 25 75

5 BMH-505 Statics 5 1 0 6 25 75

Credits: 30

Semester-VI

Sr.

No.

Course

Code


L T P

Credits Max. Marks

Internal External

1 BMH-601 Complex Analysis 5 1 0 6 25 75

2 BMH-602 Metric Spaces 5 1 0 6 25 75

3 BMH-603 Special Functions 5 1 0 6 25 75

4 BMH-604 Dynamics 5 1 0 6 25 75

5 BMH-605 Seminar -- - -- 6 100 ---

Credits: 30

CALCULUS-I

(BMH-101)

Contact Hours: 60 hours Total Marks: 100

External Evaluation: 75 Marks Internal Assessment: 25 Marks

Objectives: The objective of this course is to encourage students to model a written description of a

physical situation with a function, a differential equation or an Integral.

Outcomes: Students will able to work with functions. They will understand the meaning of

derivative in terms of rate of change and local linear approximation.

PART - I

Ԑ-δ definition of the limit of a function, algebra of limits, Continuity, Differentiability, Successive

differentiation, Leibnitz theorem, Rolle’s Theorem, Mean value theorems, Taylor’s series,

Maclaurin series and indeterminate forms.

Asymptotes, Test of concavity and convexity, Points of inflexion, Multiple points, Tracing of

curves in cartesian and polar coordinates, Curvature, cartesian, polar and parametric formulae for

radius of curvature.

PART - II

Functions of several variables, domain and range, level curves and level surfaces, Limit and

continuity in two variables, partial derivatives, total differential, Fundamental lemmas, differential

of functions of n variables and of vector functions, Jacobian matrix, derivatives and differentials of

composite functions and general chain rule.

Implicit functions, inverse functions, curvilinear coordinates, geometrical applications, directional

derivatives, partial derivatives of higher order, higher derivatives of composite functions, Laplacian

in polar, cylindrical and spherical coordinates, higher derivatives of implicit functions, Maxima and

minima of functions of several variables and Lagrange Multiplier method.

Text Books

1. Thomes, G.B. and Finney, R.L., Calculus and Analytic Gemetry, Pearsons education, Ninth

edition, 2010.

2. Kreyszig, E., Advanced Engineering Mathematics, John Wiley and Sons, 1999.

3. Jain, R.K. and Iyenger, S.R.K., Advanced Engineering Mathematics, Narosa Publication,

2012.

References

1. Louis Liethold., Calculus with Analytic Geometry, HarperCllins Publication, 1986.

2. Khalil Ahmad, Text Book of Calculus, World Education Publishers, 2012.

BASIC ALGEBRA

(BMH-102)



Objectives: The objective of this course is to recognize the importance of real number system.

Outcomes: Students will be able to produce and interpret graphs of basic functions. They will able

to solve equations and inequalities both algebraically and graphically. Students will able to

recognize technical terms and appreciate its uses in applied science and engineering.

PART - I

De-Moivre’s theorem, its applications to find n nth roots of a complex number, to solve an

algebraic equation with real coefficients, expansions of sin^n x, cos^n, sin nx, cos nx.

Exponential function, circular function, hyperbolic function, logarithmic function, inverse circular

function, inverse hyperbolic function, summation of series using C+iS method.

PART - II

Polynomials, Euclid’s algorithm, greatest common divisor, unique factorization of polynomials

over a field F of numbers (statement only), fundamental theorem of algebra (statement only), roots

and their multiplicity, relationship between roots and the coefficients, evaluation of integral powers

of roots and symmetric functions of roots.

Transformation of equations, Descartes rule of signs, solution of cubic equations using Cardan's

method and trigonometric method and solution of biquadratic equation using Descartes method and

Ferrari's method.

Text Books

1. Chandrika Prasad, Text Book of Algebra, 2005.

2. Sharma and Shah, Algebra-I, Pearson Ed, 2000.

References

1. Kurosh, A., Higher Algebra, Moscow Mir Publisher, 1972.

2. Kreyszig, E., Advanced Engineering Mathematics, John Wiley and Sons, 1999.

3. Jain, R.K. and Iyenger, S.R.K., Advanced Engineering Mathematics, Narosa Publication,

2012.

COORDINATE GEOMETRY

(BMH-103)



Objectives: The objective of the course is to get basic knowledge about Circle, Parabola,

Hyperbola, Ellipse and polar equation of conic.

Outcomes: Students will be able to understand the concepts and advance topics related to two-

dimensional geometry i.e. concepts of tangent, normal, pole and polar and how to trace the conic.

PART - I

Pair of lines: homogeneous equation of second degree, General Equation of 2nd degree, Pair of

lines joining the origin to the points of intersection of a curve and a line,

Change of Axis: Translation of axes, rotation of axes, general transformation, invariants

Circle: definition of the circle, tangents and normal, chord of contact, pole and polar, chord with

given middle point, polar equation of circle.

Parabola: tangents and normal, tangents from a point, chord of contact, pole and polar, chord with

given middle point, parametric coordinates, diameter, geometrical properties.

Ellipse: Properties of ellipse, parametric representation of ellipse, tangents, normals, equation of

chord joining two points on ellipse. Director circle of ellipse, chord of contact, conjugate lines and

conjugate diameter, geometrical properties.

PART - II

Hyperbola: tangents and normal, tangents from a point, chord of contact, pole and polar, chord

with given middle point, fundamental rectangle, parametric representation of hyperbola, asymptotes

of hyperbola, Conjugate hyperbola, rectangular hyperbola

Polar equation of a conic, polar equation of tangent, normal, polar and asymptotes, general equation

of second degree, tracing of parabola, ellipse and hyperbola.

Text Books

1. Shanti Narayan, Analytical Solid Geometry, S. Chand and Company, 2007.

2. Jain P.K. and Khalil Ahmad, Textbook of Analytical Geometry, New Age International (P)

Ltd.Publishers, Second edition, 2005.

References

1. Loney, S.L., The elements of coordinate geometry, Michigan Historical Reprint Series, Second

edition, 1896.

FUNDAMENTALS OF COMPUTER SCIENCE (BMH-104)



Objectives: The main objective of this course is to help the students in understanding the basic

concepts and technologies which constitute information technology.

Outcomes: Students will be able to demonstrate a basic understanding of fundamental concepts of

information technology.

PART -I

Historical Evolution of Computer: Characterization of Computers, types of Computers, the

Computer generations.

Basic Anatomy of Computers: Memory unit, input-output unit, arithmetic logic unit, control unit,

central processing unit, RAM, ROM, PROM, EPROM.

Input-Output Devices: Punched hole devices, magnetic media devices, printers, keyboard,

scanners, OCR, OMR.

Number System: Non-positional and positional number systems, base conversion, fractional

numbers, various operations on binary numbers: addition, subtraction, multiplication and division.

Secondary Storage: sequential vs random storage, floppy, hard disk, optical disk.

PART – II

Computer Code: BCD, EBCDIC, ASCII, Grey Code

Computer Software: Introduction, types of software: application and systems software.

Computer Languages: Machine Language, assembly language, high level language, 4GL,

assembler, compiler and interpreter.

Networking: Basics, types of networks (LAN, WAN, MAN), topologies, communication media Internet: Internet and its applications, working knowledge of Search engines, E-commerce:

meaning, advantages and application of e-commerce, Virus, Threats.

Text Books

1. V Rajaraman, "Fundamentals of Computers", PHI, N. Delhi, 1996.

2. N Subramanium, "Introduction to Computers", Volume-I.

References

1. Norton Peter, Introduction to Computers, Tata McGraw Hill (2005).

2. Shelly G.B., Cashman T.J., Vermaat M.E., Introduction to computers, Cengage India Pvt

Ltd (2008).

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aukweIkwr dI jvwb qlbI kIqI jwvy

176. Express pRgt krnw 177. Extracts taken tUkW lY leIAW 178. Extraordinary AswDwrx

179. Fertilizer demonstration officer Kwd pRdrSn APsr 180. Field investigator KyqrI pVqwlkwr 181. File dwier krnw, PweIl krnw, imsl 182. File in play action kwrvweI ADIn PweIl 183. Financial commissioner iv`q kimSnr, mwl qy sk`qr 184. Financial commissioner Revenue,

Punjab

iv`q kimSnr, mwl pMjwb

185. Financial year mwlI swl, ivqI swl 186. Finger print expert auNgl inSwn mwihr 187. First class magistrate mYijstRyt pihlw drjw 188. Fixation of pay qnKwh insicq krnw 189. For approval prvwngI leI 190. For comments it`pxI leI 191. For consideration ivcwr leI 192. For discussion ivcwr- vtWdry leI 193. For disposal or report inptwry jW irport leI 194. For favour of doing the needful loVINdI kwrvweI leI 195. For gross negligence on your part Awp dI AiqAMq AxgihlI leI, Awp dI BwrI

lwprvwhI krky 196. For information jwxkwrI leI, sUcnw leI 197. For spot enquiry mOky qy pVqwl leI 198. Formal approval is necessary rsmI prvwngI zrUrI hY 199. Fortnightly pMdrvwVy dw, ADmwisk 200. Forwarded for immediate

compliance

qurMq pwlxw ih`q ByijAw jWdw hY

201. Forwarding letter Awmu`K p`qr, iBjvweI p`qr 202. Geologist BoN ivigAwnI 203. Goods clerk mwl klrk 204. Government account jmWH kIqw 205. Grand total kul joV 206. Guarantee of service nOkrI dI gwrMtI, syvw dI gwrMtI 207. Guardian srpRsq, gwrfIAn 208. Halting allowance pVw-B`qw 209. Hand writing expert ilKweI mwihr 210. Head Master mu`K AiDAwpk 211. Head of department ivBwg dw muKI 212. Head office mu`K dPqr 213. Hearsay evidence suxI-suxweI gvwhI 214. Here with enclosed ies dy nwl n`QI hY 215. Here with please nwl hI pyS hY 216. Hereby ies duAwrw 217. Hereinafter ies auprMq 218. Home Minister gRih mMqrI 219. Honorarium mwn-Bytw 220. Horticulture Department bwgvwnI ivBwg 221. House building advance mkwn auswrI krjw 222. Immigration authority Awvws AiDkwrI 223. In anticipation of your sanction and

approval

Awp jI dI mnzUrI qy pRvwngI dI Aws ivc

224. In due course auicq smyN qy, mOky isr 225. In duplicate do prqW ivc, nkl smyq 226. In lieu of dI QW

227. In question ivcwr ADIn, pu`C ADIn 228. In the circumstances Aijhy hwlq ivc 229. In the interest of public lok ih`q leI 230. In writing ilKqI rUp ivc 231. Incidental charges pRsMigk Krcy 232. Increment qnKwh-qr`kI, swlwnw qr`kI 233. Increment stopped swlwnw qr`kI rokI geI 234. Indian administrative service Bwrq pRbMD syvw 235. Indian penal code BwrqI dMf kof 236. Information sUcnw, jwxkwrI 237. Information Bureau sUcnw ibaUro 238. Information officer sUcnw APsr 239. Initial pay mu`FlI qnKwh 240. Initials shI 241. Inspector generals of prison ieMspYktr-jnrl, jylHW 242. Institution sMsQw 243. Instructions hdwieqW 244. Interview mulwkwq, ieMtrivauU 245. Investigation officer qPqIS APsr 246. Invigilator prIiKAw ingrwn 247. Irregular byinXmW, bykwiedw, AinXimq 248. Issue immediate remainder qqkwl Xwd p`qr ByijAw jwvy 249. Issue immediately qqkwl ByijAw jwvy 250. Issue today A`j hI ByijAw jwvy 251. It has been brought to my notice ieh myry iDAwn ivc ilAWdw igAw hY 252. It is regretted that Kyd hY ik 253. It will be highly appreciated if bhuq ikrpw hovygI jykr 254. Item m`d 255. Jurisdiction AiDkwr Kyqr 256. Keep pending Ajy rok r`iKAw jwvy 257. Knowingly jwx bu`J ky 258. Labour Commissioner Punjab ikrq kimSnr, pMjwb 259. Lapsed and credited to the

