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| Vectors, Matrices, and Applications | |
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| Vectors | |
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| Applications in Geometry and Physics | |
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| The Dot Product | |
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| Matrices and Determinants | |
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| The Cross Product | |
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| Chapter Review | |
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| Calculus of Functions of Several Variables | |
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| Real-Valued and Vector-Valued Functions of Several Variables | |
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| Graph of a Function of Several Variables | |
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| Limits and Continuity | |
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| Derivatives | |
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| Paths and Curves in R[superscript 2]-and R[superscript 3] | |
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| Properties of Derivatives | |
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| Gradient and Directional Derivative | |
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| Cylindrical and Spherical Coordinate Systems | |
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| Chapter Review | |
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| Vector-Valued Functions of One Variable | |
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| World of Curves | |
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| Tangents, Velocity, and Acceleration | |
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| Length of a Curve | |
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| Acceleration and Curvature | |
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| Introduction to Differential Geometry of Curves | |
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| Chapter Review | |
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| Scalar and Vector Fields | |
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| Higher-Order Partial Derivatives | |
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| Taylor's Formula | |
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| Extreme Values of Real-Valued Functions | |
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| Optimization with Constraints and Lagrange Multipliers | |
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| Flow Lines | |
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| Divergence and Curl of a Vector Field | |
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| Implicit Function Theorem | |
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| Appendix: Some Identities of Vector Calculus | |
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| Chapter Review | |
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| Integration Along Paths | |
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| Paths and Parametrizations | |
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| Path Integrals of Real-Valued Functions | |
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| Path Integrals of Vector Fields | |
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| Path Integrals Independent of Path | |
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| Chapter Review | |
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| Double and Triple Integrals | |
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| Double Integrals: Definition and Properties | |
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| Double Integrals Over General Regions | |
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| Examples and Techniques of Evaluation of Double Integrals | |
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| Change of Variables in a Double Integral | |
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| Triple Integrals | |
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| Chapter Review | |
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| Integration Over Surfaces, Properties, and Applications of Integrals | |
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| Parametrized Surfaces | |
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| World of Surfaces | |
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| Surface Integrals of Real-Valued Functions | |
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| Surface Integrals of Vector Fields | |
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| Integrals: Properties and Applications | |
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| Chapter Review | |
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| Classical Integration Theorems of Vector Calculus | |
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| Green's Theorem | |
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| The Divergence Theorem | |
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| Stokes' Theorem | |
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| Differential Forms and Classical Integration Theorems | |
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| Vector Calculus in Electromagnetism | |
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| Vector Calculus in Fluid How | |
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| Chapter Review | |
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| Various Results Used in This Book and Proofs of Differentiation Theorems | |
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| Answers to Odd-Numbered Exercises | |
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| Index | |