With an accessible, informal style, this upper-level undergraduate textbook covers traditional mathematical concepts and tools essential in physics and engineering. Interesting physics examples are leveraged throughout to instill physical insight into the math, and mathematical intuition into the physics, alongside problems to deepen understanding.
With an accessible, informal style, this upper-level undergraduate textbook covers traditional mathematical concepts and tools essential in physics and engineering. Interesting physics examples are leveraged throughout to instill physical insight into the math, and mathematical intuition into the physics, alongside problems to deepen understanding.
Alec J. Schramm is a professor of physics at Occidental College, Los Angeles. In addition to conducting research in nuclear physics, mathematical physics, and particle phenomenology, he teaches at all levels of the undergraduate curriculum, from courses for non-majors through general relativity and relativistic quantum mechanics. After completing his Ph.D., he lectured at Duke University and was a KITP Scholar at the Kavli Institute for Theoretical Physics at UC Santa Barbara. He is regularly nominated for awards for his physics teaching and clear exposition of complex concepts.
Inhaltsangabe
Preface Part I. Things You Just Gotta' Know: 1. Prelude: symbiosis 2. Coordinating coordinates 3. Complex numbers 4. Index algebra 5. Brandishing binomials 6. Infinite series 7. Interlude: orbits in a central potential 8. Ten integration techniques and tricks 9. The Dirac delta function 10. Coda: statistical mechanics Part II. The Calculus of Vector Fields: 11. Prelude: visualizing vector fields 12. grad, div & curl 13. Interlude: irrotational and incompressible 14. Integrating scalar & vector fields 15. The theorems of Gauss & Stokes 16. Simply connected regions 17. Coda: mostly Maxwell Part III. Calculus in the Complex Plane: 18. Prelude: path independence in the complex plane 19. Series, singularities & branches 20. Interlude: conformal mapping 21. The calculus of residues 22. Coda: analyticity & causality Part IV. Linear Algebra: 23. Prelude: superposition 24. Vector space 25. The inner product 26. Interlude: rotations 27. The Eigenvalue problem 28. Coda: normal modes Entr'acte: Tensors 29. Cartesian tensors 30. Beyond cartesian Part V. Orthogonal Functions: 31. Prelude: 1 2 3 . . . infinity 32. Eponymous polynomials 33. Fourier series 34. Convergence and completeness 35. Interlude: beyond the straight & narrow 36. Fourier transforms 37. Coda: of time intervals and frequency bands Part VI. Differential Equations: 38. Prelude: first order first 39. Second-order ODEs 40. Interlude: the Sturm-Liouville Eigenvalue problem 41. Partial differential equations 42. Green's functions 43. Coda: quantum scattering Appendix A. Curvilinear coordinates Appendix B. Rotations in R3 Appendix C. The Bessel family of functions References Index.
Preface Part I. Things You Just Gotta' Know: 1. Prelude: symbiosis 2. Coordinating coordinates 3. Complex numbers 4. Index algebra 5. Brandishing binomials 6. Infinite series 7. Interlude: orbits in a central potential 8. Ten integration techniques and tricks 9. The Dirac delta function 10. Coda: statistical mechanics Part II. The Calculus of Vector Fields: 11. Prelude: visualizing vector fields 12. grad, div & curl 13. Interlude: irrotational and incompressible 14. Integrating scalar & vector fields 15. The theorems of Gauss & Stokes 16. Simply connected regions 17. Coda: mostly Maxwell Part III. Calculus in the Complex Plane: 18. Prelude: path independence in the complex plane 19. Series, singularities & branches 20. Interlude: conformal mapping 21. The calculus of residues 22. Coda: analyticity & causality Part IV. Linear Algebra: 23. Prelude: superposition 24. Vector space 25. The inner product 26. Interlude: rotations 27. The Eigenvalue problem 28. Coda: normal modes Entr'acte: Tensors 29. Cartesian tensors 30. Beyond cartesian Part V. Orthogonal Functions: 31. Prelude: 1 2 3 . . . infinity 32. Eponymous polynomials 33. Fourier series 34. Convergence and completeness 35. Interlude: beyond the straight & narrow 36. Fourier transforms 37. Coda: of time intervals and frequency bands Part VI. Differential Equations: 38. Prelude: first order first 39. Second-order ODEs 40. Interlude: the Sturm-Liouville Eigenvalue problem 41. Partial differential equations 42. Green's functions 43. Coda: quantum scattering Appendix A. Curvilinear coordinates Appendix B. Rotations in R3 Appendix C. The Bessel family of functions References Index.
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