Government account

lYps hox auprMq srkwrI Kwqy ivc jmW kIqw

260. Law and order kwnUMn qy ivvsQw 261. Leave account Cu`tI dw lyKw 262. Leave on average pay AOsq qnKwh qy Cu`tI 263. Leave preparatory to retirement inivrqI pUrv Cu`tI 264. Leave vacancy Cu`tI kwrx KwlI AwswmI 265. Lecturer applied science lYkcrwr, ivhwrk ivigAwn 266. Legal adviser kwnUMnI slwhkwr 267. Legal assistant kwnUMnI shwiek 268. Legal assistant kwnUMnI shwiek 269. Legislative assembly ivDwn sBw 270. Legislature ivDwn mMfl 271. Leprosy officer koVH-rok APsr 272. Lexicographer koSkwr 273. Liable to disciplinary action AnuSwsnI kwrvweI dw BwgI 274. Livestock development officer pSU-Dn ivkws APsr 275. Magazine rswlw, AslwKwnw, mYgzIn 276. Maintenance pwlx-pyS, inrbwh, guzwrw, sMBwl, dyK Bwl 277. Managing Director Punjab, mYnyijMg-fwierYktr, pMjwb mwl gudwm, pMjwb

Warehousing corporation

278. May be excused mwP kIqw jwvy, iKmw kIqw jwvy 279. Ministerial staff dPqrI Amlw, dPqrI stwP 280. Minor nwbwlg, Cotw 281. Misbehaviour burw vqIrw, bdslUkI 282. Miscellaneous Putkl 283. Mistake is much regretted Bu`l leI bhuq Kyd hY 284. Modification soD, Adlw bdlI 285. Most immediate Aiq qqkwilk 286. Namely ArQwq 287. National rwStrI, koOmI 288. Necessary action zrUrI kwrvweI, loVINdI-kwrvweI 289. Negligence AxgihlI, gPlq koqwhI 290. News editor smwcwr sMpwdk 291. No exact precedent is available TIk pUrv-audwhrx nhI iml skI 292. Nominated nwmzd, nwmzd kIqw 293. Note not, it`pxI, not krnw 294. Notice sUcnw, noits 295. Notification AiDsUcnw 296. Notified hereby ies duAwr AiDsUicq 297. Notwithstanding dy bwvjUd vI, dy huMdy hoey vI 298. Null and void ivArQ qy inhPl 299. Nutrition extension officer poSx ivsqwr APsr 300. Objectionable ieqrwzXog 301. Obtain formal sanction rsmI mnzUrI pRwpq kro 302. Occupational information officer pySvwrwnw sUcnw APsr 303. Octroi inspector cuMgI jWckwr 304. Octroi Superintendent cUMgI suprfYNt 305. Office dPqr, pd, Ahudw 306. Office copy dPqrI nkl 307. Office copy and fair copy for

signatures

dPqrI qy Asl kwpI hsqwKrW ihq

308. Office order dPqrI hukm 309. Office please examine dPqr ies dI pVqwl kry 310. Office will put up draft dPqr KrVw pyS krygw 311. Office-bearer pdDwrI Ahudydwr 312. Officer on special duty ivSyS kwrj APsr 313. Officer under training isKlweI ADIn APsr 314. Official krmcwrI, srkwrI, dPqrI 315. Officiating kwiem mukwmI, kwiem mukwm 316. Omission aukweI 317. On account of dy kwrx 318. Opinion rwey, mq 319. Ordinance AiDAwdyS, AwrfInYNs 320. Organization sMgTn, jQybMdI 321. Original mOilk, mUl 322. Over payment AiDk AdwiegI, AiDk Bugqwn 323. Overleaf ipCly pwsy 324. Paper under consideration ivcwr ADIn p`qr 325. Paper under disposal inptwry ADIn p`qr 326. Parliamentary secretary sMsd sk`qr 327. Particulars Vyrvw

328. Pay and account office qnKwh qy lyKw dPqr 329. Penalty dMf, szw 330. Peon Syvwdwr 331. Per capita pRqI jI 332. Per cent pRqI sYNkVw, pRqISq, PI-sdI 333. Percentage pRqI sYNkVw, pRiqSqqw insbq 334. Permanent p`kw, sQweI 335. Personal assistant in`jI shwiek 336. Personal attention is required in`jI iDAwn dI loV hY 337. Petition pRwrQnw p`qr, auzrdwrI, ArzI 338. Petition writer ArzI nvIs 339. Petitioner pRwrQk, auzrdwr 340. Photographer PotogRwPr 341. Physiologist srIr-ikirAw-ivigAwnI 342. Placement officer inXukqI APsr 343. Planning commission XojnwbMdI kimSn 344. Planning cum survey officer XojnwbMdI qy srvyKx APsr 345. Planning officer XojnwbMdI APsr 346. Please acknowledge receipt phuMc rsId ByjI jwvy jI 347. Please discuss ivcwr vtWdry leI imlo jIy 348. Please do the needful loVINdI kwrvweI kIqI jwvy jI 349. Please examine jWc kro jI, jWicAw jwvy jI 350. Please expedite CyqI kro jI 351. Please expedite compliance pwlxw CyqI kIqI jwvy jI 352. Please explain sPweI pyS kro jI, sp`St kro jI 353. Please give top priority to nUM prm Agyq idau jI 354. Please hand over charge to nUM cwrj dy idau 355. Please put up case file imsl pyS kIqI jwvy jI, kys Pwiel pyS kro jI 356. Please reconcile the discrepancy KwmI dUr kIqI jwvy jI 357. Please treat it as most urgent ies nUM AiqAMq zrUrI smiJAw jwvy jI 358. Point out sMkyq krnw, d`sxw 359. Positively insicq rUp ivc, zrUr 360. Post AwswmI, nOkrI, KMBw, cOkI, fwk 361. Post and telegraph department fwk qy qwr ivBwg 362. Post script(P.S) auprMq ilKq 363. Pre-page ipClw pMnw 364. Prescribed inXq 365. President rwStrpqI, pRDwn 366. Press representative pRYs pRiqinD 367. Previous pUrv 368. Previous sanction is necessary pUrv mnzUrI zrUrI hY 369. Prime Minister pRDwn mMqrI 370. Principal ipRMsIpl, mu`K, mUl, mUlDn 371. Printing press CwpwKwnw 372. Priority Agyq 373. Private affairs in`jI mwmly 374. Privilege leave ivSyS AiDkwr Cu`tI 375. Probation prK, AzmwieS 376. Probation period prK kwl, AzmwieS dw smW 377. Proceedings kwrvweI 378. Promotion qr`kI, au`nqI 379. Proof reader soDkwr

380. Proposer qzvIzkwr 381. Province sUbw, pRdys 382. Proviso Srq, SrqI iPkrw 383. Psychiatrist Mnoicikqsk 384. Psychologist mnoivigAwnI 385. Public authority srkwrI AiDkwrI 386. Public grievance officer lok iSkwieq invwrx APsr 387. Public Health Department lok ishq ivBwg 388. Public Notice Awm sUcnw 389. Public prosecutor srkwrI vkIl 390. Public relation officer lok sMprk APsr 391. Public Relations Department lok sMprk ivBwg 392. Public service commission lok syvw kimSn 393. Punctual smW-pwbMd 394. Punjab agriculture department pMjwb KyqI bwVI syvw 395. Purchase officer KrId APsr 396. Put up connected papers sbMDq kwgz pyS kIqy jwx 397. Qualification Xogqw 398. Question at issue ivcwr ADIn pRSn 399. Questionnaire pRSnwvlI 400. Radiologist ikrn ivigAwnI 401. Receipt clerk fwk pRwpqI klrk 402. Receptionist suAwgq krqw 403. Reclamation officer BoN suDwr APsr 404. Registrar Rijstrwr 405. Registrar co-operative society Punjab rijstrwr, sihkwrI sBwvW, pMjwb 406. Regulation inXm 407. Reimbursement of medical expenses fwktrI Krc dI muVpUrqI 408. Relevant papers be put up sbMDq kwgz pyS kIqy jwx 409. Remainder icqwvnI p`qr, Xwd p`qr 410. Remarks ivSyS kQn, ivSyS rwey, it`pxI, kYPIAq 411. Remuneration syvw Pl, imhnqwnw 412. Rent controller ikrwieAw kMtRolr 413. Representation pRiqinDqw 414. Resignation AsqIPw, iqAwg pqr 415. Resolution Mqw 416. Respectively kRmvwr 417. Retrenchment CWtI 418. Revenue clerk mwl klrk 419. Revenue officer mwl APsr 420. Rural development officer pyNfU ivkws APsr 421. Sanction mnzUr krnw, mnzUrI 422. Satisfactory sMqoKjnk, qs`lIbKS 423. Schedule AnusUcI 424. Script ilpI, lyK 425. Scrutineer pVqwlkwr 426. Scrutiny Cwx-bIx, pVqwl 427. Secretary Architecture, Punjab sk`qr, auswrI klw, pMjwb 428. Secretary Punjab, Legislative council sk`qr pMjwb ivDwn sBw 429. Secretary to Government, Punjab

