Mathematical Methods: For Students of Physics and Related Fields, Second Edition (Lecture Notes in Physics)

Description

Intended to follow the usual introductory physics courses, this book has the unique feature of addressing the mathematical needs of sophomores and juniors in physics, engineering and other related fields. Many original, lucid, and relevant examples from the physical sciences, problems at the ends of chapters, and boxes to emphasize important concepts help guide the student through the material. Beginning with reviews of vector algebra and differential and integral calculus, the book continues with infinite series, vector analysis, complex algebra and analysis, ordinary and partial differential equations. Discussions of numerical analysis, nonlinear dynamics and chaos, and the Dirac delta function provide an introduction to modern topics in mathematical physics. This new edition has been made more user-friendly through organization into convenient, shorter chapters. Also, it includes an entirely new section on Probability and plenty of new material on tensors and integral transforms. Cover......Page 1 Contents......Page 16 Part I / Coordinates and Calculus......Page 26 1. Coordinate Systems and Vectors......Page 28 2. Differentiation......Page 68 3. Integration: Formalism......Page 102 4. Integration: Applications......Page 126 5. Dirac Delta Function......Page 164 Part II / Algebra of Vectors......Page 196 6. Planar and Spatial Vectors......Page 198 7. Finite-Dimensional Vector Spaces......Page 240 8. Vectors in Relativity......Page 262 Part III / Infinite Series......Page 282 9.Infinite Series......Page 284 10. Application of Common Series......Page 308 11.Integrals and Series as Functions......Page 342 Part IV / Analysis of Vectors......Page 366 12. Vectors and Derivatives......Page 368 13. Flux and Divergence......Page 390 14. Line Integral and Curl......Page 412 15. Applied Vector Analysis......Page 432 16. Curvilinear Vector Analysis......Page 448 17. Tensor Analysis......Page 464 Part V / Complex Analysis......Page 500 18. Complex Arithmetic......Page 502 19. Complex Derivative and Integral......Page 522 20. Complex Series......Page 540 21. Calculus of Residues......Page 550 Part VI / Differential Equations......Page 564 22. From PDEs to ODEs......Page 566 23. First-Order Differential Equations......Page 576 24. Second-Order Linear Differential Equations......Page 588 25. Laplace’s Equation: Cartesian Coordinates......Page 616 26. Laplace’s Equation: Spherical Coordinates......Page 632 27. Laplace’s Equation: Cylindrical Coordinates......Page 664 28. Other PDEs of Mathematical Physics......Page 686 Part VII / Special Topics......Page 716 29. Integral Transforms......Page 718 30. Calculus of Variations......Page 752 31. Nonlinear Dynamics and Chaos......Page 778 32. Probability Theory......Page 806 Bibliography......Page 840 Index......Page 842