高等微积分

《Springer大学数学图书:高等微积分(英文)(影印版)》是本科生的微积分教学用书，主要内容为：牛顿运动学基本定律（开篇），向量代数.天体力学简介，线性变换，微分形式和微分演算，隐函数反函数定理，重积分演算，曲线曲面积分，微积分基本定理，经典场论基本定理，爱因斯坦狭义相对论简介。《Springer大学数学图书:高等微积分(英文)(影印版)》特别注意数学与物理、力学等自然科学的内在联系和应用。作者在理念导引、内容选择、程度深浅、适用范围等方面都有相当周密的考虑。从我们国内重点大学的教学角度看，《Springer大学数学图书:高等微积分(英文)(影印版)》的难易程度与物理、力学和电类专业数学课的微积分相当，而思想内容则要深刻和生动些，因此适于用作这些专业本科生的教科书或学习参考书。

Preface 1 F =ma 1.1 Prelude to Newton's Principia 1.2 Equal Area in Equal Time 1.3 The Law of Gravity 1.4 Exercises 1.5 Reprise with Calculus 1.6 Exercises 2 Vector Algebra 2.1 Basic Notions 2.2 The Dot Product 2.3 The Cross Product 2.4 Using Vector Algebra 2.5 Exercises 3 Celestial Mechanics 3.1 The Calculus of Curves 3.2 Exercises 3.3 OrbitM Mechanics 3.4 Exercises 4 Differential Forms 4.1 Some History 4.2 Differential 1-Forms 4.3 Exercises 4.4 Constant Differential 2-Forms 4.5 Exercises 4.6 Constant Differential k-Forms 4.7 Prospects 4.8 Exercises 5 Line Integrals, Multiple Integrals 5.1 The Riemann Integral 5.2 Line Integrals 5.3 Exercises 5.4 Multiple Integrals 5.5 Using Multiple Integrals 5.6 Exercises 6 Linear Transformations 6.1 Basic Notions 6.2 Determinants 6.3 Hk, tory and Comments 6.4 Exercises 6.5 Invertibility 6.6 Exercises 7 Differential Calculus 7.1 Limits 7.2 Exercises 7.3 Directional Derivatives 7.4 The Derivative 7.5 Exercises 7.6 The Chain Rule 7.7 Using the Gradient 7.8 Exercises 8 Integration by Pullback 8.1 Change cf Variables 8.2 Interlude with Lagrange 8.3 Exercises . 8.4 The Surface Integral 8.5 Heat Flow 8.6 Exercises 9 Techniques of Differential Calculus 9.1 Implicit Differentiation 9.2 Invertibility 9.3 Exercises 9.4 Locating Extrema 9.5 Taylor's Formula in Several Variables 9.6 Exercises 9.7 Lagrange Multipliers 9.8 Exercises 10 The Fundamental Theorem of Calculus 10.1 Overview 10.2 Independence of Path 10.3 Exercises 10.4 The Divergence Theorems 10.5 Exercises 10.6 Stokes' Theorem 10.7 Summary for R3 10.8 Exercises 10.9 Potential Theory 11 E = mc2 11.1 Prelude to Maxwell's Dynamical Theory 11.2 Flow in Space-Time 11.3 Electromagnetic Potential 11.4 Exercises 11.5 Special Relativity 11.6 Exercises Appendices A An Opportunity Missed B Bibliography C Clues and Solutions Index