Calculus: Single Variable / Edition 6

Calculus: Single Variable / Edition 6

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by Deborah Hughes-Hallett, William G. McCallum, Andrew M. Gleason, Eric Connally
     
 

Instructor's Manual with Sample Exams, Instructor's Solution Manual, Orientation Video, Workshop Video, Calculus Project Book, Student's Solution Manual, Answer Manual, Discovering Calculus with Derive and Univ. of Arizona Software Manual available. See more details below

Overview

Instructor's Manual with Sample Exams, Instructor's Solution Manual, Orientation Video, Workshop Video, Calculus Project Book, Student's Solution Manual, Answer Manual, Discovering Calculus with Derive and Univ. of Arizona Software Manual available.

Product Details

ISBN-13:
9780470888643
Publisher:
Wiley, John & Sons, Incorporated
Publication date:
11/06/2012
Edition description:
New Edition
Pages:
768
Sales rank:
158,676
Product dimensions:
8.50(w) x 10.40(h) x 1.00(d)

Table of Contents

1A Library of Functions1
1.1Functions and Change2
1.2Exponential Functions9
1.3New Functions from Old17
1.4Logarithmic Functions23
1.5Trigonometric Functions29
1.6Powers, Polynomials, and Rational Functions37
1.7Introduction to Continuity45
2Key Concept: The Derivative55
2.1How Do We Measure Speed?56
2.2Limits62
2.3The Derivative at a Point70
2.4The Derivative Function78
2.5Interpretations of the Derivative85
2.6The Second Derivative89
2.7Continuity and Differentiability95
3Short-Cuts to Differentiation105
3.1Powers and Polynomials106
3.2The Exponential Function113
3.3The Product and Quotient Rules118
3.4The Chain Rule123
3.5The Trigonometric Functions128
3.6Applications of the Chain Rule133
3.7Implicit Functions138
3.8Parametric Equations141
3.9Linear Approximation and the Derivative150
3.10Using Local Linearity to Find Limits154
4Using the Derivative165
4.1Using First and Second Derivatives166
4.2Families of Curves176
4.3Optimization180
4.4Applications to Marginality189
4.5Optimization and Modeling196
4.6Hyperbolic Functions203
4.7Theorems about Continuous and Differentiable Functions207
5Key Concept: The Definite Integral221
5.1How Do We Measure Distance Traveled?222
5.2The Definite Integral229
5.3Interpretations of the Definite Integral236
5.4Theorems about Definite Integrals244
6Constructing Antiderivatives261
6.1Antiderivatives Graphically and Numerically262
6.2Constructing Antiderivatives Analytically268
6.3Differential Equations273
6.4Second Fundamental Theorem of Calculus278
6.5The Equations of Motion282
7Integration289
7.1Integration by Substitution290
7.2Integration by Parts298
7.3Tables of Integrals304
7.4Algebraic Identities and Trigonometric Substitutions309
7.5Approximating Definite Integrals317
7.6Approximation Errors and Simpson's Rule322
7.7Improper Integrals326
7.8Comparison of Improper Integrals334
8Using the Definite Integral345
8.1Areas and Volumes346
8.2Applications to Geometry352
8.3Density and Center of Mass360
8.4Applications to Physics368
8.5Applications to Economics377
8.6Distribution Functions383
8.7Probability, Mean, and Median390
9Series405
9.1Geometric Series406
9.2Convergence of Sequences and Series412
9.3Tests for Convergence417
9.4Power Series423
10Approximating Functions433
10.1Taylor Polynomials434
10.2Taylor Series441
10.3Finding and Using Taylor Series446
10.4The Error in Taylor Polynomial Approximations453
10.5Fourier Series457
11Differential Equations477
11.1What is a Differential Equation?478
11.2Slope Fields482
11.3Euler's Method488
11.4Separation of Variables492
11.5Growth and Decay497
11.6Applications and Modeling506
11.7Models of Population Growth514
11.8Systems of Differential Equations523
11.9Analyzing the Phase Plane532
11.10Second-Order Differential Equations: Oscillations537
11.11Linear Second-Order Differential Equations544
App. ARoots, Accuracy, and Bounds560
App. BPolar Coordinates568
App. CComplex Numbers570
App. DNewton's Method577
Ready Reference581
Answers to Odd Numbered Problems598
Index615

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