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# Calculus : Concepts and Contexts

**by**Stewart,James

2nd

### 9780534437367

0534437362

Hardcover

12/13/2000

Brooks Cole

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## Summary

James Stewart's well-received CALCULUS: CONCEPTS AND CONTEXTS, Second Edition follows in the path of the other best-selling books by this remarkable author. The First Edition of this book was highly successful because it reconciled two schools of thought: it skillfully merged the best of traditional calculus with the best of the reform movement. This new edition continues to offer the balanced approach along with Stewart's hallmark features: meticulous accuracy, patient explanations, and carefully graded problems. The content has been refined and the examples and exercises have been updated. In addition, CALCULUS: CONCEPTS AND CONTEXTS, Second Edition now includes a free CD-ROM for students that contains animations, activities, and homework hints. The book integrates the use of the CD throughout by using icons that show students when to use the CD to deepen their understanding of a difficult concept. In CALCULUS: CONCEPTS AND CONTEXTS, this well respected author emphasizes conceptual understanding - motivating students with real world applications and stressing the Rule of Four in numerical, visual, algebraic, and verbal interpretations. All concepts are presented in the classic Stewart style: with simplicity, character, and attention to detail. In addition to his clear exposition, Stewart also creates well thought-out problems and exercises. The definitions are precise and the problems create an ideal balance between conceptual understanding and algebraic skills.

## Table of Contents

1. FUNCTIONS AND MODELS | |

Four Ways to Represent a Function | |

Mathematical Models | |

New Functions from Old Functions | |

Graphing Calculators and Computers | |

Exponential Functions | |

Inverse Functions and Logarithms | |

Parametric Curves | |

Review | |

Principles of Problem Solving | |

2. LIMITS AND DERIVATIVES | |

The Tangent and Velocity Problems | |

The Limit of a Function | |

Calculating Limits Using the Limit Laws | |

Continuity | |

Limits Involving Infinity | |

Tangents, Velocities, and Other Rates of Change | |

Derivatives | |

The Derivative as a Function | |

Linear Approximations | |

What does f' say about f? | |

Review | |

Focus on Problem Solving | |

3. DIFFERENTIATION RULES | |

Derivatives of Polynomials and Exponential Functions | |

The Product and Quotient Rules | |

Rates of Change in the Natural and Social Sciences | |

Derivatives of Trigonometric Functions | |

The Chain Rule | |

Implicit Differentiation | |

Derivatives of Logarithmic Functions | |

Linear Approximations and Differentials | |

Review | |

Focus on Problem Solving | |

4. APPLICATIONS OF DIFFERENTIATION | |

Related Rates | |

Maximum and Minimum Values | |

Derivatives and the Shapes of Curves | |

Graphing with Calculus and Calculators | |

Indeterminate Forms and l'Hospital's Rule | |

Optimization Problems | |

Applications to Economics | |

Newton's Method | |

Antiderivatives | |

Review | |

Focus on Problem Solving | |

5. INTEGRALS | |

Areas and Distances | |

The Definite Integral | |

Evaluating Definite Integrals | |

The Fundamental Theorem of Calculus | |

The Substitution Rule | |

Integration by Parts | |

Additional Techniques of Integration | |

Integration Using Tables and Computer Algebra Systems | |

Approximate Integration | |

Improper Integrals | |

Review | |

Focus on Problem Solving | |

6. APPLICATIONS OF INTEGRATION | |

More about Areas | |

Volumes | |

Arc Length | |

Average Value of a Function | |

Applications to Physics and Engineering | |

Applications to Economics and Biology | |

Probability | |

Review | |

Focus on Problem Solving | |

7. DIFFERENTIAL EQUATIONS | |

Modeling with Differential Equations | |

Direction Fields and Euler's Method | |

Separable Equations | |

Exponential Growth and Decay | |

The Logistic Equation | |

Predator-Prey Systems | |

Review | |

Focus on Problem Solving | |

8. INFINITE SEQUENCES AND SERIES | |

Sequences | |

Series | |

The Integral and Comparison Tests; Estimating Sums | |

Other Convergence Tests | |

Power Series | |

Representation of Functions as Power Series | |

Taylor and Maclaurin Series | |

The Binomial Series | |

Applications of Taylor Polynomials | |

Using Series to Solve Differential Equations | |

Review | |

Focus on Problem Solving | |

9. VECTORS AND THE GEOMETRY OF SPACE | |

Three Dimensional Coordinate Systems | |

Vectors | |

The Dot Product | |

The Cross Product | |

Equations of Lines and Planes | |

Functions and Surfaces | |

Cylindrical and Spherical Coordinates | |

Review | |

Focus on Problem Solving | |

10. VECTOR FUNCTIONS | |

Vector Functions and Space Curves | |

Derivatives and Integrals of Vector Functions | |

Arc Length and Curvature | |

Motion in Space | |

Parametric Surfaces | |

Review | |

Focus on Problem Solving | |

11. PARTIAL DERIVATIVES | |

Functions of Several Variables | |

Limits and Continuity | |

Partial Derivatives | |

Tangent Planes and Linear Approximations | |

The Chain Rule | |

Directional Derivatives and the Gradient Vector | |

Maximum and Minimum Values | |

Lagrange Multipliers | |

Review | |

Focus on Problem Solving | |

12. MULTIPLE INTEGRALS | |

Double Integrals over Rectangles | |

Integrated Integrals | |

Double Integrals over General Regions | |

Double Integrals in Polar Coordinates | |

Applications of Double Integrals | |

Surface Area | |

Triple Integrals | |

Triple Integrals in Cylindrical and Spherical Coordinates | |

Change of Variables in Multiple Integrals | |

Review | |

Focus on Problem Solving | |

13. VECTOR CALCULUS | |

Vector Fields | |

Line Integrals | |

The Fundamental Theorem for Line Integrals | |

Green's Theorem | |

Curl and Divergence | |

Surface Integrals | |

Stokes' Theorem | |

The Divergence Theorem | |

Summary | |

Review | |

Focus on Problem Solving | |

Appendix A: Intervals, Inequalities, And Absolute Values | |

Appendix B: Coordinate Geometry | |

Appendix C: Trigonometry | |

Appendix D: Precise Definitions Of Limits | |

Appendix E: A Few Proofs | |

Appendix F: Sigma Notation | |

Appendix G: Integration Of Rational Functions By Partial Fractions | |

Appendix H: Polar Coordinates | |

Appendix I: Complex Numbers | |

Appendix J: Answers To Odd-Numbered Exercises | |

Index |