A guided tour of mathematical methods for the physical sciences

Description

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.  Read more... 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.