Vector calculus / created by Jerrold E. Marsden, California Institute of Technology, Pasadena, Anthony Tromba, University of California, Santa Cruz.

Includes index.

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

This textbook by respected authors helps students foster computational skills and intuitive understanding with a careful balance of theory, applications, historical development and optional materials