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Tables of Contents for Single Variable Calculus
Chapter/Section Title
Page #
Page Count
Functions and Models
Four Ways to Represent a Function
2
9
Mathematical Models
11
6
New Functions from Old Functions
17
4
Graphing Calculators and Computers
21
2
Exponential Functions
23
4
Inverse Functions and Logarithms
27
9
Technology Plus
33
3
Limits and Rates of Change
The Tangent and Velocity Problems
36
3
The Limit of a Function
39
8
Calculating Limits Using the Limit Laws
47
7
The Precise Definition of a Limit
54
5
Continuity
59
4
Limits at Infinity; Horizontal Asymptotes
63
6
Tangents, Velocities, and Other Rates of Change
69
3
Derivatives
72
5
The Derivative as a Function
77
11
Technology Plus
83
5
Derivatives
Derivatives of Polynomials and Exponential Functions
88
3
The Product and Quotient Rules
91
2
Rates of Change in the Natural and Social Sciences
93
3
Derivatives of Trigonometric Functions
96
3
The Chain Rule
99
4
Implicit Differentiation
103
7
Higher Derivatives
110
3
Derivatives of Logarithmic Functions
113
3
Hyperbolic Functions
116
4
Related Rates
120
6
Linear Approximations and Differentials
126
8
Technology Plus
130
4
Applications of Differentiation
Maximum and Minimum Values
134
6
The Mean Value Theorem
140
4
How Derivatives Affect the Shape of a Graph
144
8
Indeterminante Forms and L' Hospital's Rule
152
4
Summary of Curve Sketching
156
5
Graphing with Calculus and Calculators
161
2
Optimization Problems
163
3
Applications to Business and Economics
166
2
Newton's Method
168
2
Antiderivatives
170
8
Technology Plus
173
5
Integrals
Areas and Distances
178
6
The Definite Integral
184
6
The Fundamental Theorem of Calculus
190
2
Indefinite Integrals and the Net Change Theorem
192
4
The Substitution Rule
196
6
The Logarithm Defined as an Integral
202
8
Technology Plus
207
3
Applications of Integration
Areas between Curves
210
5
Volumes
215
4
Volumes by Cylindrical Shells
219
2
Work
221
2
Average Value of a Function
223
6
Technology Plus
226
3
Techniques of Integration
Integration by Parts
229
3
Trigonometric Integrals
232
4
Trigonometric Substitution
236
4
Integration of Rational Functions by Partial Fractions
240
5
Strategy for Integration
245
2
Using Tables of Integrals and Computer Algebra Systems
247
2
Approximate Integration
249
5
Improper Integrals
254
8
Technology Plus
258
4
Further Applications of Integration
Arc Length
262
5
Area of a Surface of Revolution
267
2
Applications to Physics and Engineering
269
4
Applications to Economics and Biology
273
2
Probability
275
5
Technology Plus
278
2
Differential Equations
Modeling with Differential Equations
280
2
Direction Fields and Euler's Method
282
3
Separable Equations
285
3
Exponential Growth and Decay
288
3
The Logistic Equation
291
2
Linear Equations
293
2
Predator-Prey Systems
295
5
Technology Plus
297
3
Parametric Equations and Polar Coordinates
Curves Defined by Parametric Equations
300
4
Calculus with Parametric Curves
304
6
Polar Coordinates
310
7
Areas and Lengths in Polar Coordinates
317
3
Conic Sections
320
4
Conic Section in Polar Coordinates
324
6
Technology Plus
327
3
Infinite Sequences and Series
Sequences
330
5
Series
335
4
The Integral Test and Estimates of Sums
339
3
The Comparison Tests
342
3
Alternating Series
345
3
Absolute Convergence and the Ratio and Root Tests
348
5
Strategy for Testing Series
353
2
Power Series
355
3
Representations of Functions as Power Series
358
4
Taylor and Maclaurin Series
362
7
The Binomial Series
369
2
Applications of Taylor Polynomials
371
8
Technology Plus
375
4
On Your Own
Chapter 1 On Your Own
379
6
Chapter 2 On Your Own
385
9
Chapter 3 On Your Own
394
11
Chapter 4 On Your Own
405
11
Chapter 5 On Your Own
416
6
Chapter 6 On Your Own
422
5
Chapter 7 On Your Own
427
8
Chapter 8 On Your Own
435
5
Chapter 9 On Your Own
440
7
Chapter 10 On Your Own
447
6
Chapter 11 On Your Own
453
12
Answers to On Your Own
465