Template No (12) Course Specification

University/Academy: Suez canal university

Faculty/Institute: Faculty of Science

Department: Mathematics

1-Course data

Academic year/Level:

Second Level

CourseTitle: Ordinary

Differntial

Equations

Code: MT210

Department/program:

Mathematics, Computer Science,

Statistics, Mathematics

&Computer Science, Statistics

&Computer Science

Credit/ Taught Hours: 3 Theoretical: 2 Practical: 2

1 Apply some of mathematical methods for solving ordinary differential

equations.

2 Develop critical, analytical and personal skills that prepare students to be able to solve some types of ordinary differential equations.

3 Learn the tools and ethics of ordinary differential equations.

4 Develop continuously his knowledge in the specialized field to be qualified

for solving ordinary differential equations.

2- Course aim(s)

3- Intended Learning Outcomes (ILOs):

a1- Describe the importance of mathematics and the relation between

mathematics and other sciences in solving Society problems.

a3-Interpret the theoretical theorems for ordinary differential equations

a4-Illustrate discussion and thought, leading to solution of problems for

ordinary differential equations .

3.A- Knowledge

and

understandings: B1-Conclude the essential facts, concepts, principles and theories relating to

ordinary differential equations.

B2-Analyze the theories of ordinary differential equations.

B4-Apply some mathematical methods in solving problems in ordinary

differential equations. .

3.B- Intellectual

Skills:

C2 - Apply mathematical methods to solve several types of ordinary differential

equations.

C4 - Perform suitable model for different problems through communication

with other branches of basic science.

3.C- Professional

Skills:

D1- Employ recent information and tools effectively in solving some problems

in other fields.

D2- Lead team work effectively for solving problems; appreciating the values

of independent thinking, continuous learning, time management, collaboration,

neatness, property rights, ethics and traditions.

3.D- General

Skills:

Theoretical part content

No. of

Lecture(s)

Week(s)

No.

No. of

Hours

Topic

One 1 2

1- Equations of

order one:

Introduction to

ordinary

differential

equations –

Existence of

solution –

Isoclines and

curves of solution

– Forming

differential

equations.

Three 2,3,4 6

2 Methods of

solutions of first

order ordinary

differential

equations:

Separation of

variables –

Homogeneous

equations, Exact

equations, Linear

equation of first

order

Two 5,6 4

3. Additional

topics on

equations of first

order: Integrating

factor and

methods to

determine an

integrating factor

-Solving an

equation by using

4- Course

content:

(theoretical and

then practical)

substitution

suggested by

equation –

Bernoulli ,Ricatii

and Calauriate

equations

Three 7,8,9 6

4 -Linear

differential

equations of

higher orders:

General form of a

linear equation –

Linearly

independent

solutions - An

existence and

uniqueness

theorem –The

Wroskian

determinant.

General solution

of a

homogeneous

equation –

General solution

of a non-

homogeneous

equation – The

differential

operator and its

fundamental laws

and its properties.

Two 10,11 4

5- Non-

homogeneous

equations:

Solution of a

non-

homogeneous

equation – The

method of

undetermined

coefficients -

Solving by

inspection –

Reduction of

order – Variation

of parameters.

Two 12,13 4

6- Power series:

Linear equation

and power series

– Convergence of

power series –

Ordinary and

singular points –

Solution near an

ordinary point.

One 14 2

7- Numerical

solution of

ordinary

differential

equation: Picard

method Practical part content

Tutorial Practical week(s)

No.

No. of

Hours Topic

One - 1 2

1-solving

problems to

forming the

differential

equations.

Three - 2,3,4 6

2 solving

problems in

ordinary

differential

equations of first

order using:

Separation of

variables –

Homogeneous

equations, Exact

equations, Linear

equation)

three - 5,6,7 6

3. Solving

problems in

ordinary

differential

equations of first

order using::

Integrating factor

and methods to

determine an

integrating factor

-Solving an

equation by using

substitution

suggested by

equation –solving

problems for

Bernoulli, Ricatii

and Caulurit's

equations.

One - 8 2

4- Solving

problems for

homogeneous

linear differential

equations of

higher order with

constant

coefficients.

Three - 9,10,11 6

5 Solving

problems for non-

homogeneous

linear differential

equations of

higher order with

constant

coefficients: The

method of

– Reduction of

order

–undetermined

coefficients

–Variation of

parameters

–simple method.

Two - 12,13 4

6- Solving

problems for

linear ordinary

differential

equations of

second order

using Power

series solutions

for Ordinary and

singular

One - 14 2

7- Solving

problems for

Numerical

solution of

ordinary

differential

equation: Picard

method

5.1- Lectures using whiteboard or occasionally using data

show.

5.2- Problem discussion sessions with students.

5.3- Presentation by student teams of some independent

work relevant to the course. 5.4- Independent search of students about certain results or applications

5- Teaching and

learning methods:

6- Teaching and

learning methods

for limited

capability

students: 7- Students assessment:

4.1- 7.A.1-Assignments, quizzes, and presentations to assess

aaaaa1,a4; b1,b4; c2,d2.

7. A.2- Mid term tests to assess a1-a4; c2.

7. A.3-Oral examination to assess a1-a3; d2,

7. A.4- Final examination to assess a4-a3; b1, b2, b4;

c2;d1.

7.A- Assessment

Methods:

Assessment 1: Four Assignments Week2, 5, 8, 11. Four

quizzes.