State Archives Department

sk`qr, pMjwb srkwr rwj purwlyK ivBwg

430. Secretary to Governor, Punjab sk`qr, rwjpwl, pMjwb 431. Secretary Vigilance Commission,

Punjab

sk`qr, cOksI kimSn, pMjwb

432. Secretary, Rehabilitation Department sk`qr, muV vsybw ivBwg 433. See and returned with thanks vyiKAw qy DMnvwd sihq vwps kIqw 434. Seed production officer bIj auqpwdk APsr 435. Seen file vyK ilAw, PweIl kr lau 436. Seen file with previous papers vyK ilAw, ipCly kwgzW nwl n`QI kr idau 437. Self-contained note svY-pUrx not 438. Separate notification is necessary v`KrI AiDsUcnw zrUrI hY 439. Service book syvw p`qrI, srivs bu`k 440. Service postage stamp srkwrI fwk itkt 441. Service verification syvw dI qsdIk 442. Session iezlws smwgm, sYSn 443. Settlement commissioner bMdobsq APsr 444. Show cause kwrx d`s, vjHw ibAwn kroo 445. Sit over the Papers kwgz d`b ky bYTxw 446. Social welfare smwj BlweI 447. Solemnly affirm s`cy idloN pRiqigAw krdw hW 448. Sorter CWtIkwr 449. Specialist mwihr, ivSyS`g 450. Spinning and Weaving Master kqweI Aqy buxweI mwstr 451. Staff Amlw, stwP 452. Standard pRmwixk, mwn, imAwr, p`Dr 453. State ibAwn krnw, kihxw, rwj pRdyS, hwlq 454. State liaison officer rwj sMprk APsr 455. Statistical assistant AMkVw shwiek 456. Statistician AMkVw-ivigAwnI 457. Stoppage of increment qnKwh qr`kI rok 458. Stuck off k`t id`qw, k`itAw 459. Subordinate ADIn, mwqihq 460. Substantive pay mUl-AwswmI qnKwh, mUlk qnKwh 461. Substitute ievzI, bdl, QW-lyvw 462. Table swrxI, sUcI, myz 463. Tax assessor kr inrDwrk 464. Technical adviser qknIkI slwhkwr 465. Temporary AsQweI, AwrzI 466. This is certify that qsdIk kIqw jWdw hY ik 467. Through paper channel Xog pRxwlI rwhIN 468. Translation Anuvwd, qrzmw 469. Translator Anuvwdk 470. Transliteration ilpI-AMqrx 471. Transport controller AwvwjweI sMcwlk 472. Treasure KzwncI 473. Treasury officer Kzwnw APsr 474. Turner KrwdIAw 475. Under consideration ivcwr ADIn 476. Under intimation to this office ies dPqr nUM sUicq krdy hoey 477. Under rule inXm ADIn 478. Un-official gYr-srkwrI, AxAiDkwirq, gYr-rsmI 479. University ivSv ividAwlw 480. Urban economist SihrI ArQ ivigAwnI

481. Vacancy KwlI AwswmI, KwlI QW 482. Verterinary department pSU icikqsw ivBwg 483. Veterinary assistant surgeon pSU icikqsw shwiek srjn 484. vice chancellor aup-kulpqI 485. Vide vyKo-dy hvwly, Anuswr 486. Visitor mulwkwqI, drSk 487. Viz ArQwq 488. Vocational adviser pySwvrwnw slwhkwr 489. Warning qwVnw 490. Watch and ward assistant pihrw-ingrwnI shwiek 491. Ways and means aupw qy swDn 492. Welfare centre BlweI kyNdr 493. Wild life inspector jMglI jIv jWckwr 494. With permission to prefix and suffix AwrMB qy AMq ivc joVn dI AwigAw smyq 495. With reference to your letter Awp dy p`qr dy hvwly ivc 496. With regard to dy sbMD ivc 497. With retrospective effect ipClI imqI qoN, pUrvlI imqI qoN 498. Without fail lwzmI qOr qy 499. Yours faithfully ivSvwspwqr 500. Yours sincerely Awp dw ihqU

mu`FlI pMjwbI (BMH-105B)

pMjwbI (n.p.k.) bwhrI AMk:75 AMdrUnI AMk:25

(Elementary Punjabi for foreign or other state or any other student who did not study Punjabi in

school at any level)

Bwg (a)

1. gurmuKI vrxmwlw: svr qy ivAMjn sUck A`Kr; lgw mwqrW Aqy lgwKrW dI pCwx qy vrqoN 2. pMjwbI Sbd bxqr: DwqU, vDyqr 3. Sbd SryxIAW: ilMg, vcn, kwl, purK 4. pMjwbI pYryH dw auqwrw, AMgryzI qoN pMjwbI Anuvwd, romn qoN gurmuKI ilpIAMqrx[ 5. vwk bxwauxw: sDwrn, sMXukq qy imSrq; iksmW- ibAwnIAw, nWhvwcI, pRSnvwcI, ivsimk

Bwg (A)

1. zrUrI SbdwvlI: AMk pRbMD-100 q`k, hPqy dy idn, srIr dy AMg, gihxy, iq`Q-iqauhwr, rMg, swkwdwrI, Kwx-pIx, ik`qy, sMd, PslW, pMCI qy jwnvr, [

2. bhuqy SbdW dI QW ie`k Sbd (pMjwbI pRboD, BwSw ivBwg, pMjwb) 3. ivroDI Sbd (pMjwbI pRboD, BwSw ivBwg, pMjwb) 4. smwnwrQk Sbd (pMjwbI pRboD, BwSw ivBwg, pMjwb) 5. Su`D-ASu`D (pMjwbI pRboD, BwSw ivBwg, pMjwb) 6. ivSrwm icMnHW dI vrqoN (pMjwbI pRboD, BwSw ivBwg, pMjwb)

Bwg (e)

1. ic`TI p`qr- ibmwrI Aqy zrUrI kMm leI Cu`tI lYx sbMDI leI ArzI, irSqydwrW nUM sDwrn ic`TI p`qr[

2. do kivqwvW: 'A`j AwKW vwirs Swh nUM'- AMimRqw pRIqm Aqy 'AwieAw nMd ikSor'- surjIq pwqr (SbdwrQ Aqy pRsMg)

Bwg (s)

1. sMKyp rcnw 2. AMgryzI qoN pMjwbI Anuvwd (10 vwk)

AiBAws- swrIAW pMjwbI lgW mwqrW nwl A`Kr lwauxy, Sbd ilKxy, Awpxy bwry 10 sqrW ilKxIAW, pMjwbI lok jIvn bwry koeI pMj qsvIrW lY ky hryk bwry 10 sqrW ilKxIAW, XUnIvristI (hostl, kYNtIn Awid) bwry 10-10 sqrW dy pMj lyK ilKxy[

mOiKk pRIiKAw- pVHn Aqy bolx (sDwrx g`lbwq, AwpxI jwx-pCwx, svwgqI Sbd qy inrdyS) dI smr`Qw dw tYst

shwiek pusqkW

0. sic`qr pMjwbI vrxmwlw, BwSw ivBwg pMjwb, pitAwlw[

1. pMjwbI pRboD, BwSw ivBwg pMjwb, pitAwlw[

2. siqnwm sMG sMDU, AwE pMjwbI is`KIey (ihMdI qoN pMjwbI is`Kx leI), pblIkySn ibaUro, pMjwbI XUnIvristI, pitAwlw[

3. siqnwm sMG sMDU, AwE gurmuKI is`Ko (AMgRyjI qoN pMjwbI is`Kx leI), pblIkySn ibaUro, pMjwbI XUnIvristI, pitAwlw[

4. sIqw rwm bwhrI, pMjwbI is`KIey, pblIkySn ibaUro, pMjwbI XUnIvristI, pitAwlw[ (ihMdI)

5. hrkIrq isMG, igAwnI lwl isMG, pMjwbI ivAwkrx, pMjwb styt tYkst bu`k borf, cMfIgV[

6. rwjivMdr isMG, pMjwbI igAwn sI.fI. (kMipaUtr AYplIkySn tU lrn AYNf tIc pMjwbI), pblIkySn ibaUro, pMjwbI XUnIvristI, pitAwlw[

7. Gill, H.S. & H.A. Gleason, A reference Grammar of Punjabi, Punjabi University, Patiala.

8. Bhatia, T.K., Punjabi: A descriptive and cognitive grammar.

9. Hardev Bahri, Teach Yourself Punjabi, Publication Bureau, Punjabi University, Patiala.

10. Henry A. Gleason and Harjeet Singh Gill, A start in Punjabi, Publication Bureau, Punjabi

University, Patiala.

11. Ujjal Singh Bahri and Paramjit Singh Walia, Introductory Punjabi, Publication Bureau,

Punjabi University, Patiala.

AMk vMf Aqy pypr sYtr leI hdwieqW

bwhrly pRIiKAk dw pRSn p`qr 75 AMkW dw hovygw, ijsdw smW 3 GMty hovygw[ ies pRSn p`qr dy ku`l iqMn Bwg 1, 2, 3 hoxgy[ Bwg 1 iv`c 10 lGU svwl 2-2 AMkW dy hoxgy[ ieh swrw Bwg lwzmI hovygw[ Bwg 2 ivc 8 svwl 5-5 AMkW dy hoxgy Aqy pRIiKAwrQI ny koeI 6 svwl hl krny hoxgy[ Bwg 3 ivc iqMn lMby au~qrW vwly 12.5-12.5 AMkW dy svwl hoxgy, ijnHW ivcoN ividAwrQI ny do dy au~qr dyxy hoxgy[ ieh pRSn p`qr muFlI pMjwbI dy ividAwrQIAW dy p`Dr nUM iDAwn ivc rK ky pwieAw jwvy jo Ajy gurmuKI Aqy pMjwbI is`Kx dy muFly pVwA qy hn[

CALCULUS-II

(BMH-201)



Objectives: This course helps students to determine the reasonable solutions, including size, sign,

relative accuracy and units of measurement. Students should develop an appreciation of calculus as

a coherent body of knowledge and as a human accomplishment.

Outcomes: Students will able to demonstrate basic symbol manipulation skills pertaining to

integeration. They will be able to use convergence tests to anaylze the behavior of infinite series.

PART - I

Limits of sequence of numbers. Theorems for calculating limits of sequences, Infinite Series.

Bounded and Monotonic sequences, Cauchys convergence criterion. Series of non-negative terms.

Comparison tests. Cauchys’ Integral test. Ratio tests. Alternating series. Absolute and conditional

convergence. Leibnitz Theorem, Convergence of Taylor Series, Error Estimates. Applications of

Power Series.

Line integrals, Integrals with respect to arc length, Basic properties of line integrals. Double and

triple integral and their evaluation, change of order of integration, change of variable, Application

of double and triple integration to find areas, Volumes, Center of gravity, Center of mass and

moment of inertia.

PART - II

Scalar and vector fields, Differentiation of vectors, Velocity and acceleration. Vector differential

operators: Del, Gradient, Divergence and Curl, their physical interpretations. Vector identities.

Formulae involving Del applied to point functions and their products.

Flux, Solenoidal and Irrotational vectors. Green’s theorem in plane, Stoke’s theorem, Gauss

Divergence theorem. and their applications to line, surface and volume integrals.

Text Books

1. Narayan Shanti, Differential Calculus, S Chand, 1962.

2. Narayan Shanti, Integral Calculus, S Chand, 2005.

3. Thomes, G.B, Finney R.L. Calculus and Analytic Gemetry, Ninth Edition, Peason Education.,

2010.

