Applied mathematics

This third edition of a textbook on mathematical methods and modeling has been fully revised to add new ideas and applications. Its goal is to equip readers to build and analyze models of natural, social, and technological systems, with particular attention to how mathematics ties into the applied and natural sciences. The coverage spans both classical and newer material, including scaling and dimensional analysis, regular and singular perturbation, the calculus of variations, Green's functions and integral equations, nonlinear wave propagation, and stability and bifurcation.

The revision introduces a new chapter on discrete-time models, which includes a section on stochastic models. Its roughly 300 exercises have been thoroughly reworked to reflect current problems and methods. The text also extends its treatment of linear transformations in R^n, such as matrices and eigenvalues, so readers can compare them with the results obtained from integral equations. A new block on mathematical biology covers age-structured models, diffusion and advection, and biological modeling, with accompanying MATLAB programs.

The book has been reorganized for classroom use. The first part develops models that lead to ordinary differential equations and integral equations, and the second part concentrates on partial differential equations and their uses. Exercises range from routine practice of core techniques to demanding problems that call for advanced problem solving.

It is intended for upper-undergraduate and beginning graduate students in mathematics, engineering, and the natural sciences, and it also serves working scientists and engineers as a reference and for independent study.