Vendetta

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. 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 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