References

1. Kaplan Wilfred, Advanced Calculus, Addison- Wesley Publishing Company, 1973.

2. Weatherburn C.E, Elementary Vector Calculus, 1921.

3. Widder David, Advanced Calculus, Prentice- Hall of India, 1999.

MATRIX ALGEBRA

(BMH-202)



Objectives: This course has wide range of applications in modern mathematics making it an

essential component of all scientific courses.

Outcomes: Students will be able to evaluate mathematical expressions to compute quantities that

deal with linear systems and eigen value problems. They will be able to apply matrix algebra

concepts to model, solve and analyze real-world situations.

PART - I

Matrices, algebra of matrices, types of matrices, elementary operations on matrices, inverse of a

matrix using Gauss-Jordan method, row rank, column rank, rank of a matrix, equivalence of row

and column rank, linear dependence and independence vectors.

Application of matrices to a system of linear (both homogeneous and non-homogeneous) equations.

Eigen values and eigen vectors of a matrix, algebraic and geometric multiplicity of an eigen value,

and eigen vectors, Cayley-Hamilton theorem and its application to find the inverse of a mtrix.

PART - II

Conjugate of a matrix, some special types of matrices and their eigen values: symmetric, skew-

symmetric, Hermitian, skew-Hermitian, unitary and orthogonal matrices, diagonalization of a

matrix, similar matrices.

Quadratic forms, definite, semi-definite, indefinite forms, matrix representation, linear

transformation of a quadratic, canonical form, index and signature of a quadratic form, Hermitian

forms, linear transformations of a Hermitian form, conjunctive transformation of a matrix,

conjunctive reduction of a Hermitian matrix, conjunctive reduction of a skew-Hermitian matrix.

Text Books

1. Narayan, S. and Mittal, P. K., A textbook of Matrices, S. Chand & Company Ltd. Edition, 2001.

2. Seymour L., Marc L. L., Linear Algebra, Schaum’s outline Series, 2013.

References

3. Datta K.B., Matrix and Linear Algebra. Prentice Hall of India Pvt. Ltd., New Delhi-(2000).

4. Bhattacharya P.B. Jain S.K. and Nagpaul S. R., First course in Linear Algebra, Wiley Eastern,

New Delhi (1983).

5. Lax.P, Linear Algebra, John Wiley & Sons, New York. Indian, 1997.

6. Hoffman, K. and Kunje, R. Linear Algebra, Prentice-Hall of India, 2nd Edition, 1989.

ANALYTICAL SOLID GEOMETRY

(BMH-203)



Objectives: The objective of the course is to get basic knowledge about Sphere, Cone, Cylinder

and Central Conicoids and their applications.

Outcomes: After the completion of the course, Students will be able to find the equation of plane

and lines in three dimensions, equation of sphere and get knowledge about coaxal system of

spheres. They would be able to understand the concept of cone and cylinder and the shapes of

central conicoids.

PART - I

The Plane: Various forms of the equation of a plane, general equation of 1st degree, angle between

two planes, perpendicular distanceof a point from a plane, positive and negative sides of plane,

bisectors of angles, systems of planes, pair of palnes, area of a triangle and volume of a tetrahedron

The straight line: various forms of the equations of a line, plane and line, shortest distance,

intersection of three planes, intersection of lines.

Sphere: General equation of a sphere, Plane section of a sphere, Intersection of two spheres,

Sphere through a given circle, Intersection of a straight line and a sphere, Equation of a tangent

plane to sphere, Condition of tangency. Plane of contact, Orthogonal Spheres, Angle of intersection

of two spheres, Length of tangent, Radical plane, Coaxal spheres, Conjugate system of coaxal

spheres.

PART - II

Cone: Equation of a cone whose vertex is at origin, Equation of a cone with a given vertex and a

given conic as base, Condition that general equation of second degree represent a cone, Equation of

a tangent plane, Condition of tangency of a plane and a cone, Reciprocal cone, Right circular cone,

Enveloping cone

Cylinder: Equation of cylinder, Enveloping and right circular Cylinders.

The Central Conicoids: Shapes of the central conicoids, intersection of conicoid and a line,

Normal, plane of contact and polar plane, Diameters and diametral planes equations of Paraboloid: Paraboloid and its simple properties.

Text Books

1. P.K. Jain and Khalil Ahmad: A Text Book of Analytical Geometry of two Dimensions, Wiley

Eastern Ltd. 1994.

2. N. Saran and R.S. Gupta: Analytical Geometry of Three Dimensions, Pothishala Pvt. Ltd.

Allahabad.

DISCRETE MATHEMATICS-I

(BMH-204)



Objective: The main objective of this course is to provide the necessary background of discrete

structures. It emphasizes on basic properties of relations, recursive relations, mathematical

arguments and essential concepts in Boolean algebra.

Outcome: In the end of this course the students will learn basic concepts of discrete structures and

will be able to apply this knowledge in problem solving.

PART - I

Sets, Relations and Functions: Operations on sets, Inclusion- exclusion principle, Binary

relations, Properties of binary relations in a set, Equivalence relations, Composition of binary

relations, Partial ordering, Partial ordered set and Hasse diagram, Bijective functions, Inverse

functions and composition of functions, Recursive functions, Generating functions.

Recurrence Relations and Recursive Algorithm: Linear recurrence relations with constant

coefficients, Homogeneous Solutions, Particular Solutions, Total Solution, Solution by method of

Generating Functions.

Mathematical Logic: Statement and notations, Connectives (negation, conjunction, disjunction),

Statement formulas and truth table, Conditional and biconditional statements, Tautologies,

Equivalence of formulas, Tautological implications, Validity using truth table.

PART - II

Lattices: POSET, Greatest and least element of a POSET, Comparable and non-comparable

elements in POSETs, Totally linearly ordered set, Hasse diagram of partially ordered sets, JOIN,

MEET, Product of lattices, Properties of lattice, Duality of lattices, Complete lattice, Sub lattice,

Bounded lattice, Isomorphic lattice, Distributive lattice, Complemented lattices, Uniqueness

Theorem.

Boolean Algebra: Algebraic structure, Boolean algebra as lattices, Principle of Duality for Boolean

algebra, De-Morgan’s Law, Atom, Sub-algebra, Isomorphic Boolean algebra, Finite Boolean

algebra, Boolean function, Boolean Expression and simplifications of Boolean expressions,

Equivalence Boolean expressions. Disjunctive normal form, Conjunctive normal form, Karnaugh

Maps, Logical gates and relations of Boolean function, Applications of Boolean algebra to

Switching theory.

Text Books

1. Joshi, K.D., Foundations of discrete mathematics, John Wiley and Sons, 1989.

2. Ram Babu, Discrete Mathematics, Vinayak Publication, 2007.

References

1 Tremblay, J. P. and Manohar, R., A First course in Discrete Structures with applications to

Computer Science, Tata McGraw Hill, 1999.

2. Truss, J. K., Discrete Mathematical Structures for Computer Science, Pearson education ,

1994.

3. Grimaldi, R. P. and Ramana, B. V., Discrete and Combinatorial Mathematics-An Applied

Introduction, Pearson education, 2004.

4. Kenneth H. Rosen, “Discrete Mathematics and Its Applications”, Tata McGraw-Hill, Edition

4th

COMMUNICATION SKILLS IN ENGLISH

(BMH-205)



PART-I

LITERATURE

Popular Short Stories, Oxford University Press, 1989. Rpt. 2008.

The following short stories from this anthology are prescribed: 1. A Cup of Tea

2. The Open Window

3. The Necklace

4. The Gateman’s Gift

5. Living or Dead?

PART-II

GRAMMAR

1. Use of Tenses

2. Change of Voice

3. Change of Narration

4. Use of Conjunctions

5. Use of Prepositions

COMPOSITION

1. Paragraph writing

2. Writing a review of a TV Serial

3. Translation of News item/ Article in newspaper / excerpt from Short Story into Punjabi or

Hindi.

4. Expansion of a given concept into a paragraph

5. Picture Caption Writing

VOCABULARY

1. One Word Substitution

2. Words often confused and misspelt

3. Common errors in the usage of English language

PRESCRIBED BOOKS: 1. Best, Wilfred D. The Student’s Companion. New Delhi: Rupa & Co., 1958. 29th impression,

1994

2. Popular Short Stories. Oxford University press, 1989. Rpt. 2008.

3. Singh, Achhru. University English Grammar and Vocabulary Study. Chandigarh: Unistar

Publishers.

SUGGESTED READINGS 1. Frank, O’Holo. Writer’s Work: A Guide to Effective Composition. Prentice Hall, New Delhi,

1976.

2. Sanyal, Mukti & Prasad. Tulika, Fluency in English. Macmillan.

3. Sharma, S.C., Sharma, Pankaj. A Textbook of Grammar and Composition. Macmillan.

REAL ANALYSIS

(BMH-301)



Objectives: This course provides well-proven framework to support the intuitive ideas that we

frequently take into consideration.

Outcomes: After the completion of this course, the students will be able to use results and

techniques involving the contents to solve a variety of problems especially differential equations.

PART - I

Sets, bounded sets, open sets, closed sets, partitions, upper and lower sums, upper and lower

integrals, Riemann integrability, conditions and existence of Riemann integrals, properties of

integrals, integral as a limit of sums, integrability of continuous and monotonic functions.

Algebra of integrable functions, the fundamental theorem of integral calculus, change of variable in

an integral, integration by parts, mean value theorems of integral calculus, evaluation of certain

definite integrals.

PART - II

Limit of functions, continuous functions, monotone functions, sequences, bounded sequences,

subsequences, limit superior and limit inferior of a real sequence, algebra of sequences, pointwise

and uniform convergence, Cauchy criterion for uniform convergence, Weierstrass M-test, Abel’s

and Dirichlet’s tests for uniform convergence, uniform convergence and continuity.

Uniform convergence and differentiation, uniform convergence and integration, Weierstrass

approximation theorem (statement only), absolute convergence, alternating series, addition and

multiplication of series, rearrangement of absolutely convergent series, Riemann’s arrangement

theorem (statement only).

Text Books

1. Rudin, W., Principles of Mathematical Analysis, McGraw-Hill, 1976.

2. Malik, S. C. and Arora S., Mathematical Analysis, Wiley Eastern, 2010.

References

2. Narayan, S., A Course of Mathematical Analysis, S. Chand, 1973

3. Apostol, T.M., Mathematical Analysis, Narosa Publication, 2002.

ORDINARY DIFFERENTIAL EQUATIONS

(BMH-302)



Objectives: The main objective of this course is to explain the concepts of solution of linear and

non-linear differential equations. In addition to this, this course also emphasizes applications of

Ordinary differential equations to electric circuit, deflection of beams and simple harmonic motion.

Outcomes: In the end of the course the students will be able to solve first order linear and non-

linear differential equations. They will also learn methods of solving special type of second order

and higher order linear differential equations and their applications in various fields of engineering.

