Calculus: Single Variable / Edition 5

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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.
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Editorial Reviews

Booknews
Calculus can be taught as nothing but rules and procedures--losing sight of both the mathematics and its inherent practical value. In 1989, the Calculus Consortium based at Harvard was formed to create a completely new calculus curriculum. A part of their endeavor is this textbook, which presents a radically different approach to the teaching and learning of the subject. The two guiding principles: 1) every topic should be presented geometrically, numerically, and algebraically; and 2) formal definitions and procedures evolve from the investigation of practical problems (the way of Archimedes). Annotation c. Book News, Inc., Portland, OR (booknews.com)
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Product Details

  • ISBN-13: 9780470089156
  • Publisher: Wiley
  • Publication date: 12/3/2008
  • Edition description: Older Edition
  • Edition number: 5
  • Pages: 736
  • Sales rank: 245,571
  • Product dimensions: 8.50 (w) x 10.40 (h) x 1.20 (d)

Table of Contents

1 A Library of Functions 1
1.1 Functions and Change 2
1.2 Exponential Functions 9
1.3 New Functions from Old 17
1.4 Logarithmic Functions 23
1.5 Trigonometric Functions 29
1.6 Powers, Polynomials, and Rational Functions 37
1.7 Introduction to Continuity 45
2 Key Concept: The Derivative 55
2.1 How Do We Measure Speed? 56
2.2 Limits 62
2.3 The Derivative at a Point 70
2.4 The Derivative Function 78
2.5 Interpretations of the Derivative 85
2.6 The Second Derivative 89
2.7 Continuity and Differentiability 95
3 Short-Cuts to Differentiation 105
3.1 Powers and Polynomials 106
3.2 The Exponential Function 113
3.3 The Product and Quotient Rules 118
3.4 The Chain Rule 123
3.5 The Trigonometric Functions 128
3.6 Applications of the Chain Rule 133
3.7 Implicit Functions 138
3.8 Parametric Equations 141
3.9 Linear Approximation and the Derivative 150
3.10 Using Local Linearity to Find Limits 154
4 Using the Derivative 165
4.1 Using First and Second Derivatives 166
4.2 Families of Curves 176
4.3 Optimization 180
4.4 Applications to Marginality 189
4.5 Optimization and Modeling 196
4.6 Hyperbolic Functions 203
4.7 Theorems about Continuous and Differentiable Functions 207
5 Key Concept: The Definite Integral 221
5.1 How Do We Measure Distance Traveled? 222
5.2 The Definite Integral 229
5.3 Interpretations of the Definite Integral 236
5.4 Theorems about Definite Integrals 244
6 Constructing Antiderivatives 261
6.1 Antiderivatives Graphically and Numerically 262
6.2 Constructing Antiderivatives Analytically 268
6.3 Differential Equations 273
6.4 Second Fundamental Theorem of Calculus 278
6.5 The Equations of Motion 282
7 Integration 289
7.1 Integration by Substitution 290
7.2 Integration by Parts 298
7.3 Tables of Integrals 304
7.4 Algebraic Identities and Trigonometric Substitutions 309
7.5 Approximating Definite Integrals 317
7.6 Approximation Errors and Simpson's Rule 322
7.7 Improper Integrals 326
7.8 Comparison of Improper Integrals 334
8 Using the Definite Integral 345
8.1 Areas and Volumes 346
8.2 Applications to Geometry 352
8.3 Density and Center of Mass 360
8.4 Applications to Physics 368
8.5 Applications to Economics 377
8.6 Distribution Functions 383
8.7 Probability, Mean, and Median 390
9 Series 405
9.1 Geometric Series 406
9.2 Convergence of Sequences and Series 412
9.3 Tests for Convergence 417
9.4 Power Series 423
10 Approximating Functions 433
10.1 Taylor Polynomials 434
10.2 Taylor Series 441
10.3 Finding and Using Taylor Series 446
10.4 The Error in Taylor Polynomial Approximations 453
10.5 Fourier Series 457
11 Differential Equations 477
11.1 What is a Differential Equation? 478
11.2 Slope Fields 482
11.3 Euler's Method 488
11.4 Separation of Variables 492
11.5 Growth and Decay 497
11.6 Applications and Modeling 506
11.7 Models of Population Growth 514
11.8 Systems of Differential Equations 523
11.9 Analyzing the Phase Plane 532
11.10 Second-Order Differential Equations: Oscillations 537
11.11 Linear Second-Order Differential Equations 544
App. A Roots, Accuracy, and Bounds 560
App. B Polar Coordinates 568
App. C Complex Numbers 570
App. D Newton's Method 577
Ready Reference 581
Answers to Odd Numbered Problems 598
Index 615
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