Synopses & Reviews
Mathematical methods are essential tools for all physical scientists. This novel textbook provides a comprehensive guided tour of the mathematical knowledge and techniques needed by students. In contrast to more traditional textbooks, all the material is presented in the form of problems in which mathematical theory and its physical applications are very well integrated. Topics include vector calculus, linear algebra, Fourier analysis, scale analysis, Green's functions, normal modes, tensor calculus, and perturbation theory. This volume can be used by undergraduates or by 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.
Review
"...engaging...I highly recommend this book to students and teachers of geophysics." The Leading Edge
Synopsis
Problems based mathematical methods textbook for undergraduates and lower-level graduate students in the physical sciences.
Description
Includes bibliographical references (p. 416-421) and index.
About the Author
Roel Snieder currently holds the Keck Foundation Endowed Chair of Basic Exploration Science at the Colorado School of Mines (USA).
Table of Contents
1. Introduction; 2. Power series; 3. Spherical and cylindrical coordinates; 4. The gradient; 5. The divergence of a vector field; 6. The curl of a vector field; 7. The theorem of Gauss; 8. The theorem of Stokes; 9. The Laplacian; 10. Conservation laws; 11. Scale analysis; 12. Linear algebra; 13. The 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 theory; 21. Cartesian tensors; 22. Perturbation theory; 23. Epilogue, on power and knowledge; References.