9781429215084

Vector Calculus

Anthony Tromba, Jerrold E. Marsden

6th Edition

This bestselling vector calculus text helps students gain a solid, intuitive understanding of this important subject. The book's careful contemporary balance between theory, application, and historical development, provides readers with insights into how mathematics progresses and is in turn influenced by the natural world. The new edition offers a contemporary design,

1.1

Vectors in Two- and Three-Dimensional Space

Exercises

p.18

1.2

The Inner Product, Length, and Distance

Exercises

p.29

1.3

Matrices, Determinants, and the Cross Product

Exercises

p.49

1.4

Cylindrical and Spherical Coordinates

Exercises

p.58

1.5

n-Dimensional Euclidean Space

Exercises

p.69

Review Exercises

p.70

2.1

The Geometry of Real-Valued Functions

Exercises

p.85

2.2

Limits and Continuity

Exercises

p.103

2.3

Differentiation

Exercises

p.115

2.4

Introduction to Paths and Curves

Exercises

p.123

2.5

Properties of the Derivative

Exercises

p.132

2.6

Gradients and Directional Derivatives

Exercises

p.142

Review Exercises

p.144

7.1

The Path Integral

Exercises

p.356

7.2

Line Integrals

Exercises

p.373

7.3

Parametrized Surfaces

Exercises

p.381

7.4

Area of a Surface

Exercises

p.391

7.5

Integrals of Scalar Functions Over Surfaces

Exercises

p.398

7.6

Surface Integrals of Vector Fields

Exercises

p.411

7.7

Applications to Differential Geometry, Physics, and Forms of Life

Exercises

p.423

Review Exercises

p.423