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.
Author(s): Jerrold E. Marsden, Anthony Tromba
Edition: 6
Publisher: W. H. Freeman
Year: 2011
Language: English
Commentary: dcisneros
Pages: 576
City: New York
Front Cover
Title Page
Copyright Page
Opening Quotes
Jerrold E. Marsden, 1942-2010
Preface
Historical Introduction: A Brief Account
Prerequisites and Notation
CONTENTS (with direct page links)
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
Review Exercises for Chapter 1
2. Differentiation
2.1 The Geometry of Real-Valued Functions
2.2 Limits and Continuity
2.3 Differentiation
2.4 Introduction to Paths and Curves
2.5 Properties of the Derivative
2.6 Gradients and Directional Derivatives
Review Exercises for Chapter 2
3. Higher-Order Derivatives: Maxima and Minima
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 [Optional]
Review Exercises for Chapter 3
4. Vector-Valued Functions
4.1 Acceleration and Newton’s Second Law
4.2 Arc Length
4.3 Vector Fields
4.4 Divergence and Curl
Review Exercises for Chapter 4
5. Double and Triple Integrals
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
Review Exercises for Chapter 5
6. The Change of Variables Formula and Applications of Integration
6.1 The Geometry of Maps from R2 to R2
6.2 The Change of Variables Theorem
6.3 Applications
6.4 Improper Integrals [Optional]
Review Exercises for Chapter 6
7. Integrals Over Paths and Surfaces
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 Fields
7.7 Applications to Differential Geometry, Physics, and Forms of Life
Review Exercises for Chapter 7
8. The Integral Theorems of Vector Analysis
8.1 Green’s Theorem
8.2 Stokes’ Theorem
8.3 Conservative Fields
8.4 Gauss’ Theorem
8.5 Differential Forms
Review Exercises for Chapter 8
ANSWERS to Odd-Numbered Exercises
ch01
1.1
1.2
1.3
1.4
1.5
review
ch02
2.1
2.2
2.3 - 2.4
2.5
2.6
review
ch03
3.1
3.2
3.3
3.4
3.5
review
ch04
4.1 - 4.2
4.3
4.4
review
ch05
5.1 - 5.2
5.3
5.4
5.5
review
ch06
6.1
6.2 - 6.3
6.4
review
ch07
7.1
7.2
7.3
7.4 - 7.5
7.6
7.7
review
ch08
8.1
8.2
8.3
8.4
8.5
review
INDEX
Photo Credits
Table of Derivatives
Table of Integrals
Symbols Index
Back Cover
