About the Book
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.
Table of Contents:
1. 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.
About the Author :
Roel Snieder holds the Keck Foundation Endowed Chair of Basic Exploration Science at the Colorado School of Mines. From 1997 to 2000, he served as Dean of the Faculty of Earth Sciences at the University of Utrecht. Snieder has served on the editorial boards of Geophysical Journal International, Inverse Problems, Reviews of Geophysics, and the European Journal of Physics. In 2000, he was elected Fellow of the American Geophysical Union. He is co-author of the textbook The Art of Being a Scientist: A Guide for Graduate Students and their Mentors (Cambridge University Press, 2009). From 2003 to 2011, he was a member of the Earth Science Council of the US Department of Energy. In 2008, Snieder worked for the Global Climate and Energy Project at Stanford University on outreach and education on global energy. That same year, he was a founding member of the humanitarian organization Geoscientists Without Borders, where he served as chair until 2013. In 2011, he was elected Honorary Member of the Society of Exploration Geophysicists. Kasper van Wijk is an Associate Professor in the Physics Department and Director of the Physical Acoustics Laboratory at the University of Auckland. He studied geophysics at the University of Utrecht from 1991 to 1996, where he specialized in inverse theory. After teaching outdoor education in the mountains of Colorado, Van Wijk obtained his PhD in geophysics from the Colorado School of Mines and taught at Boise State University. His research interests center around elastic-wave propagation in disordered media, with applications ranging from medical imaging to global seismology. Van Wijk has (co-)organized and taught geophysical field camps in Colorado, Oregon, and Thailand. His worldwide outreach efforts, as part of Seismometers in Schools, have exposed diverse audiences to the dynamic processes of our Earth.
Review :
'[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
'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
'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
'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
'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
'[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
'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: '[The] clear, simplistic approach is highly recommended for both students and teachers alike … highly informative, written with authority, fascinating to read.' Materials World
'The first and second editions of this gem of a volume were received with praise such as 'a delight of a book', 'a fantastic set of physical problems that opens the gate to the understanding of mathematical physics', and 'a refreshing alternative approach', among many others. It is difficult to find better words to describe the third edition … It is student-friendly not only in its clarity and elegance of style … The volume is both a finely honed learning tool and a good reference for most of the mathematics that a geophysicist might encounter in practice … In short, here is a book that no practicing geophysicist … should be without.' Sven Treitel, The Leading Edge
