Graduate students in the natural sciences--including not only geophysics and space physics but also atmospheric and planetary physics, ocean sciences, and astronomy--need a broad-based mathematical toolbox to facilitate their research. In addition, they need to survey a wider array of mathematical methods that, while outside their particular areas of expertise, are important in related ones. While it is unrealistic to expect them to develop an encyclopedic knowledge of all the methods that are out there, they need to know how and where to obtain reliable and effective insights into these broader areas. Here at last is a graduate textbook that provides these students with the mathematical skills they need to succeed in today's highly interdisciplinary research environment. This authoritative and accessible book covers everything from the elements of vector and tensor analysis to ordinary differential equations, special functions, and chaos and fractals. Other topics include integral transforms, complex analysis, and inverse theory; partial differential equations of mathematical geophysics; probability, statistics, and computational methods; and much more. Proven in the classroom, Mathematical Methods for Geophysics and Space Physics features numerous exercises throughout as well as suggestions for further reading. * Provides an authoritative and accessible introduction to the subject * Covers vector and tensor analysis, ordinary differential equations, integrals and approximations, Fourier transforms, diffusion and dispersion, sound waves and perturbation theory, randomness in data, and a host of other topics * Features numerous exercises throughout * Ideal for students and researchers alike * An online illustration package is available to professors