《Springer大學數學圖書：高等微積分》是2009年清華大學出版社出版的一本圖書，作者是(美國)戴維 (David M.Bressoud)。
基本介紹
- 書名：Springer大學數學圖書：高等微積分
- 作者：(美國)戴維 (David M.Bressoud)
- 原版名稱：Second Year Calculus
- ISBN：9787302214816
- 頁數：386頁
- 出版社：清華大學出版社
- 出版時間：2009年11月1日
- 裝幀：平裝
- 開本：16
內容簡介,目錄,
內容簡介
《Springer大學數學圖書:高等微積分(英文)(影印版)》是本科生的微積分教學用書，主要內容為：牛頓運動學基本定律（開篇），向量代數.天體力學簡介，線性變換，微分形式和微分演算，隱函式反函式定理，重積分演算，曲線曲面積分，微積分基本定理，經典場論基本定理，愛因斯坦狹義相對論簡介。《Springer大學數學圖書:高等微積分(英文)(影印版)》特別注意數學與物理、力學等自然科學的內在聯繫和套用。作者在理念導引、內容選擇、程度深淺、適用範圍等方面都有相當周密的考慮。從我們國內重點大學的教學角度看，《Springer大學數學圖書:高等微積分(英文)(影印版)》的難易程度與物理、力學和電類專業數學課的微積分相當，而思想內容則要深刻和生動些，因此適於用作這些專業本科生的教科書或學習參考書。
目錄
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
