# Calculus: Single Variable / Edition 5

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:
9780470089156
Publisher:
Wiley
Publication date:
12/03/2008
Edition description:
Older Edition
Pages:
736
Product dimensions:
8.50(w) x 10.40(h) x 1.20(d)

## Related Subjects

 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