138
Ministry of Higher Education and Scientific Research University of Baghdad Chemical Engineering Department Mathematics First year 1
Ministry of Higher Education and Scientific Research
University of Baghdad
Chemical Engineering Department
Mathematics
First year
1
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
2
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
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
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
24
25
26
27
28
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:
29
Solution:
30
31
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.
32
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.
33
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
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
1-
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
134
