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Calculus of a Single Variable

Calculus of a Single Variable - 6th edition

Calculus of a Single Variable - 6th edition

ISBN13: 9780395885789

ISBN10: 0395885787

Calculus of a Single Variable by Ron Larson, Robert P. Hostetler and Bruce H. Edwards - ISBN 9780395885789
Edition: 6TH 98
Copyright: 1998
Publisher: Houghton Mifflin Harcourt
International: No
Calculus of a Single Variable by Ron Larson, Robert P. Hostetler and Bruce H. Edwards - ISBN 9780395885789

ISBN13: 9780395885789

ISBN10: 0395885787

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For full description, see Larson et al., Calculus with Analytic Geometry, 6/e.

Table of Contents

Table of Contents

Note: Each chapter contains review exercises.

P. Preparation for Calculus

1. Graphs and Models

2. Linear Models and Rates of Change

3. Functions and their Graphs

4. Fitting Models to Data

1. Limits and Their Properties

1. A Preview of Calculus

2. Finding Limits Graphically and Numerically

3. Evaluating Limits Analytically

4. Continuity and One-Sided Limits

5. Infinite Limits

2. Differentiation

1. The Derivative and the Tangent Line Problem

2. Basic Differentiation Rules and Rates of Change

3. The Product and Quotient Rules and Higher-Order Derivatives

4. The Chain Rule

5. Implicit Differentiation

6. Related Rates

3. Applications of Differentiation

1. Extrema on an Interval

2. Rolle's Theorem and the Mean Value Theorem

3. Increasing and Decreasing Functions and the First Derivative Test

4. Concavity and the Second Derivative Test

5. Limits at Infinity

6. A Summary of Curve Sketching

7. Optimization Problems

8. Newton's Method

9. Differentials

10. Business and Economics Applications

4. Integration

1. Antiderivatives and Indefinite Integration

2. Area

3. Riemann Sums and Definite Integrals

4. The Fundamental Theorem of Calculus

5. Integration by Substitution

6. Numerical Integration

5. Logarithmic, Exponential, and Other Transcendental Functions

1. The Natural Logarithmic Function and Differentiation

2. The Natural Logarithmic Function and Integration

3. Inverse Functions

4. Exponential Functions: Differentiation and Integration

5. Bases Other than e and Applications

6. Differential Equations: Growth and Decay

7. Differential Equations: Separation of Variables

8. Inverse Trigonometric Functions and Differentiation

9. Inverse Trigonometric Functions and Integration

10. Hyperbolic Functions

6. Applications of Integration

1. Area of a Region Between Two Curves

2. Volume: The Disc Method

3. Volume: The Shell Method

4. Arc Length and Surfaces of Revolution

5. Work

6. Moments, Centers of Mass, and Centroids

7. Fluid Pressure and Fluid Force

7. Integration Techniques, L'Hopital's Rule, and Improper Integrals

1. Basic Integration Rules

2. Integration by Parts

3. Trigonometric Integrals

4. Trigonometric Substitution

5. Partial Fractions

6. Integration by Tables and Other Integration Techniques

7. Indeterminate Forms and L'Hopital's Rule

8. Improper Integrals

8. Infinite Series

1. Sequences

2. Series and Convergence

3. The Integral Test and p-Series

4. Comparisons of Series

5. Alternating Series

6. The Ratio and Root Tests

7. Taylor Polynomials and Approximations

8. Power Series

9. Representation of Functions by Power Series

10. Taylor and Maclaurin Series

9. Conics, Parametric Equations, and Polar Coordinates

1. Conics and Calculus

2. Plane Curves and Parametric Equations

3. Parametric Equations and Calculus

4. Polar Coordinates and Polar Graphs

5. Area and Arc Length in Polar Coordinates

6. Polar Equations of Conics and Kepler's Laws

  • Appendix A Precalculus Review
  • 1. Real Numbers and the Real Line
  • 2. The Cartesian Plane
  • 3. Review of Trigonometric Functions
  • Appendix B Proofs of Selected Theorems
  • Appendix C Basic Differentiation Rules for Elementary Functions
  • Appendix D Integration Tables
  • Appendix E Rotation and the General Second-Degree Equation
  • Appendix F Complex Numbers
  • Answers to Odd-Numbered Exercises
  • Index