Republic of Iraq Ministry of Higher Education & Scientific Research University of Technology
Ministry of Higher Education and Scientific Research · Web viewMinistry of Higher Education and...
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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.
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Chapter Three: Trigonometric FunctionsGraphs of trigonometric functions, periodicity, Trigonometric functions, Inverse trigonometric functions, hyperbolic trigonometric functions, inverse hyperbolic trigonometric function
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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.
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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
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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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