Rather than follow the traditional approach of stating mathematical principles and then citing some physical examples for illustration, Professor Mei puts applications at center stage. Beginning with the problem, he finds the mathematics that suits it and closes with a mathematical analysis of the physics. He selects physical examples primarily from applied mechanics. Among topics included 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. Engineering students, who often feel more awe than confidence and enthusiasm toward applied mathematics, will find this approach to mathematics goes a long way toward a sharper understanding of the physical world.