A Guided Tour of Mathematical Methods

For the Physical Sciences

Roel Snieder (Autor)

Buch | Softcover

524 Seiten

2009 | 2nd Revised edition
Cambridge University Press (Verlag)
978-0-521-54261-6 (ISBN)

Infos

This second edition provides a comprehensive tour of the essential mathematical knowledge and techniques needed by students in the physical sciences. Unlike traditional textbooks, the material is presented in the form of problems. A stand-alone text for undergraduates and lower-level graduate students, or as a source of problems and examples.

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Mathematical methods are essential tools for all physical scientists. This second edition provides a comprehensive tour of the mathematical knowledge and techniques that are needed by students in this area. In contrast to more traditional textbooks, all the material is presented in the form of problems. Within these problems the basic mathematical theory and its physical applications are well integrated. The mathematical insights that the student acquires are therefore driven by their physical insight. Topics that are covered include vector calculus, linear algebra, Fourier analysis, scale analysis, complex integration, Green's functions, normal modes, tensor calculus and perturbation theory. The second edition contains new chapters on dimensional analysis, variational calculus, and the asymptotic evaluation of integrals. This book can be used by undergraduates and lower-level graduate students in the physical sciences. It can serve as a stand-alone text, or as a source of problems and examples to complement other textbooks.

Inhalt

1. Introduction; 2. Dimensional analysis; 3. Power series; 4. Spherical and cylindrical co-ordinates; 5. The gradient; 6. The divergence of a vector field; 7. The curl of a vector field; 8. The theorem of Gauss; 9. The theorem of Stokes; 10. The Laplacian; 11. Conservation laws; 12. Scale analysis; 13. Linear algebra; 14. The Dirac delta function; 15. Fourier analysis; 16. Analytic functions; 17. Complex integration; 18. Green's functions: principles; 19. Green's functions: examples; 20. Normal modes; 21. Potential theory; 22. Cartesian tensors; 23. Perturbation theory; 24. Asymptotic evaluation of integrals; 25. Variational calculus; 26. Epilogue, on power and knowledge; References.

Produkt-Details

• Erscheint lt. Verlag: 9.4.2009
• Zusatzinfo: 6 Tables, unspecified; 6 Halftones, unspecified; 126 Line drawings, unspecified
• Verlagsort: Cambridge
• Sprache: englisch
• Maße: 170 x 244 mm
• Gewicht: 830 g
• Themenwelt: Mathematik / Informatik ► Mathematik ► Angewandte Mathematik
• Themenwelt: Naturwissenschaften ► Physik / Astronomie
• ISBN-10: 0-521-54261-8 / 0521542618
• ISBN-13: 978-0-521-54261-6 / 9780521542616
• Zustand: Neuware