ISBN-10:
130527914X
ISBN-13:
9781305279148
Pub. Date:
05/08/2015
Publisher:
Cengage Learning
Study Guide for Stewart's Single Variable Calculus: Early Transcendentals, 8th / Edition 8

Study Guide for Stewart's Single Variable Calculus: Early Transcendentals, 8th / Edition 8

by James Stewart, Richard St. Andre

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Product Details

ISBN-13: 9781305279148
Publisher: Cengage Learning
Publication date: 05/08/2015
Edition description: Study Guid
Pages: 512
Sales rank: 588,510
Product dimensions: 7.20(w) x 9.00(h) x 1.00(d)

About the Author

The late James Stewart received his M.S. from Stanford University and his Ph.D. from the University of Toronto. He did research at the University of London and was influenced by the famous mathematician George Polya at Stanford University. Stewart was most recently Professor of Mathematics at McMaster University, and his research field was harmonic analysis. Stewart was the author of a best-selling calculus textbook series published by Cengage Learning, including CALCULUS, CALCULUS: EARLY TRANSCENDENTALS, and CALCULUS: CONCEPTS AND CONTEXTS, as well as a series of precalculus texts.


Richard St. Andre is Associate Dean of the College of Science and Technology at Central Michigan University. Dr. St. Andre's teaching interests are quite diverse with a particular interest in lower division service courses in both mathematics and computer science.

Table of Contents

1 Functions and Models

1.1 Four Ways to Represent a Function 1

1.2 Mathematical Models 11

1.3 New Functions from Old Functions 17

1.4 Exponential Functions 22

1.5 Inverse Functions and Logarithms 26

Practice Test for Chapter 1 36

2 Limits and Derivatives

2.1 The Tangent and Velocity Problems 41

2.2 The Limit of a Function 45

2.3 Calculating Limits Using Limit Laws 56

2.4 The Precise Definition of a Limit 64

2.5 Continuity 71

2.6 Limits at Infinity; Horizontal Asymptotes 77

2.7 Derivatives and Rates of Change 83

2.8 The Derivative as a Function 91

Practice Test for Chapter 2 100

3 Derivatives

3.1 Derivatives of Polynomials and Exponential Functions 108

3.2 The Product and Quotient Rules 112

3.3 Derivatives of Trigonometric Functions 114

3.4 The Chain Rule 117

3.5 Implicit Differentiation 121

3.6 Derivatives of Logarithmic Functions 126

3.7 Rates of Change in the Natural and Social Sciences 129

3.8 Exponential Growth and Decay 131

3.9 Related Rates 135

3.10 Linear Approximations and Differentials 140

3.11 Hyperbolic Functions 144

Practice Test for Chapter 3 149

4 Applications of Differentiation

4.1 Maximum and Minimum Values 156

4.2 The Mean Value Theorem 165

4.3 How Derivatives Affect the Shape of a Graph 170

4.4 Indeterminate Forms and l'Hospital's Rule 181

4.5 Summary of Curve Sketching 186

4.6 Graphing with Calculus and Calculators 192

4.7 Optimization Problems 194

4.8 Newton's Method 199

4.9 Antiderivatives 202

Practice Test for Chapter 4 205

5 Integrals

5.1 Areas and Distances 212

5.2 The Definite Integral 218

5.3 The Fundamental Theorem of Calculus 225

5.4 Indefinite Integrals and the Net Change Theorem 228

5.5 The Substitution Rule 232

Practice Test for Chapter 5 239

6 Applications of Integration

6.1 Areas between Curves 243

6.2 Volumes 253

6.3 Volumes by Cylindrical Shells 258

6.4 Work 261

6.5 Average Value of a Function 264

Practice Test for Chapter 6 267

7 Techniques of Integration

7.1 Integration by Parts 271

7.2 Trigonometric Integrals 274

73 Trigonometric Substitution 281

7.4 Integration of Rational Functions by Partial Fractious 285

7.5 Strategy for Integration 292

7.6 Using Tables of Integrals and Computer Algebra Systems 296

7.7 Approximate Integration 299

7.8 Improper Integrals 306

Practice Test for Chapter 7 312

8 Further Applications of Integration

8.1 Arc Length 317

8.2 Area of a Surface of Revolution 322

8.3 Applications to Physics and Engineering 325

8.4 Applications to Economics and Biology 330

8.5 Probability 332

Practice Test for Chapter 8 337

9 Differential Equations

9.1 Modeling with Differential Equations 341

9.2 Direction Fields and Euler's Method 344

9.3 Separable Equations 348

9.4 Models for Population Growth 351

9.5 Linear Equations 355

9.6 Predator-Prey Systems 357

Practice Test for Chapter 9 360

10 Parametric Equations and Polar Coordinates

10.1 Curves Defined by Parametric Equations 364

10.2 Calculus with Parametric Curves 371

10.3 Polar Coordinates 378

10.4 Areas and Lengths in Polar Coordinates 386

10.5 Conic Sections 389

10.6 Conic Sections in Polar Coordinates 393

Practice Test for Chapter 10 397

11 Infinite Sequences and Series

11.1 Sequences 402

11.2 Series 409

11.3 The Integral Test and Estimates of Sums 414

11.4 The Comparison Tests 419

11.5 Alternating Series 423

11.6 Absolute Convergence and the Ratio and Root Tests 427

11.7 Strategy for Testing Series 432

11.8 Power Series 435

11.9 Representations of Functions as Power Series 439

11.10 Taylor and Maclaurin Series 445

11.11 Applications of Taylor Polynomials 460

Practice Test for Chapter 11 465

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