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by Jerrold E. Marsden and Anthony Tromba

Edition: 5TH 03Copyright: 2003

Publisher: W.H. Freeman

Published: 2003

International: No

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Now in its fifth edition, Vector Calculus helps students gain an intuitive and solid understanding of this important subject. The book's careful account is a contemporary balance between theory, application, and historical development, providing it's readers with an insight into how mathematics progresses and is in turn influenced by the natural world.

- Expanded historical discussion introduction precedes first chapter
- Expanded historical remarks throughout the text
- Revised presentation of Implicit Function Theorem--now more readable and accessible to students
- New section 7.7, "Application to Differential Geometry, Physics and Forms of Life"--with more on geometry and surface integrals
- Revised section 6.4, "Improper Integrals"
- 15% revised exercise material, including new and new graduated exercises
- Enhanced material on Maxwell's Equations in Chapter 8
- Optional Material moved to the Web site
- Improved readability and accessibility for students
- Completely revised, color art program

**Marsden, Jerrold E. : California Institute of Technology Tromba, Anthony : University of California, Santa Cruz**

**1. THE GEOMETRY OF EUCLIDEAN SPACE **

1.1 Vectors in Two- and Three-Dimensional Space

1.2 The Inner Product, Length, and Distance

1.3 Matrices, Determinants, and the Cross Product

1.4 Cylindrical and Spherical Coordinates

1.5 n-Dimensional Euclidean Space

2.1 The Geometry of Real-Valued Functions

2.2 Limits and Continuity

2.3 Differentiation

2.4 Introduction to Paths

2.5 Properties of the Derivative

2.6 Gradients and Directional Derivatives

3.1 Iterated Partial Derivatives

3.2 Taylor's Theorem

3.3 Extrema of Real-Valued Functions

3.4 Constrained Extrema and Lagrange Multipliers

3.5 The Implicit Function Theorem

4.1 Acceleration and Newton's Second Law

4.2 Arc Length

4.3 Vector Fields

4.4 Divergence and Curl

5.1 Introduction

5.2 The Double Integral Over a Rectangle

5.3 The Double Integral Over More General Regions

5.4 Changing the Order of Integration

5.5 The Triple Integral

6.1 The Geometry of Maps from R2 to R2

6.2 The Change of Variables Theorem

6.3 Applications of Double and Triple

6.4 Improper Integrals

7.1 The Path Integral

7.2 Line Integrals

7.3 Parametrized Surfaces

7.4 Area of a Surface

7.5 Integrals of Scalar Functions Over Surfaces

7.6 Surface Integrals of Vector Functions

7.7 Applications to Differential Geometry, Physics and Forms of Life

8.1 Green's Theorem

8.2 Stokes' Theorem

8.3 Conservative Fields

8.4 Gauss' Theorem

8.5 Applications to Physics, Engineering, and Differential Equations

8.6 Differential Forms

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Summary

Now in its fifth edition, Vector Calculus helps students gain an intuitive and solid understanding of this important subject. The book's careful account is a contemporary balance between theory, application, and historical development, providing it's readers with an insight into how mathematics progresses and is in turn influenced by the natural world.

- Expanded historical discussion introduction precedes first chapter
- Expanded historical remarks throughout the text
- Revised presentation of Implicit Function Theorem--now more readable and accessible to students
- New section 7.7, "Application to Differential Geometry, Physics and Forms of Life"--with more on geometry and surface integrals
- Revised section 6.4, "Improper Integrals"
- 15% revised exercise material, including new and new graduated exercises
- Enhanced material on Maxwell's Equations in Chapter 8
- Optional Material moved to the Web site
- Improved readability and accessibility for students
- Completely revised, color art program

