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Gathering an extensive range of mathematical topics into a plenary reference/text for solving science and engineering problems, Advanced Mathematical Models in Science and Engineering elucidates integral methods, field equation derivations, and operations applicable to modern science systems. Applying academic skills to practical problems in science and engineering, the author reviews basic methods of integration and series solutions for ordinary differential equations; introduces derivations and solution methods for linear boundary value problems in one dimension, covering eigenfunctions and eigenfunction expansions, orthogonality, and adjoint and self-adjoint systems; discusses complex variables, calculus, and integrals as well as application of residues and the integration of multivalued functions; considers linear partial differential equations in classical physics and engineering with derivations for the topics of wave equations, heat flow, vibration, and strength of materials; clarifies the calculus for integral transforms; explains Green's functions for ordinary and partial differential equations for unbounded and bounded media; examines asymptotic methods; presents methods for asymptotic solutions of ordinary differential equations; and more.

This text presents concepts on chaos in discrete time dynamics that are accessible to anyone who has taken a first course in undergraduate calculus. Retaining its commitment to mathematical integrity, the book, originating in a popular one-semester middle level undergraduate course, constitutes the first elementary presentation of a traditionally advanced subject.

Back by popular demand, the MAA is pleased to reissue this outstanding collection of problems and solutions from the Putnam Competitions covering the years 1938-1964. Problemists the world over, including all past and future Putnam Competitors, will revel in mastering the difficulties posed by this collection of problems from the first 25 William Lowell Putnam Competitions. Solutions to all 347 problems are given. In some cases multiple solutions are included, some which contestants could reasonably be expected to find under examination conditions, and others which are more elegant or utilize more sophisticated techniques. Valuable references and historical comments on many of the problems are presented. The book concludes with four articles on the Putnam competition written by G. Birkhoff, L. E. Bush, L. J. Mordell, and L. M. Kelly which are reprinted from the American Mathematical Monthly. There is great appeal here for all; teachers, students, and all those who love good problems and see them as an entree to beautiful and powerful ideas.