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Tables of Contents for Essential Calculus
Chapter/Section Title
Page #
Page Count
To the Instructor
To the Student
Mathematical Background
Introductory Remarks
1
1
Sets
2
2
Numbers
4
6
Inequalities
10
4
The Absolute Value
14
3
Intervals and Neighborhoods
17
3
Rectangular Coordinates
20
4
Straight Lines
24
4
More about Straight Lines
28
7
Differential Calculus
Functions
35
7
More about Functions
42
4
Graphs
46
6
Derivatives and Limits
52
7
More about Derivatives
59
7
More about Limits
66
8
Differentiation Technique
74
7
Further Differentiation Technique
81
7
Other Kinds of Limits
88
12
Differentiation as a Tool
Velocity and Acceleration
100
4
Related Rates and Business Applications
104
5
Properties of Continuous Functions
109
3
Properties of Differentiable Functions
112
5
Applications of the Mean Value Theorem
117
4
Local Extrema
121
6
Concavity and Inflection Points
127
4
Optimization Problems
131
6
Integral Calculus
The Definite Integral
137
7
Properties of Definite Integrals
144
9
The Logarithm
153
6
The Exponential
159
6
More about the Logarithm and Exponential
165
7
Integration Technique
172
9
Improper Integrals
181
5
Integration as a Tool
Elementary Differential Equations
186
6
Problems of Growth and Decay
192
7
Problems of Motion
199
9
Functions of Several Variables
From Two to n Dimensions
208
7
Limits and Differentiation
215
8
The Chain Rule
223
5
Extrema in n Dimensions
228
7
Tables
235
4
Selected Hints and Answers
239
21
Supplementary Hints and Answers
260
26
Index
286