A guided tour of mathematical methods for the physical sciences /
Roel Snieder, Colorado School of Mines, Kasper van Wijk, University of Auckland.
- Third edition.
- Cambridge : Cambridge University Press, 2015.
- 1 online resource (xxi, 560 pages) : digital, PDF file(s).
Title from publisher's bibliographic system (viewed on 05 Oct 2015).
Introduction -- Dimensional analysis -- Power series -- Spherical and cylindrical coordinates -- Gradient -- Divergence of a vector field -- Curl of a vector field -- Theorem of Gauss -- Theorem of Stokes -- The Laplacian -- Scale analysis -- Linear algebra -- Dirac delta function -- Fourier analysis -- Analytic functions -- Complex integration -- Green's functions: principles -- Green's functions: examples -- Normal modes -- Potential field theory -- Probability and statistics -- Inverse problems -- Perturbation theory -- Asymptotic evaluation of integrals -- Conservation laws -- Cartesian tensors -- Variational calculus -- Epilogue, on power and knowledge.
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.