PART - I

Review of first order and firsr degree equations. Leibnitz linear equations and Bernoulli equations,

Exact differential equations, integrating factors. Equations of the first order and higher degree:

Equations solvable for p, y and x, Clairaut equation, Riccati's equations. Geometrical interpretation

of first order differential equations. Successive approximations, Lipschitz condition, Statement of

Existence and Uniqueness of solution of first order differential equations.

Solution of Linear differential equations with constant coefficients: solution of homogeneous

and non-homogeneous equations using operator method, method of undetermined multipliers and

method of variation of parameters. Linear differential equations with variable coefficients: Cauchy's

and Legendre's equation. Simultaneous differential equations.

PART - II

Power series solution about an ordinary point: Euler's equation, regular singular points, ordinary

points, series solution. Method of Frobenius, series solutions of Bessel's and Legendre's equations.

Applications of Ordinary Differential Equations: Applications to electric R-L-C circuits,

Deflection of beams, Simple harmonic motion.

Text Books

1. Ross S.L., Differential equations, John Wiley and Sons (2004).

2. Jain R.K and Iyengar S.R.K., Advanced Engineering Mathematics, Narosa Publishing

Company, Edition 3rd (2007)

3. Raisinghania, M.D., Ordinary and Partial Differential Equation, S. Chand, 2013.

References

1. G.F. Simmons, Differential Equations with Applications and Historical Notes, 2nd Ed.,

McGraw- Hill, 1991.

2. Zafar Ahsan, Text Book of Differential Equations and their Applications, Prentice Hall of

India. (2004)

3. Ahmad Khalil, Text Book of Differential Equations, World Education Publishers (2012).

MATHEMATICAL METHODS

(BMH-303)



Objectives: The objective of the course is to enable the students to understand the basic concepts

related to Fourier series, Fourier Transform, Laplace Transform, Z Transform and their applications.

Outcomes: After the completion of the course, Students will be able to get the knowledge about

periodic functions, Fourier Transform, Laplace Transform and Z-Transform.They will be able to solve

problems relating to Fourier Transform, Laplace Transform and Z-Transform and their applications in

solving various differential equations.

PART - I

Introduction to periodic functions, Introduction about Fourier series, Dirichlet’s conditions for

Fourier series, Derivation of Fourier coefficients or Euler’s constants, Fourier series for functions

with arbitrary intervals, Introduction to odd and even functions Fourier series for odd and even

functions, Half range cosine series, Half range sine series, Problems on arbitrary interval-half range

series

Fourier Transforms (FT) Definition, Properties evaluation of Fourier and inverse Fourier transforms

of functions, Convolution theorem for FT. Sine and Cosine Fourier transforms. Solution of

differential equations using Fourier Transforms.

PART - II

Definition Properties, evaluation of Laplace and Inverse Laplace transforms of functions.

Convolution theorem for Laplace Transforms, Solution of Ordinary Differential Equations with

constant coefficients with variable coefficients, Solution of Simultaneous Ordinary Differential

Equations

Z-Transforms, Z-transform of common functions, inverse Z-transform, initial and final value

theorems, Convolution theorem, Formation of difference equations, Applications to solution of

difference equations, Pulse transfer function.

Text Books

1. Babu Ram, Advanced Engineering Mathematics, Pearson Education (2010).

2. Jain, R.K. and Iyenger, S.R.K., Advanced Engineering Mathematics, Narosa Publication, 2012.

References

1. Vasistha, A.R., Integral Transforms Krishna Prakashan Media Pvt. Ltd, Meerut (2010).

2. Churchill, Operational Mathematicsl, Mc Graw Hill Company.

PROGRAMMING IN C

(BMH-304)



Objectives: The objective of this course is to introduce various fundamental terms and operations

in C language that will enable the students to implement programming using this language.

Outcomes: Student will learn to write algorithms for solutions to various problems and they will

be able to convert these algorithms into computer programming using C language.

PART- I

C Language preliminaries: C character set, Identifiers and keywords, Data types,

Declarations, Expressions, statement and symbolic constants

Input-Output: getchar, putchar, scanf, printf, gets, puts Pre-processor commands: #include,

#define, #ifdef Preparing and running a complete C program

Operators and expressions: Arithmetic, unary, logical, bit-wise, assignment and conditional

operator

Control statements: While, do-while, for statements, nested loops, if else, switch, break,

Continue, and goto statements, comma operators

Storage types: Automatic, external, register and static variables.

Array: Defining, declaration and initialization of 1-dim array,2-dim array, character array

String: Defining, declaration and initialization of string variable, reading string from terminal

writing string to screen.

PART - II

FUNCTION: Classification of function-library function and user defined function. Need for user

defined functions, Definition of function, prototypes, call by value and call by reference, recursion.

Structures: Defining, declaration and initialization of structure

Unions: Defining, declaration and initialization of unions

Pointers: Declaration, initialization, operation on pointers, pointers and arrays.

Text Books

2. Balagurusamy, E., C programming, Tata McGraw Hill, 2012

3. Kanetkar, Y., Let Us C, Infinity Science Press, 2008

References

1. Complete reference with C, Tata McGraw Hill.

2. Kerninghan and Ritchie, The C programming language, 2001

3. Ramkumar Agarwal, Programming in ANSI C, 2011.

PROGRAMMING IN C Lab

(BMH-304L)


External Evaluation: 37.5 Marks Internal Assessment: 12.5 Marks

Objectives: The objective of this course is to enhance the practical knowledge of C language that

will enable the students to implement programming using this language.

Outcomes: Student will learn to write programs for solving various real life problems.

Implementation of concepts studied in Programming in C (BMH- 304)

1. To Add and Subtract two numbers.

2. To find Simple Interest.

3. To Swap three numbers.

4. Use of Control Statements: if else, While, do-while, for statements, nested loops, switch,

break, continue and goto statements.

5. Use of conditional Operator.

6. To print 1

2 2

3 3 3

4 4 4 4

5 5 5 5 5

7. To print *(star) pattern in triangle.

8. To implement the concept of one-dimensional and two-dimensional array .

9. To print a line of text containing a series of words using String.

10. To calculate the area of a Rectangle using Functions.

11. To implement the concept of recursion.

12. To illustrate the concept of pass by value and pass by reference.

13. To illustrate the concept of displaying the address of a pointer variable.

14. To find Sum of two numbers using Pointer.

15. To implement the concept of Structure.

16. To implement the concept of Union.

PHYSICS (BMH-305)



Objectives: The objective of this course is to introduce some fundamental concepts of Physics

and overview of different branches of physics that will enable the students to build logics about

universal phenomenon.

Outcomes: Student will learn solutions to various daily life physics problems and they will be

able to easily understood logics behind them.

PART–I

Elements of Vectors : Classification of physical quantities, Resolution of a vector into

components, Null vector, Unit vector, Position vector and its magnitude, Addition of vectors:

Parallelogram law of addition of vectors, Triangle law and polygon law of vectors, triangle law of

addition of vectors, polygon law of addition of vectors, Subtraction of vectors, Concept of relative

velocity, Multiplication of vector with a scalar, Product of two vectors: Scalar and vector products,

Their properties.

Rotational Dynamics

Angular momentum of a particle and system of particles, Torque, Conservation of angular

momentum, Rotation about a fixed axis, Moment of inertia: Calculation of moment of inertia for

rectangular, cylindrical and spherical bodies, Kinetic energy of rotation, Two body problem and its

reduction to one body problem, Kepler’s laws (Ideas Only), Orbits of artificial satellites. Equation

of motion of a rigid body, Rotational motion of a rigid body in general and that of plane lamina

.

PART-II

Special theory of Relativity: Michelson-Morley experiment, Basic postulates of special theory of

relativity, Lorentz transformations, Simultaneity and order of events, Concept of length contraction

and Time-dilation, Mass-energy relationship.

Quantum mechanics and Statistical Physics: De Broglie hypothesis, Davisson-Germer

experiment, Wave function and its properties, Expectation value, Wave packet, Uncertainty

principle, Schrödinger equation for free particle, Time-dependent Schrödinger equation,

Applications of Schrodinger equation: Particle in a one-dimensional box.

References:

1. An introduction to mechanics by Daniel Kleppner, Robert J. Kolenkow (McGraw-Hill,

1973)

2. Mechanics Berkeley physics course, v.1: By Charles Kittel, Walter Knight, Malvin

Ruderman, Carl Helmholz, Burton Moyer, (Tata McGraw-Hill, 2007)

3. Mechanics by D S Mathur (S. Chand & Company Limited, 2000)

4. Mechanics by Keith R. Symon (Addison Wesley; 3rd edition, 1971)

5. Concepts of Modem Physics: A Beiser (McGraw Hill, 1987).

6. Analytical Mechanics: Satish K. Gupta-Modern Publishers.

7. Fundamentals of Physics: D. Halliday, R. Resnick and J. Walker (sixth edition)-Wiley

India Pvt. Ltd., New Delhi.

PHYSICS LAB (BMH-305L)



Objectives: The objective of this course is to do hand on practice about the fundamental concepts

of Physics learned theoretically.

Outcomes: Student will be able to easily understood logics behind theoretical concepts.

LABORATORY EXPERIMENTS / PRACTICLE COURSE:

1. To find the thickness of a given slab using vernier calliper.

2. To find the diameter of a wire using screw gauge.

3. To determine the radius of curvature of a convex or concave mirror using spherometer.

4. To find the moment of inertia of a flywheel.

5. To plot a graph between the distance of the knife- edges from the centre of gravity and the time

period of a compound pendulum. From the graph find the acceleration due to gravity.

6. To compare the velocity of light in glass and water using travelling microscope.

7. To determine the frequency of a tuning fork using a sonometer.

8. To find the frequency of a.c. mains using electrical vibrator.

BASIC LINEAR ALGEBRA

(BMH-401)



Objectives: The objective of this course is to encourage the students to apply linear algebra

concepts to model, solve and anlyze real-world situations.

Outcomes: Students will get insight of basic concepts of linear algebra.

PART- I

Vector spaces: Definition, examples, vector subspace, linear span, linear dependence and

independence of vectors, basis and dimension of a vector space, sum of vector spaces, row and

column spaces of a matrix, basis and dimension of the solution space of a system of linear

equations.

Homomorphism of vector spaces, properties of homomorphism, kernel of a homomorphism,

isomorphism of vector spaces, quotient spaces, direct sum of spaces, complementary subspaces, co-

ordinates, dual space, dual basis, reflexivity, annihilators,

PART-II

Linear transformation: Definition, algebra of linear transformations, rank and nullity of a linear

transformation, singular and non-singular transformations, invertible operators.

Matrices and linear transformation: Matrix representation of a linear transformation, change of

basis, equivalent and similar matrices, trace and transpose of a linear transformation.

Text Books

1. Krishnamurthy V, Mainra V P, Arora J L, An Introduction to Linear Algebra, Affiliated East

West Press Pvt. Limited, 1976.

