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by Jerrold E. Marsden and Anthony J. Tromba

Edition: 4TH 96Copyright: 1996

Publisher: W.H. Freeman

Published: 1996

International: No

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Intended for one-semester courses in the calculus of functions of several variables and vector analysis, Vector Calculus is widely used at the sophomore and junior level. Acclaimed authors Jerrold Marsden and Anthony Tromba help students foster computational skills and intuitive understanding with a careful balance of theory, applications, optional materials, and historical notes.

- Sophisticated presentation--concrete, student-oriented, yet rigorous
- Many applications, especially from fluid mechanics, gravitation, electromagnetics theory, and economics
- Optional advanced sections and exercises

**Marsden, Jerrold E. : California Institute of Technology**

**Tromba, Anthony : University of California-Santa Cruz**

**1. The Geometry of Euclidean Space**

Vectors in Two- and Three-Dimensional Space

The Inner Product, Length, and Distance

Matrices, Determinants, and the Cross Product

Cylindrical and Spherical Coordinates

n-Dimensional Euclidean Space

**2. Differentiation Space**

The Geometry of Real-Valued Functions

Limits and Continuity

Differentiation

Introduction to Paths

Properties of the Derivative

Gradients and Directional Derivatives

Some Technical Differentiation Theorems

**3. Higher-Order Derivatives: Maxima and Minima**

Taylor's Theorem

Extrema of Real-Valued Functions

Constrained Extrema and Lagrange Multipliers

The Implicit Function Theorem

Some Applications

**4. Vector-Valued Functions**

Acceleration and Newton's Second Law

Arc Length

Vector Fields

Divergence and Curl

**5. Double and Triple Integrals**

Introduction

The Double Integral Over a Rectangle

The Double Integral Over More General Regions

Changing the Order of Integration

Some Technical Integration Theorems

The Triple Integral

**6. The Change of Variables Formula and Applications of Integration**

The Geometry of Maps from R2 to R2

The Change of Variables Theorem

Applications of Double and Triple

Integrals

Improper Integrals

**7. Integrals Over Paths and Surfaces**

The Path Integral

Line Integrals

Parametrized Surfaces

Area of a Surface

Integrals of Scalar Functions Over Surfaces

Surface Integrals of Vector Functions

**8. The Integral Theorems of Vector Analysis**

Green's Theorem

Stokes' Theorem

Conservative Fields

Gauss' Theorem

Applications to Physics, Engineering, and Differential Equations

Differential Forms

Answers to Odd-Numbered Exercises

Index

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Summary

Intended for one-semester courses in the calculus of functions of several variables and vector analysis, Vector Calculus is widely used at the sophomore and junior level. Acclaimed authors Jerrold Marsden and Anthony Tromba help students foster computational skills and intuitive understanding with a careful balance of theory, applications, optional materials, and historical notes.

- Sophisticated presentation--concrete, student-oriented, yet rigorous
- Many applications, especially from fluid mechanics, gravitation, electromagnetics theory, and economics
- Optional advanced sections and exercises

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**

Vectors in Two- and Three-Dimensional Space

The Inner Product, Length, and Distance

Matrices, Determinants, and the Cross Product

Cylindrical and Spherical Coordinates

n-Dimensional Euclidean Space

**2. Differentiation Space**

The Geometry of Real-Valued Functions

Limits and Continuity

Differentiation

Introduction to Paths

Properties of the Derivative

Gradients and Directional Derivatives

Some Technical Differentiation Theorems

**3. Higher-Order Derivatives: Maxima and Minima**

Taylor's Theorem

Extrema of Real-Valued Functions

Constrained Extrema and Lagrange Multipliers

The Implicit Function Theorem

Some Applications

**4. Vector-Valued Functions**

Acceleration and Newton's Second Law

Arc Length

Vector Fields

Divergence and Curl

**5. Double and Triple Integrals**

Introduction

The Double Integral Over a Rectangle

The Double Integral Over More General Regions

Changing the Order of Integration

Some Technical Integration Theorems

The Triple Integral

**6. The Change of Variables Formula and Applications of Integration**

The Geometry of Maps from R2 to R2

The Change of Variables Theorem

Applications of Double and Triple

Integrals

Improper Integrals

**7. Integrals Over Paths and Surfaces**

The Path Integral

Line Integrals

Parametrized Surfaces

Area of a Surface

Integrals of Scalar Functions Over Surfaces

Surface Integrals of Vector Functions

**8. The Integral Theorems of Vector Analysis**

Green's Theorem

Stokes' Theorem

Conservative Fields

Gauss' Theorem

Applications to Physics, Engineering, and Differential Equations

Differential Forms

Answers to Odd-Numbered Exercises

Index

Publisher Info

Publisher: W.H. Freeman

Published: 1996

International: No

Published: 1996

International: No

Intended for one-semester courses in the calculus of functions of several variables and vector analysis, Vector Calculus is widely used at the sophomore and junior level. Acclaimed authors Jerrold Marsden and Anthony Tromba help students foster computational skills and intuitive understanding with a careful balance of theory, applications, optional materials, and historical notes.

- Sophisticated presentation--concrete, student-oriented, yet rigorous
- Many applications, especially from fluid mechanics, gravitation, electromagnetics theory, and economics
- Optional advanced sections and exercises

**Marsden, Jerrold E. : California Institute of Technology**

**Tromba, Anthony : University of California-Santa Cruz**

**1. The Geometry of Euclidean Space**

Vectors in Two- and Three-Dimensional Space

The Inner Product, Length, and Distance

Matrices, Determinants, and the Cross Product

Cylindrical and Spherical Coordinates

n-Dimensional Euclidean Space

**2. Differentiation Space**

The Geometry of Real-Valued Functions

Limits and Continuity

Differentiation

Introduction to Paths

Properties of the Derivative

Gradients and Directional Derivatives

Some Technical Differentiation Theorems

**3. Higher-Order Derivatives: Maxima and Minima**

Taylor's Theorem

Extrema of Real-Valued Functions

Constrained Extrema and Lagrange Multipliers

The Implicit Function Theorem

Some Applications

**4. Vector-Valued Functions**

Acceleration and Newton's Second Law

Arc Length

Vector Fields

Divergence and Curl

**5. Double and Triple Integrals**

Introduction

The Double Integral Over a Rectangle

The Double Integral Over More General Regions

Changing the Order of Integration

Some Technical Integration Theorems

The Triple Integral

**6. The Change of Variables Formula and Applications of Integration**

The Geometry of Maps from R2 to R2

The Change of Variables Theorem

Applications of Double and Triple

Integrals

Improper Integrals

**7. Integrals Over Paths and Surfaces**

The Path Integral

Line Integrals

Parametrized Surfaces

Area of a Surface

Integrals of Scalar Functions Over Surfaces

Surface Integrals of Vector Functions

**8. The Integral Theorems of Vector Analysis**

Green's Theorem

Stokes' Theorem

Conservative Fields

Gauss' Theorem

Applications to Physics, Engineering, and Differential Equations

Differential Forms

Answers to Odd-Numbered Exercises

Index