Assessment 2: Two mid term tests, first Week7, second

Week 12.

Assessment 3: Oral examination Week14.

Assessment 4: Final Examination Week15.

7.B- Assessment

schedule

Mid-term examination % 20% Final-term examination % 60%

Oral examination % 10% Semester work % 10% Total 100%

7.C- Assessments

Weights

8- List of Books and references

Not applicable.

8.A- Notes:

1- Braun, M. V., Differential Equations and Their Applications, 4th

Edition Springer Verlag, 1993.

2- Boyce, W. E. and DiPrima, R.C., Elementary Differential Equations

and Boundary Value Problems, Sixth Edition, John Wiley and Sons,

1997.

3- E. D. Rainville, P. E. Bedient, R. E. Bedient, Elementary Differential

Equations ( 8th Edition, Prentice Hall Inc., 1996.

4- Simmons, G. F., Differential Equations with Applications and

Historical Notes, Second Edition, McGraw-Hill, Inc., 1991.

8.B- Essential

books:

None

8.C- Recommended

books:

Course coordinator: Head of Department:

Dr. Zinab Abdel-Hady Dr. Abd ElGawad abou El-fadel

None 8.D- Scientific

periodicals, websites

….etc

Suez Canal University: Course code:MT210

Faculty of Science: Course title: Ordinary differential equation

Matrix of intended knowledge and skills of the course

1- Intended Learning Outcomes (ILOs):

A- Knowledge and understandings:

a3-Interpret the theoretical theorems for ordinary differential equations

a4-Illustrate discussion and thought, leading to solution of problems for ordinary differential equations

B- Intellectual Skills: B1-Conclude the essential facts, concepts, principles and theories relating to ordinary differential equations.

B2-Analyze the theories of ordinary differential equations.

B4-Apply some mathematical methods in solving problems in ordinary differential equations. .

C- Professional Skills: C2 - Apply mathematical methods to solve several types of ordinary differential equations.

C4 - Perform suitable model for different problems through communication with other branches of basic science.

D- General Skills: D1- Employ recent information and tools effectively in solving some problems in other fields.

D2- Lead team work effectively for solving problems; appreciating the values of independent thinking, continuous

learning, time management, collaboration, neatness, property rights, ethics and traditions.

a1-Describe the importance of mathematics and the relation between mathematics and other sciences in solving Society

problems.

2- Course matrix table:

Course content for theoretical part

Week (s)

No.

A knowledge and

Understanding Skills

Intellectual Skills

Professional

and Practical Skills

General

Skills

1- Equations of order

one:

Introduction to ordinary

differential equations

Existence of solution

Isoclines and curves

of solution

1 a1 b1

2- Methods of solutions

of ordinary differential

equations of first order:

Separation of variables –

Homogeneous equations,

Exact equations, Linear

equation of first order

2,3,4 a3,a4 b2,b4 c2 d1

3. Additional topics on

equations of first order:

Integrating factor and

methods to determine an

integrating factor -

Solving an equation by

using substitution

suggested by equation –

Bernoulli, Ricatii

&Cauliourat equations.

5,6

a3,a4 b2,b4 c2 d1

4 -Linear differential

equations: General forms

of a linear equation of

higher order– Linearly

independent solutions -

An existence and

7,8,9 a3,a4 b1,b4 c2 d1

uniqueness theorem –The

Wroskian determinants-

General solution of a

linear

Homogeneous equation

with constants

coefficients– The

differential operator and

its fundamental laws and

properties.

5- Non-homogeneous

equations: Solution of a

non-homogeneous

equation – The method of

undetermined

coefficients - Solving by

inspection – Reduction of

order – Variation of

parameters-Simple

method.

10,11 a3,a4 b1,b4 c2 d1

6- Power series: Linear

equation and power

series – Convergence of

power series – Ordinary

and singular points –

Solution near an ordinary

point.

12,13 a3,a4 b1,b4 c2,c4 d1,d2

7- Numerical solution of

ordinary differential

equation: Picard's method

14 a4 b4 c2 d1

Course content for practical part

Week (s)

No.

A knowledge and

Understanding Skills

Intellectual Skills

Professional

and Practical Skills

General

Skills

1-solving problems to

forming the differential

equations. 1

2 solving problems in

ordinary differential

equations of first order

using: Separation of

variables –

Homogeneous equations,

Exact equations, Linear

equation)

2,3,4 c2 d1

3. Solving problems in

ordinary differential

equations of first order

using:: Integrating factor

and methods to

determine an integrating

factor -Solving an

equation by using

substitution suggested by

equation –solving

problems for Bernoulli,

Ricatii and Caulurit's

equations.

5,6

c2 d1

4- Solving problems for

homogeneous linear

differential equations of

higher order with

constant coefficients.

7,8,9 c2 d1

Course coordinator: Head of Department:

Dr. Zinab Abdel-Hady Dr. Abd ElGawad abou El-fadel

5 Solving problems for

non-homogeneous linear

differential equations of

higher order with

constant coefficients: The

method of

– Reduction of order

–undetermined

coefficients

–Variation of parameters

–simple method.

10,11 c2 d1

6- Solving problems for

linear ordinary

differential equations of

second order using

Power series solutions

for Ordinary and singular

12,13 c2,c4 d1,d2

7- Solving problems for

Numerical solution of

ordinary differential

equation: Picard method

14 c2 d1