图书简介

Preface Foreword to the Student 1  Vectors and Sets in Rm   1.1   Vectors in Rm 1.2 Lines and Planes in R3  1.3 Points or Vectors? 1.4 Convergent Sequences in Rm  1.5 Sets in Rm    2  Functions of Several Variables 2.1 Functions, Domains and Codomains   2.2 The Graph of a Function   2.3 Level Sets  2.4 Quadric Surfaces  2.5 Curves   3  Limits and Continuity 3.1 Limit of a Function 3.2 Two-Path Test for the Nonexistence of a Limit  3.3 Functions with Limit at a Point  3.4 Continuous Functions 3.5 Continuous Extensions  4  Differentiable Functions  4.1 Partial Derivatives  4.2 The Tangent Plane to a Surface   4.3 Differentiable Functions   4.4 A Criterion for Differentiability 4.5 Differentiability of Vector Valued Functions 5  Chain Rule 5.1 Chain Rule for Several Variable Functions   5.2 Implicit Differentiation 5.3 Mean Value Theorem in Several Variables 6  Directional Derivative 6.1 Directional Derivative 6.2 A Geometric Insight   6.3 The Gradient and the Level Sets   7  Second Order Derivatives 7.1 Second Order Derivatives   7.2 Chain Rule for Second Order Derivatives  7.3 The Laplace Operator   8  Taylor’s Theorem 8.1 Higher Order Derivatives   8.3   Taylor’s Theorem 8.3 Linear and Quadratic Approximation 9  Implicit Function Theorem 9.1 Preliminaries 9.2 Two Variable Case 9.3 Three Variable Case   9.4 The General Case   10 Local and Global Extrema 10.1 Extreme Values and Cr

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