Description
Book SynopsisDirected primarily at college and university undergraduates, this book covers at basic level the essential applications of mathematics to the physical sciences. It contains all the usual topics covered in a first-year course such as vectors, matrices, differential equations, basic mathematical functions and their analysis, and power series. There is a strong emphasis on qualitative understanding (such as curve sketching) and practical methods of solution. The latter take due account of the impact of computers on the subject. The principles of mathematical expression are illustrated by copious examples taken from a wide range of topics in physics and chemistry. Each of the short chapters concludes with a summary and a large number of problems.
Table of Contents1. Introduction; 2. Errors; 3. Cartesian coordinates; 4. Vectors; 5. The scalar product; 6. The vector product and rotation; 7. Matrices in physics; 8. The transformation of matrices; 9. The matrix eigenvalue equation; 10. Exponential and logarithm functions; 11. Sine and cosine functions; 12. Graph plotting and curve sketching; 13. Differentiation; 14. Approximations; 15. Power series and Taylor's expansion; 16. Partial differentiation; 17. Integration; 18. The differential equation; 19. Solving first-order differential equations; 20. Second-order differential equations; 21. Solving second-order differential equations; 22. The complex exponential; 23. The circuit equation; 24. Harmonics and Fourier series; 25. The diffusion equation; 26. Waves; 27. The rate of change of a vector; 28. The scalar field and gradient operator; 29. The vector field; 30. Line integration; 31. The potential field; 32. Surface and volume integration; 33. Flux and divergence; 34. Circulation and the curl; 35. Conclusion; 36. Miscellaneous exercises.