Author Bio

**Marsden, Jerrold E. : California Institute of Technology Tromba, Anthony : University of California, Santa Cruz**

Table of Contents

**1. THE GEOMETRY OF EUCLIDEAN SPACE **

1.1 Vectors in Two- and Three-Dimensional Space

1.2 The Inner Product, Length, and Distance

1.3 Matrices, Determinants, and the Cross Product

1.4 Cylindrical and Spherical Coordinates

1.5 n-Dimensional Euclidean Space

2.1 The Geometry of Real-Valued Functions

2.2 Limits and Continuity

2.3 Differentiation

2.4 Introduction to Paths

2.5 Properties of the Derivative

2.6 Gradients and Directional Derivatives

3.1 Iterated Partial Derivatives

3.2 Taylor's Theorem

3.3 Extrema of Real-Valued Functions

3.4 Constrained Extrema and Lagrange Multipliers

3.5 The Implicit Function Theorem

4.1 Acceleration and Newton's Second Law

4.2 Arc Length

4.3 Vector Fields

4.4 Divergence and Curl

5.1 Introduction

5.2 The Double Integral Over a Rectangle

5.3 The Double Integral Over More General Regions

5.4 Changing the Order of Integration

5.5 The Triple Integral

6.1 The Geometry of Maps from R2 to R2

6.2 The Change of Variables Theorem

6.3 Applications of Double and Triple

6.4 Improper Integrals

7.1 The Path Integral

7.2 Line Integrals

7.3 Parametrized Surfaces

7.4 Area of a Surface

7.5 Integrals of Scalar Functions Over Surfaces

7.6 Surface Integrals of Vector Functions

7.7 Applications to Differential Geometry, Physics and Forms of Life

8.1 Green's Theorem

8.2 Stokes' Theorem

8.3 Conservative Fields

8.4 Gauss' Theorem

8.5 Applications to Physics, Engineering, and Differential Equations

8.6 Differential Forms

Publisher Info

Publisher: W.H. Freeman

Published: 2003

International: No

Published: 2003

International: No

Now in its fifth edition, Vector Calculus helps students gain an intuitive and solid understanding of this important subject. The book's careful account is a contemporary balance between theory, application, and historical development, providing it's readers with an insight into how mathematics progresses and is in turn influenced by the natural world.

- Expanded historical discussion introduction precedes first chapter
- Expanded historical remarks throughout the text
- Revised presentation of Implicit Function Theorem--now more readable and accessible to students
- New section 7.7, "Application to Differential Geometry, Physics and Forms of Life"--with more on geometry and surface integrals
- Revised section 6.4, "Improper Integrals"
- 15% revised exercise material, including new and new graduated exercises
- Enhanced material on Maxwell's Equations in Chapter 8
- Optional Material moved to the Web site
- Improved readability and accessibility for students
- Completely revised, color art program

Tromba, Anthony : University of California, Santa Cruz

**1. THE GEOMETRY OF EUCLIDEAN SPACE **

1.1 Vectors in Two- and Three-Dimensional Space

1.2 The Inner Product, Length, and Distance

1.3 Matrices, Determinants, and the Cross Product

1.4 Cylindrical and Spherical Coordinates

1.5 n-Dimensional Euclidean Space

2.1 The Geometry of Real-Valued Functions

2.2 Limits and Continuity

2.3 Differentiation

2.4 Introduction to Paths

2.5 Properties of the Derivative

2.6 Gradients and Directional Derivatives

3.1 Iterated Partial Derivatives

3.2 Taylor's Theorem

3.3 Extrema of Real-Valued Functions

3.4 Constrained Extrema and Lagrange Multipliers

3.5 The Implicit Function Theorem

4.1 Acceleration and Newton's Second Law

4.2 Arc Length

4.3 Vector Fields

4.4 Divergence and Curl

5.1 Introduction

5.2 The Double Integral Over a Rectangle

5.3 The Double Integral Over More General Regions

5.4 Changing the Order of Integration

5.5 The Triple Integral

6.1 The Geometry of Maps from R2 to R2

6.2 The Change of Variables Theorem

6.3 Applications of Double and Triple

6.4 Improper Integrals

7.1 The Path Integral

7.2 Line Integrals

7.3 Parametrized Surfaces

7.4 Area of a Surface

7.5 Integrals of Scalar Functions Over Surfaces

7.6 Surface Integrals of Vector Functions

7.7 Applications to Differential Geometry, Physics and Forms of Life

8.1 Green's Theorem

8.2 Stokes' Theorem

8.3 Conservative Fields

8.4 Gauss' Theorem

8.5 Applications to Physics, Engineering, and Differential Equations

8.6 Differential Forms