A Guided Tour of Mathematical Methods for the Physical Sciences

Mathematical methods are essential tools for all physical scientists. This book provides a comprehensive tour of the mathematical knowledge and techniques that are needed by students across the physical sciences. In contrast to more traditional textbooks, all the material is presented in the form of exercises. Within these exercises, basic mathematical theory and its applications in the physical sciences are well integrated. In this way, the mathematical insights that readers acquire are driven by their physical-science insight. This third edition has been completely revised: new material has been added to most chapters, and two completely new chapters on probability and statistics and on inverse problems have been added. This guided tour of mathematical techniques is instructive, applied, and fun. This book is targeted for all students of the physical sciences. It can serve as a stand-alone text, or as a source of exercises and examples to complement other textbooks. Advance praise: '[This] is an excellent textbook for young people to acquire practical mathematical methods; furthermore, it is a wonderful guidebook for them to learn a mathematical thinking style. I highly recommend this splendid book to students and teachers in [the] sciences.' Haruo Sato, Tohoku University, Japan Advance praise: 'A delight of a book, original, and highly informative with many hidden gems. A must for the physical scientist. Using calculus to show why life is not possible in a five dimensional world was just one piece of magic.' Malcolm Sambridge, Australian National University Advance praise: 'Two bright minds [have] created a fantastic set of physical problems that opens the gates to the understanding of mathematical physics for undergraduate and graduate students alike. Solving these problems is not only instructive, but fun - almost addictive.' Jurgen Neuberg, University of Leeds Advance praise: 'Snieder and van Wijk have written a book that offers a refreshing alternate approach to the learning (and appreciation) of mathematical methods, in which the methods are introduced and illustrated by explicit problems in the physical sciences. For persons who genuinely like mathematics, and who want to strengthen their problem solving capabilities, but who nevertheless want to keep their focus on the physics, this book is highly recommended for self-study and leisure reading.' Allan D. Pierce, Boston University and the Acoustical Society of America Advance praise: 'The third edition builds on the strengths of the earlier editions and is insightful, accessible and enjoyable to read. Exercises are nicely woven into the fabric of the text to more fully engage the reader. Chapters on 'Probability and Statistics' and 'Inverse Problems' are important new additions.' Robert L. Nowack, Purdue University and the Journal of Geophysical Research: Solid Earth Advance praise: '[A Guided Tour of] Mathematical Methods for the Physical Sciences introduces the tools required to describe and interpret the physical world. Using clear, instructive examples, Snieder and van Wijk demonstrate how to tackle complex problems step by step and how to develop an understanding of what equations really mean.' John Townend, Victoria University of Wellington, New Zealand Advance praise: 'This book makes learning difficult mathematics easier. Each concept is presented through a series of clear explanations and tractable problems, so students gain both the understanding, and the ability to use mathematics in any field. You can't ask for more from a maths book.' Andrew Curtis, University of Edinburgh Review of previous edition: '... a splendid book ... excellent.' International Journal of Numerical Modelling Review of previous edition: 'The publisher says that this book is 'instructive, applied and fun'. I agree ...' Times Higher Education Supplement Review of previous edition: 'I can highly recommend this book to students and teachers in the physical sciences.' Astronomy and Geophysics Review of previous edition: 'Guided by [this] textbook, learning mathematical methods can be fun ... I highly recommend [it].' Eos, Transactions, American Geophysical Union Review of previous edition: '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 Review of previous edition: '[The] clear, simplistic approach is highly recommended for both students and teachers alike ... highly informative, written with authority, fascinating to read.' Materials World1. Introduction; 2. Dimensional analysis; 3. Power series; 4. Spherical and cylindrical coordinates; 5. Gradient; 6. Divergence of a vector field; 7. Curl of a vector field; 8. Theorem of Gauss; 9. Theorem of Stokes; 10. The Laplacian; 11. Scale analysis; 12. Linear algebra; 13. Dirac delta function; 14. Fourier analysis; 15. Analytic functions; 16. Complex integration; 17. Green's functions: principles; 18. Green's functions: examples; 19. Normal modes; 20. Potential-field theory; 21. Probability and statistics; 22. Inverse problems; 23. Perturbation theory; 24. Asymptotic evaluation of integrals; 25. Conservation laws; 26. Cartesian tensors; 27. Variational calculus; 28. Epilogue on power and knowledge.