The Third Edition of this critically acclaimed text is thoroughly updated and revised with new concepts and applications to assist readers in modeling and analyzing natural, social, and technological processes. Readers are introduced to key ideas in math-ematical methods and modeling, with an emphasis on the connections between mathematics and the applied and natural sciences. The book covers the gamut of both standard and modern topics, including scaling and dimensional analysis; regular and singular perturbation; calculus of variations; Green's functions and integral equations; nonlinear wave propagation; and stability and bifurcation.Readers will discover many special features in this new and revised edition, such as:* A new chapter on discrete-time models, including a section devoted to stochastic models* A thorough revision of the text's 300 exercises, incorporating contemporary problemsand methods* Additional material and applications of linear transformations in Rn (matrices, eigenvalues, etc.) to compare to the integral equation results* New material on mathematical biology, including age-structured models, diffusion and advection, and biological modeling, including MATLAB programsMoreover, the text has been restructured to facilitate its use as a textbook. The first section covers models leading to ordinary differential equations and integral equations, and the second section focuses on partial differential equations and their applications. Exercises vary from routine calculations that reinforce basic techniques to challenging problems that stimulate advanced problem solving.With its new exercises and structure, this book is highly recommended for upper-undergraduateand beginning graduate students in mathematics, engineering, and natural sciences. Scientists and engineers will find the book to be an excellent choice for reference and self-study.