2. Herstein, I. N., Topics in Algebra, Willey Eastern Ltd, 2005.

References

1. Hoffman, K, and Kunze, R., Linear Algebra, Prentice Hall of India, 2006.

2. Strang, G., Linear Algebra and its applications, Academic press, 2006.

3. Vasishtha, A. R. and Vasishtha, A. K., Modern Algebra, Krishna Prakashan Media (P) Ltd.,

Thirty eighth edition, 1999.

4. Arora, O. P., Bhandari, V. K. and Mann, J. S., Linear Algebra, S. Dinesh & Co. Circular Road,

Jalandhar, eighth edition, 1996

PARTIAL DIFFERENTIAL EQUATIONS

(BMH-402)



Objectives: This is an introductory course aiming to help students in solving linear and non-linear

partial differential equations of first order and higher orders. This course also emphasizes

applications of partial differential equations in many mathematical modelling problems describing

physical phenomenon and engineering problems.

Outcomes: In the end of the course the students will learn methods to solve first order linear and

non-linear partial differential equations. They will also learn special methods of solving higher

order partial differential equations, classification of second order equations and solution of heat,

wave and laplace equations.

PART-I

Partial differential equations: Formation, order and degree, Linear and Non-Linear Partial

differential equations of the first order: Complete solution, singular solution, General solution,

Solution of Lagrange’s linear equations, Charpit’s general method of solution.

Linear partial differential equations of second and higher orders, linear homogenous and non-

homogenous equations with constant co-efficients, Partial differential equation with variable co-

efficients reducible to equations with constant coefficients, their complimentary functions and

particular Integrals.

PART-II

Classification of linear partial differential equations of second order, Hyperbolic, parabolic and

elliptic types, Reduction of second order linear partial differential equations to Canonical (Normal)

forms and their solutions, Monge’s method for partial differential equations of second order (only

in Cartesian coordinates).

Method of Separation of variables in a PDE, Solution of Laplace’s equation, Wave equation, in one

and two dimensions, Diffusion (Heat) equation, Elementary solution of diffusion equation.

Text Books


2. Sharma J.N. and Singh.K, Partial Differential Equations for Engineers and Scientists,

Narosa Publications, 2nd edition, 2009.

References

2. Copson E.T., Partial Differential Equations Cambridge University Press, 2nd edition (1995).

3. Sneddon I.N., Elements of Partial Differential Equation McGraw Hill Book Company, 3rd

edition, 1998.

4. K. Sankara Rao, Introduction to Partial Differential Equations, Prentice Hall of India

Private Limited, New Delhi, 1997.

NUMERICAL METHODS

(BMH-403)



Objectives: The objective of this course is to introduce different numerical techniques for solving

algebraic, transcendental equations, large system of equations, finding approximate value of

definite integrals of functions etc.

Outcomes: Students will able to tackle complicated functions by approximating the functions by

some convenient polynomials upto desired accuracy. They will able to solve differential equations

arising in various fields of applied science and engineering.

PART-I

Number System, Error in evaluating a function, Absolute, Relative, Truncation and round off

errors, Floating Point Arithmetic, Bounds on error, Arithmetic accuracy in computers, Loss of

significance and error propagation.

Bisection method, Secant method, Regula-Falsi method, Fixed point method and Newton-Raphson

methods, Order of convergence, Method for Multiple roots-Newton Raphson method, Muller’s

method, Solution of Non-linear Simultaneous equations- Fixed point iteration method and Newton

Raphson method.

PART-II

Solution of linear equations-Gauss-elimination method (using Pivoting strategies), Jordan’s

method, Gauss-Jacobi method, Gauss-Seidel Iteration method, S.O.R. method, Condition number

and instability, Rayleigh’s power method for eigen-values and eigen-vectors.

Finite differences, Newton’s Forward and Backward difference formula, Gauss’s Forward and

Backward central difference formula, Stirling’s formula, Bessel’s formula, Everett’s formulae,

Lagrange method, Newton’s divided difference interpolation formula with error analysis,

Numerical differentiation using finite differences; Newton-Cotes quadrature formulae (with error)

and Gauss - Legendre quadrature formulae.

Text Books

1. Conte, S.D and Carl D. Boor, Elementary Numerical Analysis: An Algorithmic approach,

Tata McGraw Hill, New York (2005).

2. Jain M.K., Iyengar, S.R.K., and Jain, R.K. Numerical Methods for Scientific and

Engineering Computation, New Age International (2008) 5th ed.

References

1. Mathew, J.H., Numerical Methods for Mathematics, Science and Engineering, Prentice Hall

Inc.J (2002).

2. Gerald C.F and Wheatley P.O., Applied Numerical Analysis, Pearson Education (2008) 7th

ed.

NUMERICAL METHODS LAB

(BMH-403L)



Objectives: This course develops student’s understanding through laboratory activities to solve

problems related to key concepts taught in the classroom.

Outcomes: Student will be able to use approximation algorithms in real world problems.

To prepare the programs for following methods:

1. Bisection Method

2. Secant Method

3. Fixed Point Method

4. Newton-Raphson Method

5. Newton’s Forward Interpolation

6. Trapezoidal rule

7. Simpson 1/3 rule

8. Euler’s Method

9. Taylor Series Method

10. Range- Kutta Method

CHEMISTRY

(BMH-404) Contact Hours: 60 hours Total Marks: 100


PART-I

Covalent Bond:

Various types of hybridization and shapes of simple inorganic molecules and ions (BeF2, BF3, CH4,

PF5, SF6, IF7, XeF4, ClF3, SF4, ClO4‾, ClO3‾, NO3‾). Concept of molecular orbitals. Molecular

orbital theory of homonuclear (Li2 to Ne2) molecules and ions and heteronuclear diatomic

molecules (CO, CO+, NO, NO+). Concept of electronegativity, polarity of bonds and dipole

moments.

Chemical Equilibrium:

General characteristics of chemical equilibrium, thermodynamic derivation of the law of chemical

equilibrium, Van’t Hoff reaction isotherm. Relation between Kp and Kc, homogeneous &

heterogreneous equilibria, Le Chetalier’s principle.

Acids and Bases

Arrhenius, Bronsted-Lowry and Lewis concept of acid and base, relative strength of acids and

bases, Electrolytes, Strong and weak electrolytes, Ionic product of water, pH scale, Common ion

effect, Buffer solutions.

PART-II

Stereochemistry

Basics of stereochemistry. Configuration and conformation. Optical activity due to chirality; d, l,

meso and diastereoisomerism. Geometrical isomerism – determination of configuration of cis-trans

geometric isomers. E & Z system of nomenclature. Newman projection and Sawhorse formula,

Fischer and flying wedge formulae. Conformational isomerism – conformational analysis of ethane

and n-butane; conformations cyclohexane, axial and equatorial bonds, conformations of

monosubstituted cyclohexane derivatives.

Electro-Chemistry

Specific conductance, molar conductance and their dependence on electrolyte concentration. Ionic

Equilibria and conductance, Essential postulates of the Debye-Huckel theory of strong electrolytes,

Mean ionic activity coefficient and ionic strength, Transport number and its relation to ionic

conductance and ionic mobility, Acid-base indicators, Conductometric titrations.

Text Books:

1. Puri B.R., Sharma L. R. and Pathania M. S., Principles of Physical Chemistry, Pubs: Vishal

Publishing Company, 2003.

2. Puri B.R., Sharma L. R. and Kalia K. C., Advanced Inorganic Chemistry, Pubs: Vishal

Publishing Company, 2008.

3. Mukerji S. M., Singh S. P. and Kapoor R. P., Organic Chemistry Vol. I/II, Pubs: Wiley Eastern

Ltd., New Delhi, 1985.

Reference Books:

1. Cotton F.A., Wilkinson G.W. and Gaus P.L., Basic Inorganic Chemistry, Pubs: John Wiley &

Sons ,1987.

2. Sienko M.J. and Plane R.A., Chemistry principles and properties, Pubs: MC Graw-Hill, New

York 1975.

3. Morrison R.T.N. and Boyd R.N., Organic Chemistry, 5th edn., Pubs: Allyn and Bacon, London,

1987.

CHEMISTRY LAB

(BMH-404L) Contact Hours: 60 hours Total Marks: 100


Qualitative Analysis

Analysis of inorganic mixture for acidic and basic radicals including interfering radicals like

Phosphate, Tartrate, oxalate and similar radicals

Gravimetric Methods

1. To estimation of Barium as Barium sulphate in the solution of Barium chloride.

2. To estimate Nickel as nickel dimethylglyoxime complex in nickel salt solution.

3. To estimate lead as lead chromate in the given solution of lead nitrate.

Viscosity measurements

1. To determine the coefficient of viscosity of a given liquid by Ostwald’s viscometer.

2. Determination of viscosity of aqueous solutions of (i) polymer (ii) ethanol and (iii) sugar at

room temperature.

3. Study the variation of viscosity of sucrose solution with the concentration of solute.

4. Determination of surface tension of a given liquid by drop number method using

Stalagmometer.

5. To determine the unknown composition of a given mixture of two liquids by surface tension

measurements.

6. Determination of surface tension of a given liquid by drop weight method.

7. Determination of surface tension of a mixture of two miscible liquids and hence the

parachor of the mixture.

8. To determine the strength of given acid pH metrically.

9. To determine the pH of various mixtures of sodium acetate and acetic acid in aqueous solution

and hence determine the dissociation constant of the acid.

10. pH metric titration of

(i) strong acid vs. strong base

(ii) weak acid vs. strong base.

SUGGESTED BOOKS

1. Svehla, G & Sivasankar, B. Vogel’s Qualitative Inorganic Analysis.

2. Agarwala, S. K.; Lal, K. Advanced Inorganic Analysis.

3. Vogel's Quantitative Chemical Analysis, J. Mendham, Pearson Education, 2009.

4. Vogels Qualitative Inorganic Analysis, G. Svehla, Pearson Education, 2012.

5. Experiments in Applied Chemistry, Sunita Rattan, S. K. Kataria & Sons, 2012.

6. Advanced Practical Physical Chemistry, J. B. Yadav, Krishna Prakashan Media (P) Ltd.,

2012.

7. Khosla, B. D.; Garg, V. C.; Gulati, A. Senior Practical Physical Chemistry, R. Chand & Co.:

New Delhi (2011).

http://www.flipkart.com/author/j-mendham

http://www.flipkart.com/author/g-svehla

ENVIRONMENT SCIENCE (BMH-405)

Contact Hours: 50 hours L/T/P:5/1/0 Total Marks: 100


PART-I

Introduction to environmental studies: Multidisciplinary nature of environmental studies; Scope

and importance; Concept of sustainability and sustainable development

Natural Resources: Renewable and Non-renewable Resources

• Land resources and land use change; Land degradation, soil erosion and desertification.

• Deforestation: Causes and impacts due to mining, dam building on environment, forests,

biodiversity and tribal populations.

• Water: Use and over-exploitation of surface and ground water, floods, droughts, conflicts

over water (international & inter-state).

