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Vector Calculus

Vector Calculus - 4th edition

ISBN13: 978-0716724322

Cover of Vector Calculus 4TH 96 (ISBN 978-0716724322)
ISBN13: 978-0716724322
ISBN10: 0716724324
Cover type:
Edition/Copyright: 4TH 96
Publisher: W.H. Freeman
Published: 1996
International: No

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Vector Calculus - 4TH 96 edition

ISBN13: 978-0716724322

Jerrold E. Marsden and Anthony J. Tromba

ISBN13: 978-0716724322
ISBN10: 0716724324
Cover type:
Edition/Copyright: 4TH 96
Publisher: W.H. Freeman

Published: 1996
International: No
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

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