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.
• All the material is presented in the form of problems • Mathematical insights are gained by getting the reader to develop answers themselves • Many applications of the mathematics are given
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.
From reviews of the first edition: '… a splendid book, quite a delight to see mathematical models from a different perspective … treatment is so smooth that it is hard to know at any instant whether one is learning new tools or assimilating the applications to interesting examples … excellent.' Donald de Cogan, International Journal of Numerical Modelling
'… instructive, applied and fun.' David Jefferies, The Times Higher Education Supplement
'This book integrates mathematical theory with a wide range of applications in physics … it could be a stand-alone textbook for an upper-year undergraduate course, but would also provide a good accompaniment to undergraduate maths courses. Teachers may also be more generally interested in this book for its many examples that may serve as useful supplements to physics or geophysics courses … I can highly recommend this book to students and teachers in the physical sciences.' Mike Kendall, Astronomy and Geophysics
'Guided by Roel Sneider's textbook, learning mathematical methods can be fun … I highly recommend [it].' Francois Primeau, EOS
'Students will find enjoyable discussions of the concepts of mathematical methods without getting lost in mazes of equations. Teachers will be interested in the easy way concepts are developed.' The Leading Edge
'The author … has comprehensibly integrated mathematics with a range of interesting features of physical sciences … Once read, one can appreciate the author's successful attempt to dispel the general misconception that mathematics is totally isolated from physics. The unique feature of the book is the presentation of various mathematical models in simple terms, followed by a range of interesting problem-solving exercises in physical sciences. The author's clear, simplistic approach is highly recommended for both students and teachers alike. … highly informative, written with authority, fascinating to read, and reasonably priced … to be within the budget of most institutions and individuals.' Materials World