ISBN13: 978-0395869741

ISBN10: 0395869749

Cover type:

Edition/Copyright: 6TH 98

Publisher: Houghton Mifflin Harcourt

Published: 1998

International: No

ISBN10: 0395869749

Cover type:

Edition/Copyright: 6TH 98

Publisher: Houghton Mifflin Harcourt

Published: 1998

International: No

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This innovative text continues to offer a balanced approach that combines the theoretical instruction of calculus with the best aspects of reform, including creative teaching and learning techniques such as the integration of technology, the use of real data, real-life applications, and mathematical models.mensional graphs, and additional explorations and simulations.

**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

**10. Vectors and the Geometry of Space**

1. Vectors in the Plane

2. Space Coordinates and Vectors in Space

3. The Dot Product of Two Vectors

4. The Cross Product of Two Vectors in Space

5. Lines and Planes in Space

6. Surfaces in Space

7. Cylindrical and Spherical Coordinates

**11. Vector-Valued Functions**

1. Vector-Valued Functions

2. Differentiation and Integration of Vector-Valued Functions

3. Velocity and Acceleration

4. Tangent Vectors and Normal Vectors

5. Arc Length and Curvature

**12. Functions of Several Variables**

1. Introduction to Functions of Several Variables

2. Limits and Continuity

3. Partial Derivatives

4. Differentials

5. Chain Rules for Functions of Several Variables

6. Directional Derivatives and Gradients

7. Tangent Planes and Normal Lines

8. Extrema of Functions of Two Variables

9. Applications of Extrema of Functions of Two Variables

10. Lagrange Multipliers

**13. Multiple Integration**

1. Iterated Integrals and Area in the Plane

2. Double Integrals and Volume

3. Change of Variables: Polar Coordinates

4. Center of Mass and Moments of Inertia

5. Surface Area

6. Triple Integrals and Applications

7. Triple Integrals in Cylindrical and Spherical Coordinates

8. Change of Variables: Jacobians

**14. Vector Analysis**

1. Vector Fields

2. Line Integrals

3. Conservative Vector Fields and Independence of Path

4. Green's Theorem

5. Parametric Surfaces

6. Surface Integrals

7. Divergence Theorem

8. Stokes's Theorem

**15. Differential Equations**

1. Exact First-Order Equations

2. First-Order Linear Differential Equations

3. Second-Order Homogeneous Linear Equations

4. Second-Order Nonhomogeneous Linear Equations

5. Series Solutions of Differential Equations

**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**

Ron Larson, Robert P. Hostetler and Bruce H. Edwards

ISBN13: 978-0395869741ISBN10: 0395869749

Cover type:

Edition/Copyright: 6TH 98

Publisher: Houghton Mifflin Harcourt

Published: 1998

International: No

This innovative text continues to offer a balanced approach that combines the theoretical instruction of calculus with the best aspects of reform, including creative teaching and learning techniques such as the integration of technology, the use of real data, real-life applications, and mathematical models.mensional graphs, and additional explorations and simulations.

Table of Contents

**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

**10. Vectors and the Geometry of Space**

1. Vectors in the Plane

2. Space Coordinates and Vectors in Space

3. The Dot Product of Two Vectors

4. The Cross Product of Two Vectors in Space

5. Lines and Planes in Space

6. Surfaces in Space

7. Cylindrical and Spherical Coordinates

**11. Vector-Valued Functions**

1. Vector-Valued Functions

2. Differentiation and Integration of Vector-Valued Functions

3. Velocity and Acceleration

4. Tangent Vectors and Normal Vectors

5. Arc Length and Curvature

**12. Functions of Several Variables**

1. Introduction to Functions of Several Variables

2. Limits and Continuity

3. Partial Derivatives

4. Differentials

5. Chain Rules for Functions of Several Variables

6. Directional Derivatives and Gradients

7. Tangent Planes and Normal Lines

8. Extrema of Functions of Two Variables

9. Applications of Extrema of Functions of Two Variables

10. Lagrange Multipliers

**13. Multiple Integration**

1. Iterated Integrals and Area in the Plane

2. Double Integrals and Volume

3. Change of Variables: Polar Coordinates

4. Center of Mass and Moments of Inertia

5. Surface Area

6. Triple Integrals and Applications

7. Triple Integrals in Cylindrical and Spherical Coordinates

8. Change of Variables: Jacobians

**14. Vector Analysis**

1. Vector Fields

2. Line Integrals

3. Conservative Vector Fields and Independence of Path

4. Green's Theorem

5. Parametric Surfaces

6. Surface Integrals

7. Divergence Theorem

8. Stokes's Theorem

**15. Differential Equations**

1. Exact First-Order Equations

2. First-Order Linear Differential Equations

3. Second-Order Homogeneous Linear Equations

4. Second-Order Nonhomogeneous Linear Equations

5. Series Solutions of Differential Equations

**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**

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