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Tables of Contents for Technical Calculus With Analytic Geometry
Chapter/Section Title
Page #
Page Count
Preface
xi
 
Rectangular Graphing in the Plane
1
31
Rectangular Coordinates
2
4
Graphs
6
9
Graphing Calculators and Computer-Aided Graphing
15
5
Using Graphs to Solve Equations
20
12
Review
29
1
Test
30
2
An Introduction to Plane Analytic Geometry
32
54
Basic Definitions and Straight Lines
33
8
The Circle
41
6
The Parabola
47
9
The Ellipse
56
7
The Hyperbola
63
7
Translation of Axes
70
7
Rotation of Axes; The General Second-Degree Equation
77
9
Review
83
2
Test
85
1
An Introduction to Calculus
86
40
The Tangent Question
87
5
The Area Question
92
6
Limits: An Intuitive Approach
98
7
One-Sided Limits
105
5
Algebraic Techniques for Finding Limits
110
6
Continuity
116
10
Review
123
1
Test
124
2
The Derivative
126
44
The Tangent Question and the Derivative
127
7
Derivatives of Polynomials
134
6
Derivatives of Product and Quotients
140
8
Derivatives of Composite Functions
148
9
Implicit Differentiation
157
7
Higher Order Derivatives
164
6
Review
167
2
Test
169
1
Applications of Derivatives
170
46
Rates of Change
171
5
Extrema and the First Derivative Test
176
6
Concavity and the Second Derivative Test
182
6
Applied Extrema Problems
188
7
Related Rates
195
8
Newton's Method
203
2
Differentials
205
4
Antiderivatives
209
7
Review
213
1
Test
214
2
Integration
216
39
The Area Question and the Integral
217
4
The Fundamental Theorem of Calculus
221
8
The Indefinite Integral
229
7
The Area Between Two Curves
236
9
Numerical Integration
245
10
Review
252
2
Test
254
1
Applications of Integration
255
56
Average Values and Other Antiderivative Applications
256
7
Volumes of Revolution: Disk and Washer Methods
263
10
Volumes of Revolution: Shell Method
273
5
Arc Length and Surface Area
278
5
Centroids
283
10
Moments of Inertia
293
7
Work and Fluid Pressure
300
11
Review
309
1
Test
310
1
Derivatives of Transcendental Functions
311
41
Derivatives of the Sine and Cosine Functions
312
6
Derivatives of the Other Trigonometric Functions
318
4
Derivatives of Inverse Trigonometric Functions
322
5
Applications
327
6
Derivatives of Logarithmic Functions
333
4
Derivatives of Exponential Functions
337
9
Applications
346
6
Review
349
2
Test
351
1
Techniques of Integration
352
50
The General Power Formula
353
4
Basic Logarithmic and Exponential Integrals
357
7
Basic Trigonometric and Hyperbolic Integrals
364
6
More Trigonometric Integrals
370
7
Integrals Related to Inverse Trigonometric and Inverse Hyperbolic Functions
377
6
Trigonometric Substitution
383
4
Integration by Parts
387
10
Using Integration Tables
397
5
Review
400
1
Test
401
1
Parametric Equations and Polar Coordinates
402
60
Parametric Equations
403
4
Derivatives of Parametric Equations
407
7
Introduction to Vectors
414
8
Derivatives of Vectors
422
5
Polar Coordinates
427
7
Conic Sections in Polar Coordinates
434
5
Differentiation in Polar Coordinates
439
4
Arc Length and Surface Area Revisited
443
9
Intersection of Graphs of Polar Coordinates
452
3
Area in Polar Coordinates
455
7
Review
460
1
Test
461
1
Partial Derivatives and Multiple Integrals
462
52
Functions in Two Variables
463
5
Surfaces in Three Dimensions
468
5
Partial Derivatives
473
7
Some Applications of Partial Derivatives
480
7
Multiple Integrals
487
8
Cylindrical and Spherical Coordinates
495
9
Moments and Centroids
504
10
Review
510
3
Test
513
1
Infinite Series
514
41
Sequences
515
3
Series
518
8
Power and Maclaurin Series
526
6
Operations with Series
532
5
Numerical Techniques Using Series
537
5
Taylor Series
542
3
Fourier Series
545
10
Review
552
1
Test
553
2
First-Order Differential Equations
555
41
Solutions of Differential Equations
556
6
Separation of Variables
562
7
Integrating Factors
569
6
Linear First-Order Differential Equations
575
5
Applications
580
5
More Applications
585
11
Review
593
2
Test
595
1
Higher-Order Differential Equations
596
24
Higher-Order Homogeneous Equations with Constant Coefficients
597
6
Auxiliary Equations with Repeated or Complex Roots
603
5
Solutions of Nonhomogeneous Equations
608
4
Applications
612
8
Review
618
1
Test
619
1
Numerical Methods and Laplace Transforms
620
31
Euler's or the Increment Method
621
3
Successive Approximations
624
4
Laplace Transforms
628
4
Inverse Laplace Transforms and Transforms of Derivatives
632
4
Partial Fractions
636
7
Using Laplace Transforms to Solve Differential Equations
643
8
Review
649
1
Test
650
1
APPENDIX A The Electronic Hand-Held Calculator
651
13
A.1 Introduction
651
2
A.2 Basic Operations with a Calculator
653
6
A.3 Some Special Calculator Keys
659
3
A.4 Graphing Calculators and Computer-Aided Graphing
662
2
APPENDIX B The Metric System
664
10
APPENDIX C Table of Integrals
674
4
Answers to Odd-Numbered Exercises
678
68
Index of Applications
746
2
Index
748