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ISBN13: 978-0961408824

ISBN10: 0961408820 Edition: 91

Copyright: 1991

Publisher: Wellesley-Cambridge Press

Published: 1991

International: No

ISBN10: 0961408820 Edition: 91

Copyright: 1991

Publisher: Wellesley-Cambridge Press

Published: 1991

International: No

Gilbert Strang's Calculus textbook is ideal both as a course companion and for self study. The author has a direct style. His book presents detailed and intensive explanations. Many diagrams and key examples are used to aid understanding, as well as the application of calculus to physics and engineering and economics. The text is well organized, and it covers single variable and multivariable calculus in depth. An instructor's manual and student guide are available online at http://ocw.mit.edu/ans7870/resources/Strang/strangtext.htm.

**1 Introduction to Calculus**

1.1 Velocity and Distance

1.2 Calculus Without Limits

1.3 The Velocity at an Instant

1.4 Circular Motion

1.5 A Review of Trigonometry

1.6 A Thousand Points of Light

1.7 Computing in Calculus

**2 Derivatives**

2.1 The Derivative of a Function

2.2 Powers and Polynomials

2.3 The Slope and the Tangent Line

2.4 Derivative of the Sine and Cosine

2.5 The Product and Quotient and Power Rules

2.6 Limits

2.7 Continuous Functions

**3 Applications of the Derivative**

3.1 Linear Approximation

3.2 Maximum and Minimum Problems

3.3 Second Derivatives: Minimum vs Maximum

3.4 Graphs

3.5 Ellipses, Parabolas and Hyperbolas

3.6 Iterations

3.7 Newton's Method and Chaos

3.8 The Mean Value Theorem and l'Hopital's Rule

**4 The Chain Rule**

4.1 Derivatives by the Chain Rule

4.2 Implicit Differentiation and Related Rates

4.3 Inverse Functions and Their Derivatives

4.4 Inverses of Trigonometric Functions

**5 Integrals**

5.1 The Idea of the Integral

5.2 Antiderivatives

5.3 Summation vs Integration

5.4 Indefinite Integrals and Substitutions

5.5 The Definite Integral

5.6 Properties of the Integral and the Average Value

5.7 The Fundamental Theorem

5.8 Numerical Integration

**6 Exponentials and Logarithms**

6.1 An Overview

6.2 The Exponential e^x

6.3 Growth and Decay in Science and Economics

6.4 Logarithms

6.5 Separable Equations Including the Logistic Equation

6.6 Powers Instead of Exponentials

6.7 Hyperbolic Functions

**7 Techniques of Integration**

7.1 Integration by Parts

7.2 Trigonometric Integrals

7.3 Trigonometric Substitutions

7.4 Partial Fractions

7.5 Improper Integrals

**8 Applications of the Integral**

8.1 Areas and Volumes by Slices

8.2 Length of a Plane Curve

8.3 Area of a Surface of Revolution

8.4 Probability and Calculus

8.5 Masses and Moments

8.6 Force, Work, and Energy

**9 Polar Coordinates and Complex Numbers**

9.1 Polar Coordinates

9.2 Polar Equations and Graphs

9.3 Slope, Length, and Area for Polar Curves

9.4 Complex Numbers

**10 Infinite Series**

10.1 The Geometric Series

10.2 Convergence Tests: Positive Series

10.3 Convergence Tests: All Series

10.4 Taylor Series for e^x, sin x, and cos x

10.5 Power Series

**11 Vectors and Matrices**

11.1 Vectors and Dot Products

11.2 Planes and Projections

11.3 Cross Products and Determinants

11.4 Matrices and Linear Equations

11.5 Linear Algebra in Three Dimensions

**12 Motion Along a Curve**

12.1 The Position Vector

12.2 Plane Motion: Projectiles and Cycloids

12.3 Tangent Vector and Normal Vector

12.4 Polar Coordinates and Planetary Motion

**13 Partial Derivatives**

13.1 Surfaces and Level Curves

13.2 Partial Derivatives

13.3 Tangent Planes and Linear Approximations

13.4 Directional Derivatives and Gradients

13.5 The Chain Rule

13.6 Maxima, Minima, and Saddle Points

13.7 Constraints and Lagrange Multipliers

**14 Multiple Integrals**

14.1 Double Integrals

14.2 Changing to Better Coordinates

14.3 Triple Integrals

14.4 Cylindrical and Spherical Coordinates

**15 Vector Calculus**

15.1 Vector Fields

15.2 Line Integrals

15.3 Green's Theorem

15.4 Surface Integrals

15.5 The Divergence Theorem

15.6 Stokes' Theorem and the Curl of F

**16 Mathematics After Calculus**

16.1 Linear Algebra

16.2 Differential Equations

16.3 Discrete Mathematics

Answers to Odd-Numbered Problems

Index

ISBN10: 0961408820 Edition: 91

Copyright: 1991

Publisher: Wellesley-Cambridge Press

Published: 1991

International: No

Gilbert Strang's Calculus textbook is ideal both as a course companion and for self study. The author has a direct style. His book presents detailed and intensive explanations. Many diagrams and key examples are used to aid understanding, as well as the application of calculus to physics and engineering and economics. The text is well organized, and it covers single variable and multivariable calculus in depth. An instructor's manual and student guide are available online at http://ocw.mit.edu/ans7870/resources/Strang/strangtext.htm.