• Energy resources: Renewable and non-renewable energy sources, use of alternate energy

sources, growing energy needs, case studies.

Ecosystems: What is an ecosystem? Structure and function of ecosystem; Energy flow in an

ecosystem: food chains, food webs and ecological succession. Case studies of the following

ecosystems:

a) Forest ecosystem

b) Grassland ecosystem

c) Desert ecosystem

d) Aquatic ecosystems (ponds, streams, lakes, rivers, oceans, estuaries)

Biodiversity and Conservation:

• Levels of biological diversity: genetic, species and ecosystem diversity; Biogeographic

zones of India; Biodiversity patterns and global biodiversity hot spots.

• India as a mega-biodiversity nation; Endangered and endemic species of India.

• Threats to biodiversity: Habitat loss, poaching of wildlife, man-wildlife conflicts, biological

invasions; Conservation of biodiversity: In-situ and Ex-situ conservation of biodiversity.

• Ecosystem and biodiversity services: Ecological, economic, social, ethical, aesthetic and

Informational value.

PART-II

Environmental Pollution

• Environmental pollution: types, causes, effects and controls; Air, water, soil and noise

pollution

• Nuclear hazards and human health risks

• Solid waste management: Control measures of urban and industrial waste.

• Pollution case studies.

Environmental Policies & Practices

• Climate change, global warming, ozone layer depletion, acid rain and impacts on human

communities and agriculture

• Environment Laws: Environment Protection Act; Air (Prevention & Control of Pollution)

Act; Water (Prevention and control of Pollution) Act; Wildlife Protection Act; Forest

Conservation Act. International agreements: Montreal and Kyoto protocols and Convention

on Biological Diversity (CBD).

• Nature reserves, tribal populations and rights, and human wildlife conflicts in Indian

context.

Human Communities and the Environment

• Human population growth: Impacts on environment, human health and welfare.

• Resettlement and rehabilitation of project affected persons; case studies.

• Disaster management: floods, earthquake, cyclones and landslides.

• Environmental movements: Chipko, Silent valley, Bishnois of Rajasthan.

• Environmental ethics: Role of Indian and other religions and cultures in environmental

conservation.

• Environmental communication and public awareness, case studies (e.g., CNG vehicles in

Delhi).

Field work:

✓ Visit to an area to document environmental assets: river/ forest/ flora/fauna, etc.

✓ Visit to a local polluted site-Urban/Rural/Industrial/Agricultural.

✓ Study of common plants, insects, birds and basic principles of identification.

✓ Study of simple ecosystems-pond, river, Delhi Ridge, etc.

Reference:

1. Carson, R. 2002. Silent Spring. Houghton Mifflin Harcourt.

2. Odum, E.P., Odum, H.T. & Andrews, J. 1971. Fundamentals of Ecology. Philadelphia: Saunders.

3. Sharma, P.D. 1992. Ecology and Environment, Rastogi Publ. Meerut.

4. Bharucha, E. 2005. Textbook of Environmental Studies, Universities Press, Hyderabad.

5. Cunningham, W. P., Cooper, T. H., Gorhani, E. & Hepworth, M. T. 2001. Environmental

Encyclopedia, Jaico Publications House, Mumbai.

6. De, A. K. 1989. Environmental Chemistry, Wiley Eastern Ltd.

7. Pepper, I.L., Gerba, C.P. & Brusseau, M.L. 2011. Environmental and Pollution Science.

Academic Press.

8. Sengupta, R. 2003. Ecology and economics: An approach to sustainable development. OUP.

9. Singh, J.S., Singh, S.P. and Gupta, S.R. 2014. Ecology, Environmental Science and

Conservation. S. Chand Publishing, New Delhi.

10. Sodhi, N.S., Gibson, L. & Raven, P.H. (eds). 2013. Conservation Biology: Voices from the

Tropics. John Wiley & Sons.

11. Wilson, E. O. 2006. The Creation: An appeal to save life on earth. New York: Norton.

12. Chapman, J.L. and Reiss, M.J. 1988. Ecology–Principles and Applications, Cambridge

University Press, U.K.

MODERN ALGEBRA

(BMH-501)



Objectives: This course aim to provide a first approach to the subject of algebra, which is one of

the basic pillars of modern mathematics. The focus of the course will be the study of certain

structures called groups, rings, fields and some related structures.

Outcomes: Students will be able to analyze and demonstrate examples of subgroups, normal

subgroups, quotient groups; ideals and quotient rings. They will be able to use the concepts of

isomorphism and homomorphism for groups and rings.

PART -I

Permutations, combinations, pigeon-hole principle, inclusion-exclusion principle, dearragements,

Fundamental theorem of arithmetic, divisibility in Z, congruences, Chinese Remainder Theorem,

Euler’s Ø- function and primitive roots.

Binary operation, algebraic structure, semigroups, groups, examples of groups, subgroups, cosets,

order of a group, Lagrange’s theorem with proof, normal groups and quotient groups.

PART -II

Homomorphism, Fundamental theorem of group homomorphism with proof, Second theorem of

isomorphism with proof, Third theorem of isomorphism with proof, permutation groups, symmetric

groups, alternating groups, Cayley’s theorem of isomorphisms, cyclic groups and automorphisms of

groups.

Rings, examples of rings, field, subring, subfield, ideals, algebra of ideals, quotient rings,

homomorphism, Fundamental theorem of ring homomorphism with proof, Second theorem of

isomorphism with proof and Third theorem of isomorphism with proof.

Text Books

1. Herstein, I. N., Topics in Algebra, Willey Eastern Ltd, 2005.

2. Bhattacharya P.B., Jain S.K. and Nagpaul S.R., Basic Abstarct Algebra, Cambridge University

Press, 1997.

References

1. Singh Surjit and Zameeruddin Q., Modem Algebra, Vikas Publication House, 2006.

2. Musli C., Introduction to Rings and Modules, Narosa Publishing House, 2009.

DISCRETE MATHEMATICS - II

(BMH-502)



Objective: The main objective of this course is to provide the necessary background of discrete

structures. It emphasizes on essential concepts in graph theory and its applications in real life

problems.

Outcome: In the end of this course the students will learn basic concepts of graph theory and will

be able to apply this knowledge in problem solving.

PART -I

Basic counting principles, Permutations and combinations of sets, Pigeonhole principle, Binomial

and multinomial theorems, Mathematical induction.

Graph theory: Introduction to graphs, Graph terminology, Directed and Undirected graphs,

Adjacency and Incidence Matrices. Operations of graphs- Union, Intersection and Complement,

Graph Isomorphism, Graph Homeomorphism, Connectivity, Sub-graphs, Bipartite graphs, Planar

and Non-Planar graphs, Euler’s formula, Graph colouring, Chromatic number, Walks, paths and

circuits, Shortest paths, Dijkastra’s algorithm to find shortest path.

PART -II

Eulerian paths and circuits, Eulerian graphs, Fluery's algorithm for Euler's circuit. Hamiltonian

paths and circuits, Hamiltonian graphs. Travelling Salesman Problem.

Trees: Basic terminology, Binary trees, Complete Binary trees, Properties of tree, Tree Traversing:

Preorder, Postorder and Inorder Traversals. Evaluation of Prefix and Postfix expressions, Spanning

trees, Minimal spanning trees, Maximal spanning trees, Greedy's (Kruskal's) algorithm and Prim’s

Algorithm for generating minimum weight spanning graphs, Algorithms for Breadth First Search

(BFS) and Depth First Search (DFS).

Text Books

1 Joshi, K.D., Foundations of discrete mathematics, John Wiley and Sons, 1989.

2 Ram Babu, Discrete Mathematics, Vinayak Publication, 2007.

3. Grimaldi, R. P. and Ramana, B. V., Discrete and Combinatorial Mathematics-An Applied

Introduction, Pearson education, 2004.

4. Kenneth H. Rosen, “Discrete Mathematics and Its Applications”, Tata McGraw-Hill,

Edition 4th

References

5. Tremblay, J. P. and Manohar, R., A First course in Discrete Structures with applications to

Computer Science, Tata McGraw Hill, 1999.

6. Truss, J. K., Discrete Mathematical Structures for Computer Science, Pearson education ,

1994.

PROBABILITY AND STATISTICS

(BMH-503)



Objectives: The main objective of this course is to provide elementary introduction to probability

and statistics. It also demonstrates properties of probability distribution. This will also enable

students to learn about random sampling and testing of hypothesis.

Outcomes: In the end of this course the students will learn methods to find probability, measures of

central tendency, dispersion, skewness and kurtosis. They will be able to use statistical concepts to

analyze and interpret real life data.

PART - I

Important concepts in probability: experiment, trial, sample point and sample space, definition of an

event, mutually exclusive, exhaustive, independent and equally likely events. conditional

probability, Bayes theorem and its applications.

Random Variable: definition of discrete random variable, probability mass function, continuous

random variable, probability density function, probability distribution function, discrete and

continuous probability distributions: Binomial, Poisson and Normal, basic properties of the

distributions and their applications, fitting of Binomial and Poisson distributions, curve fitting by

method of least squares.

PART - II

Statistics: variable, frequency, discrete and continuous frequency distributions, measures of Central

tendency: mean, median, mode, harmonic mean, geometric mean, measures of dispersion: range,

quartile deviation, mean deviation, standard deviation, coefficient of variation, moments, measures

of skewness and kurtosis.

Sampling and Testing of Hypothesis: population, sampling, parameter, statistic, sampling

distribution, standard error, null hypothesis, alternate hypothesis, errors in sampling: type-I, type-II,

level of significance, critical region, degree of freedom, large sample tests, small sample tests:

Student's t-test, Chi-square test for goodness of fit and independence of attributes, F-test or variance

ratio test.

Text Books

1. Gupta, S.C. and Kapoor, V.K., Fundamental of Mathematical Statistics, S. Chand and Sons,

2012.

2. Meyer P.L.: Introductory Probability and Statistical Applications Addison-Wesley, 1970.

References

1. Goon A.M., Gupta M.K., Dasgupta B: Fundamental of Statistics, Vol. I, World Press, Calcutta,

1999.

2. Mood A.M., Graybill F.A and Boes D.C.: Introduction to the Theory of Statistics, McGrawh

Hill, 1974.

OPERATIONS RESEARCH

(BMH-504)



Objectives: This course aims to introduce students how to use quantitative methods and techniques

for effective decision-making, model formulation and applications that are widely used in solving

business decision problems.

Outcomes: Students will be able to formulate mathematical models of various real world problems

arising in Finance, Budegeting, and Investment etc.

PART- I

Introduction, models in operation research, general methods for solving O.R. models, Elementary

theory of convex sets, Linear programming problems, examples of LPPs, mathematical formulation

of the LPPs, Graphical solution of the problem. Simplex method, Big M method, Two Phase

method, problem of degeneracy.

Duality in linear programming: Concept of duality, fundamental properties of duality, duality

theorems, Complementary slackness theorem, duality and simplex method, dual simplex method.

