Calculus of Several Variables

Intended for University level one semester course in multivariable calculus and a one-semester course in vector calculus.This new Fourth Edition of several-variable calculus retains the qualities that have made Adams so popular: the clear, concise writing style, geometric reasoning, and fully and carefully stated theorems and proofs. Extensive reviewing has resulted in a reorganization of the material for efficiency sake, resulting in less redundancy with greater emphasis on key topics.

Table of Contents:
Chapter R: A Brief Review of Single-Variable Calculus. 1. Vectors and Coordinate Geometry in 3-Space. Analytic Geometry in 3 Dimensions. Vectors. The Cross Product in 3-Space. Planes and Lines. Quadric Surfaces. A Little Matrix Algebra. Using Maple for Vector and Matrix Calculations. Chapter Review. 2. Vector Functions and Curves. Vector Functions of One Variable. Some Applications of Vector Differentiation. Curves and Parametrizations. Curvature, Torsion, and the Frenet Frame. Curvature and Torsion for General Parametrizations. Kepler's Laws of Planetary Motion. 3. Partial Differentiation. Functions of Several Variables. Limits and Continuity. Partial Derivatives. Higher-Order Derivatives. The Chain Rule. Linear Approximations, Differentiability, and Differentials. Gradients and Directional Derivatives. Implicit Functions. Taylor Series and Approximations. Chapter Review. 4. Applications of Partial Derivatives. Extreme Values. Extreme Values of Functions Defined on Restricted Domains. Lagrange Multipliers. The Method of Least Squares. Parametric Problems. Newton's Method. Calculations with Maple. Chapter Review. 5. Multiple Integration. Double Integrals. Iteration of Double Integrals in Cartesian Coordinates. Improper Integrals and a Mean-Value Theorem. Double Integrals in Polar Coordinates. Triple Integrals. Change of Variables in Triple Integrals. Applications of Multiple Integrals. Chapter Review. 6. Vector Fields. Vector and Scalar Fields. Conservative Fields. Line Integrals. Line Integrals of Vector Fields. Surfaces and Surface Integrals. Oriented Surfaces and Flux Integrals. Chapter Review. 7. Vector Calculus. Gradient, Divergence, and Curl. Some Identities Involving Grad, Div, and Curl. Green" Theorem in the Plane. The Divergence Theorem in 3-Space. Stokes's Theorem. Some Physical Applications of Vector Calculus. Orthogonal Curvilinear Coordinates. Chapter Review. 8. Sequences, Series, and Power Series. Sequences and Convergence. Infinite Series. Convergence Tests for Positive Series. Absolute and Conditional Convergence. Power Series. Taylor and Mclaurin Series. Applications of Taylor and Maclaurin Series. Taylor's Formula Revisited. The Binomial Theorem and Binomial Series. Fourier Series. Chapter Review. 9. Ordinary Differential Equations. Classifying Differential Equations. First-Order Separable and Homogeneous Equations. Exact Equations and Integrating Factors. First-Order Linear Equations. Existence, Uniqueness, and Numerical Methods. Differential Equations of Second Order. Linear Differential Equations with Constant Coefficients. Nonhomogeneous Linear Equations. Series Solutions. Chapter Review. Appendix I. Complex Numbers. Appendix II. Complex Functions. Answers to Odd-Numbered Exercises. Index.