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Viser: Second Year Calculus - From Celestial Mechanics to Special Relativity
Second Year Calculus
From Celestial Mechanics to Special Relativity
David M. Bressoud
(2001)
Sprog: Engelsk
om ca. 10 hverdage
Detaljer om varen
- 1. Udgave
- Paperback: 404 sider
- Udgiver: Springer New York (Marts 2001)
- ISBN: 9780387976068
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 Orbital 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 History 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 of 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
361.- B Bibliography
365.- C Clues and Solutions
367.- Index
382.