Author | Bressoud, David M. author |
---|---|
Title | Second Year Calculus [electronic resource] : From Celestial Mechanics to Special Relativity / by David M. Bressoud |
Imprint | New York, NY : Springer New York : Imprint: Springer, 1991 |
Connect to | http://dx.doi.org/10.1007/978-1-4612-0959-1 |
Descript | 404 p. online resource |
1 F=ma -- 1.1 Prelude to Newtonโs 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 Taylorโs 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 Stokesโ Theorem -- 10.7 Summary for R3 -- 10.8 Exercises -- 10.9 Potential Theory -- 11 E = mc2 -- 11.1 Prelude to Maxwellโs 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