A Guided Tour of Mathematical Methods for the Physical Sciences

ISBN-13: 9781107084964 / Angielski / Twarda / 2015 / 584 str.

Roel Snieder; Kasper Van Wijk; Matthew M. Haney

Opis

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.

Recenzje

'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

Spis treści

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.