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Ministry of Higher Education and Scientific Research

University of Baghdad

Chemical Engineering Department

Mathematics

First year

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Chapter one : Revisionlines, equation of straight line, functions and graphs, function in pieces, the absolute function, how to shift graph.

2weakChapter Two: Transcendental FunctionsPower functions, exponential functions, logarithmic functions,Natural logarithmic functions.

2weak

Chapter Three: Trigonometric FunctionsGraphs of trigonometric functions, periodicity, Trigonometric functions, Inverse trigonometric functions, hyperbolic trigonometric functions, inverse hyperbolic trigonometric function

4weak

Chapter Four: Limits and ContinuityProperties, limits of trigonometric functions, limits involvinginfinity, limits of exponential functions. 4weak

- Chapter Five: DerivativesDefinition, differentiation by rules, second and higher orderderivative, application, implicit functions, the chain rule, derivativeof trigonometric functions, derivative of hyperbolic functions,derivative of inverse hyperbolic functions, derivative ofexponential and logarithmic functions.

6weak

Chapter Six: IntegrationIndefinite integration, integration of trigonometric functions,integration of inverse trigonometric functions, integration oflogarithmic and exponential functions, integration of hyperbolicfunctions, integration of inverse hyperbolic functions, integration methods; (substitution, by part, power trigonometric functions,trigonometric substitution, by part fraction), definite integration,applications; (area between two curves, length of curves, surfacearea, volumes). 8weak

Chapter Seven: First Order Differential Equation

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Definition, Separable equation, Homogeneous equation,Exacte equation, Linear equation,Bernoullies

6weak

Chapter Eight: Vector

Definition, Addition and subtraction of vector, Multiplication by sealar, Product of vector 2weak

References

Calculus by Howard Anton, Sixth Edition, Vol. 1, Wiley.2006-

- Mathematical methods for science student,G.stephenson New Art printer co.,1999

- Schaum's Outlines Advanced Calculus, 2nd Edition, Robert C. Wrede.2000

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Determine the relationship between the following two graphs :

Function: y=f(x) Function: y= ?

a. f(x)+2 b. 2f(x) c. 2f(x) d. f(x+2) e. f(2x)

Determine whether each of the following functions is even, odd or neither:

a. f ( x )=x3−5 x+4

b. f ( x )=sin24 x

c . f ( x )=e x3

HW))

Find the domain and range of f, g, f+g, and f.g for the following exercises:

1 .f ( x )=x ,g( x )=√x−1 2 .f ( x )=√ x+1 ,g( x )=√x−1

Q2/ Find the domain and range of f, g, f/g, and g/f for the following exercises:

1 .f ( x )=2 ,g( x )=x2+1 2 .f ( x )=1 ,g( x )=1+√x

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Q1/ Find the domain and range of f, g, f+g, and f.g for the following exercises:

1 .f ( x )=x ,g( x )=√x−1 2 .f ( x )=√ x+1 ,g( x )=√x−1

Solution:

Q2/ Find the domain and range of f, g, f/g, and g/f for the following exercises:

1 .f ( x )=2 ,g( x )=x2+1 2 .f ( x )=1 ,g( x )=1+√x

Solution:

Q3/

Solution:

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Solution:

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Q1/ Solve the inequalities in the following exercises. Express the solution sets as intervals or unions of intervals and show them on the real line. Use

the √a2=|a|result as appropriate.

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1 .( x−1)2<4 2 .( x+3)2<2 3 .x2−x<0 4 .x2−x−2≥0

Q2/ In the following exercises, solve the inequalities and show the solution sets on the real line.

1 .5 x−3≤7−3 x 2 .3(2−x )>2(3+x ) 3 .2 x−1

2≥7 x+ 7

6 4.

− x+52

≤12+3 x4

Q3/ Solve the equations in the following exercises:

1 .|8−3 s|=9

2 2 .|2x−4|<3

3.|r+1

2|≥1

4.

|3 r5

−1|> 25

Q4/ Graph the parabolas in the following exercises. Label the vertex, axis, and intercepts in each case.

1 .y=x2−2 x−3 2 .y=−x2+4 x−5 3 .y=−x2−6 x−5 4.

y=−14x2+2x+4

Q5/ Find the domain and range of each function.

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1 .f ( x )=1−√x 2 .F ( t )= 1

√t 3 .g( z )= 1

√4−z2

Q6/ Find the domain and range of each function and graph the function.

1 .g( x )=√−x 2.F ( t )=t /|t|

Q7/Graph the following equations and explain why they are not graphs of functions of x.

a. |y|=x b .y2=x2

1 .F (x )={3−x , x≤1

2x , x>1 2 .G( x )={1/ x , x<0

x , 0≤x

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