Sensitivity Analysis: Study of discrete changes in the cost vector, in the requirement vector and in

the co-efficient matrix.

PART- II

Transportation Problem: Introduction, mathematical formulation of the problem, initial basic

feasible solution, optimum solution, degeneracy in transportation problems, transportation

algorithm, unbalanced transportation problems.

Assignment Problems: Introduction, mathematical formulation of an assignment problem,

assignment algorithm, unbalanced assignment problems.

Integer Programming: Introduction, Gomory's all-IPP method, Gomory's mixed-integer method,

Branch and Bound method.

Games and Strategies: Introduction, Two person zero sum games, Maximum-Minimum Principle,

Games without saddle points, Mixed Strategies, Graphical solution, Dominance property, Reducing

the game problem to a LPP.

Text Books

1. Kanti Swaroop, P.K. Gupta and Man Mohan, Operations Research, Sultan Chand and Sons, 9th

Edition(2001).

2. TahaHamdy A., Operations Research, An Introduction, PHI, New Delhi, 6th Edition(1999).

References

1. S.D. Sharma, Operation research, KedarNath and Co., Meerut(2002).

2. Kasana and Kumar , Introductory Operation Research, Springer(2004).

3. Chander Mohan and Kusum Deep, Optimization Techniques, New Age International, (2009).

STATICS

(BMH-505)



Objectives: The objective of this paper is to make students understand the concepts and basics of

mechanics and to clarify the foundation of statics. The students will be made familiar about the

forces and their consequences when acting on bodies, the forces being so arranged that the bodies

remain at rest.


forces, moment of force, parallel forces and related theorems. They will be able to find the co-

efficient of friction and problems on Ladders and Beams; centre of gravity of circular arc, solid and

hollow hemisphere, solid and hollow cone.

PART- I

Basic definitions of Forces, Resultant of forces, parallelogram law of forces, Triangular law of

forces, Types of forces, Magnitude and direction of the resultant of the forces acting on a particle,

Lami's theorem, Equilibrium of a particle under several coplanar forces, parallel forces.

Moment: Moment of a force, Varignon’s theorem on moments, Generalised Theorem of Moments

Generalised Theorem of resolved parts, Centre of a number of parallel forces.

Couple: Introduction, Moment of a couple, Equilibrium of two couples, equivalence of two couples,

Resultant of a number of coplanar couples, Triangle theorem of moments, Polygon theorem of

moments, Resultant of a force and a couple, Resolution of a force into a force and couple.

PART - II

Equilibrium of three coplanar forces acting on a rigid body, m-n theorem.

Friction: Definition, Types of Friction, Laws of friction, angle of friction, co-efficient of friction,

equilibrium of a body on a rough inclined plane acted on by several forces, Problems on Ladders

and Beams only.

Centre of Gravity: Definition, Centre of mass, Centre of gravity of simple uniform bodies, Uniform

triangular lamina, rods forming a triangle, Uniform trapezium. Centre of gravity of a circular arc,

sector and segment, solid and hollow hemisphere, solid and hollow cone, catenary-simple problems.

Text Books

1. Loney, S. L., The elements of statics and dynamics –Part I (statics), Cambridge University

Press,1932(Publisher Arihant -2012.

2. Chorlton F., Text book of Dynamics, CBS Publishers,1985.

Reference Books

1. Synge, J.L., and Griffith, B.A., Principles of Mechanics, Tata McGraw Hill, 1971.

2. Roberst A.P., Statics and dynamics with background mathematics, Cambridge University

press, 2003.

COMPLEX ANALYSIS

(BMH-601)



Objectives: The objective of this course is to introduce the concept of analytic functions, harmonic

functions, conformal mappings and contour integration with its fundamental results.

Outcomes: The students will able to solve different types of contour integration and understand the

basic results of complex analysis.

PART - I

Complex plane, Stereographic projection, Riemann sphere, function of a complex variable, limits,

continuity, differentiability, analyticity, Cauchy Riemann equations, sufficient condition, harmonic

functions.

Singularities: Zero of a function, singular point, classification of singularities, isolated and non-

isolated singularities, removable, pole and essential singularities, Taylor's series expansion

(statement only), Larent series expansion (statement only) and identification of singularities through

Larent series expansion.

PART - II

Calculus of residues: Residue at a finite point and the point at infinity, residue theorem (statement

only), evaluation of integrals of the type C

dzzf )( where f(z) is a rational function with degree of

denominator polynomial greater than that of numerator polynomial by at least two and C is a circle

and

df2

0)cos,(sin . Evaluation of real integrals dxxf

−)(

Conformal mapping, elementary transformations: Translation, rotation, magnification, inversion,

bilinear transformation, Cross ratio, Schwarz-Christoffel transformation.

Text Books

1. Churchill, R. V. and Brown J.W., Complex Variables and Applications, Tata McGraw Hill

International Edition, 2009.

2. Zill, D.G., A First Course in Complex Analysis with Applications, Jones and Bartlett

Publishers Series in Mathematics, 2013.

References

1. Ponnusamy, S., Foundation of Complex Analysis, Narosa Publishing House Pvt. Ltd.

Second Edition, Sixth Reprint, 2011.

2. Kasana, H. S., Complex Variables: Theory and Applications, PHI, 2006.

3. Narayan Shanti, Theory of Functions of a Complex Variable, S. Chand and Co., Seventh

Edition, 1986.

METRIC SPACES

(BMH-602)



Objectives: The objective of this course is to make students learn fundamental concepts of metric

spaces and spaces of functions.

Outcomes: After the completion of the course, Students will be able to understand the concept of

metric space, convergence in metric spaces; compactness and connectedness in metric spaces.

PART - I

Metric Spaces: Definition and examples, bounded metric spaces, diameter of a subset in a metric

space, open sphere and closed sphere, open sets, closed sets, equivalent metrics.

Convergence in metric spaces, sequence and subsequence, Cauchy sequence, completeness of

metric spaces, Cantor’s intersection theorem, Baire’s category theorem, isometric metric spaces.

PART- II

Compactness in metric spaces: Definition and properties of a compact set, compactness and finite

intersection property, sequentially compact metric spaces.

Connectedness: Separated sets, connected sets, connectedness of real line, components of a metric

space.

Continuous functions in metric spaces: Limit, continuity, images of compact and connected sets

under a continuous function, uniform continuity, homeomorphism.

Text Books

1. Ram Babu, Metric Spaces, Vinayak Publication, 2005.

2. Copson, E.T., Metric Spaces, Cambridge University Press,1968.

References

1. Jain, P. K. and Khalil Ahmad, Metric Spaces, Narosa Publishing House, First print, 1996.

2. Sutherland, W. A., Introduction to Metric and Topological Spaces, OUP Oxford, 2009.

3. Rudin, W., Principles of Mathematical Analysis, McGraw Hill International Editors,

Mathematics Series, Third Edition, 1976.

SPECIAL FUNCTIONS

(BMH- 603)



Objectives: The objective of the course is to analyze properties of special functions by their

integral representations and symmetries.


Beta and Gamma functions, soluion of Legendre, Hermite and Hyper geometric differential

equations. They will also learn Lagurre polynomials and their orthogonal properties.

PART - I

Series solution of differential equations – Power series method, definitions of Beta and Gamma

functions, Bessel equation and its solution, Bessel's functions and their properties, convergence,

recurrence relations and generating functions, orthogonality of Bessel functions.

Legendre and Hermite differentials equations and their solutions: Legendre and Hermite functions

and their properties, recurrence relations and generating functions, orhogonality of Legendre and

Hermite polynomials, Rodrigue's formula for Legendre & Hermite polynomials.

PART - II

Hypergoemetric and Generalized Hypergeometric functions: Function 2F1(a,b;c;z) A simple

integral form evaluation of 2F1 (a,b;c;z), Gauss theorem, Vandermonde’s theorem,contiguous

function relations, Hyper geometrical differential equation and its solutions, F (a,b;c;z) as function

of its parameters, Kummer’s relation.

Laguerre Polynomials: The Laguerre Polynomials Ln(X), generating functions, pure recurrence

relations, differential recurrence relation, Rodrigo's formula, orthogonal property of Laguerre

polynomials, expansion of polynomials.

Text Books

1. Rainville, E.D, Special Functions, The Macmillan co., New York. 1971.

2. Lebdev, N.N, Special Functions and Their Applications, Prentice Hall, Englewood Cliffs, New

jersey, USA, 1995.


References

1. Srivastava, H.M. Gupta, K.C. and Goyal, S.P.; The H-functions of One and Two Variables with

applications, South Asian Publication, New Delhi.

2. Saran, N., Sharma S.D. and Trivedi, - Special Functions with application, Pragati prakashan,

1986.

DYNAMICS

(BMH-604)



Objectives: The main aim of this course is to provide knowledge about the general parameters like

velocity and acceleration. In addition to this the objective of this paper is to get acquainted the

students about the different mathematical concepts and laws during the motion of bodies under the

action of forces.

Outcomes: After studying this course, students will be able to understand the concept of velocity

and acceleration parameter . They will understand the concept of terminal speed, and use it in

solving mechanics problems in one dimension. They will be able to solve problems relating to the

motion of a projectile in the absence of air resistance and problems relating to the Central orbit.

PART - I

Kinematics and Kinetics: Motion in two dimension, Radial and transversal velocities and

accelerations, Tangential and normal velocities and accelerations, Angular velocity, Relative

motion.

Rectilinear Motion: Motion in a straight line, Simple Harmonic Motion (SHM), Geometrical

representation, Newton's laws of motion, Terminal velocity, Motion under gravity in a resisting

medium.

PART - II

Constrained Motion: Uniform circular motion, Satellite describing a circular orbit, Smooth hollow

sphere rotating with uniform angular velocity, Cycloidal Motion, Cycloidal pendulum.

Central orbit: Motion of a particle under central forces, parabolic orbit, Elliptic orbit, Hyperbolic

orbit, Apse, Apsidal distance, Apsidal angle, Kepler’s laws of planetary motion, relative motion or

the planet about the sun. Three-dimensional motion, Velocity & acceleration (in polar & cylindrical

co-ordinates).

Text Books

1. Loney, S. L., The elements of statics and dynamics –Part II(Dynamics), Cambridge

University Press,1932(Publisher Arihant -2012.

2. Chorlton F., Text book of Dynamics, CBS Publishers, 1985.

Reference Books

1. Synge, J.L., and Griffith, B.A., Principles of Mechanics, Tata McGraw Hill, 1971.

2. Roberst A.P., Statics and dynamics with background mathematics, Cambridge University

press, 2003.

SEMINAR

(BMH-605)

Total Marks: 100 Evaluation: Internal

Students are required to prepare presentations on the selected topics and present them for the

internal evaluation two times in the semester.

department of mathematics€¦ · 1 bmh-101 calculus-1 5 1 0 6 25 75 2 bmh-102 ... 5 bmh-205...

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