Table of Contents

**1 Introduction to Calculus**

1.1 Velocity and Distance

1.2 Calculus Without Limits

1.3 The Velocity at an Instant

1.4 Circular Motion

1.5 A Review of Trigonometry

1.6 A Thousand Points of Light

1.7 Computing in Calculus

**2 Derivatives**

2.1 The Derivative of a Function

2.2 Powers and Polynomials

2.3 The Slope and the Tangent Line

2.4 Derivative of the Sine and Cosine

2.5 The Product and Quotient and Power Rules

2.6 Limits

2.7 Continuous Functions

**3 Applications of the Derivative**

3.1 Linear Approximation

3.2 Maximum and Minimum Problems

3.3 Second Derivatives: Minimum vs Maximum

3.4 Graphs

3.5 Ellipses, Parabolas and Hyperbolas

3.6 Iterations

3.7 Newton's Method and Chaos

3.8 The Mean Value Theorem and l'Hopital's Rule

**4 The Chain Rule**

4.1 Derivatives by the Chain Rule

4.2 Implicit Differentiation and Related Rates

4.3 Inverse Functions and Their Derivatives

4.4 Inverses of Trigonometric Functions

**5 Integrals**

5.1 The Idea of the Integral

5.2 Antiderivatives

5.3 Summation vs Integration

5.4 Indefinite Integrals and Substitutions

5.5 The Definite Integral

5.6 Properties of the Integral and the Average Value

5.7 The Fundamental Theorem

5.8 Numerical Integration

**6 Exponentials and Logarithms**

6.1 An Overview

6.2 The Exponential e^x

6.3 Growth and Decay in Science and Economics

6.4 Logarithms

6.5 Separable Equations Including the Logistic Equation

6.6 Powers Instead of Exponentials

6.7 Hyperbolic Functions

**7 Techniques of Integration**

7.1 Integration by Parts

7.2 Trigonometric Integrals

7.3 Trigonometric Substitutions

7.4 Partial Fractions

7.5 Improper Integrals

**8 Applications of the Integral**

8.1 Areas and Volumes by Slices

8.2 Length of a Plane Curve

8.3 Area of a Surface of Revolution

8.4 Probability and Calculus

8.5 Masses and Moments

8.6 Force, Work, and Energy

**9 Polar Coordinates and Complex Numbers**

9.1 Polar Coordinates

9.2 Polar Equations and Graphs

9.3 Slope, Length, and Area for Polar Curves

9.4 Complex Numbers

**10 Infinite Series**

10.1 The Geometric Series

10.2 Convergence Tests: Positive Series

10.3 Convergence Tests: All Series

10.4 Taylor Series for e^x, sin x, and cos x

10.5 Power Series

**11 Vectors and Matrices**

11.1 Vectors and Dot Products

11.2 Planes and Projections

11.3 Cross Products and Determinants

11.4 Matrices and Linear Equations

11.5 Linear Algebra in Three Dimensions

**12 Motion Along a Curve**

12.1 The Position Vector

12.2 Plane Motion: Projectiles and Cycloids

12.3 Tangent Vector and Normal Vector

12.4 Polar Coordinates and Planetary Motion

**13 Partial Derivatives**

13.1 Surfaces and Level Curves

13.2 Partial Derivatives

13.3 Tangent Planes and Linear Approximations

13.4 Directional Derivatives and Gradients

13.5 The Chain Rule

13.6 Maxima, Minima, and Saddle Points

13.7 Constraints and Lagrange Multipliers

**14 Multiple Integrals**

14.1 Double Integrals

14.2 Changing to Better Coordinates

14.3 Triple Integrals

14.4 Cylindrical and Spherical Coordinates

**15 Vector Calculus**

15.1 Vector Fields

15.2 Line Integrals

15.3 Green's Theorem

15.4 Surface Integrals

15.5 The Divergence Theorem

15.6 Stokes' Theorem and the Curl of F

**16 Mathematics After Calculus**

16.1 Linear Algebra

16.2 Differential Equations

16.3 Discrete Mathematics

Answers to Odd-Numbered Problems

Index

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