This volume and its successor were conceived to advance the level of mathematical sophistication in the engineering community. The books particularly focus on material relevant to solving the kinds of mathematical problems regularly confronted by engineers. Suitable as a text for advanced undergraduate and graduate courses as well as a reference for professionals, Volume One's three-part treatment covers mathematical models, probabilistic problems, and computational considerations. Contributions include chapters on linear and nonlinear oscillations by Solomon Lefschetz, on hyperbolic partial differential equations and applications by Richard Courant, and on the theory of prediction by Norbert Wiener. Additional topics include game theory, applied mathematics in operations research, matrices, conformal mapping methods, and other subjects involving the intersection of engineering and mathematics.