This user-friendly text shows how to use mathematics to formulate, solve, and analyze physical problems. Rather than follow the traditional approach of stating mathematical principles and then citing some physical examples for illustration, the book puts applications at center stage; that is, it starts with the problem, finds the mathematics that suits it, and ends with a mathematical analysis of the physics. The emphasis throughout is on engineering applications rather than mathematical formalities. Physical examples are selected primarily from applied mechanics, a field central to many branches of engineering and applied science, and they range from the simple to the more sophisticated. Among mathematical topics included in the book are Fourier series, separation of variables, Bessel functions, Fourier and Laplace transforms, Green's functions, and complex function theories. Also covered are advanced topics such as Riemann-Hilbert techniques, perturbation methods, and practical topics such as symbolic computation.