Applied Mathematics, 3rd Edition
April 2006, ©2006
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 programs
Moreover, 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.
1. Dimensional Analysis, Scaling, & Differential Equations.
2. Perturbation Methods.
3. Calculus of Variations.
4. Eigenvalue Problems, Integral Equations, and Green's Functions.
5. Discrete Models.
6. Partial Differential Equations.
7. Wave Phenomena.
8. Mathematical Models of Continua.
Material new to this edition include: a chapter on stochastic models; greater emphasis on mathematical biology; sections on discrete models, deterministic and stochastic models, ODEs, PDEs, and IEs; and an overhaul of the exercises in the book
MATLAB applications have been added to show computer algebra system calculations
The author has substantially revised the content and structure of the previous edition in an effort to make the book even more usable as a textbook
Standard topics as well as modern topics are covered: scaling and dimensional analysis; regular and singular perturbation methods; nonlinear wave propagation; and stability and bifurcation
The book is written at a level that is accessible to practitioners and students in a wide range of scientific and engineering fields
Special features include over 100 illustrations and 300 exercises
"Future mathematicians, scientists and engineers should find the book to be an excellent introductory text for coursework or self-study as well as worth its shelf space for reference." (MAA Reviews, October 12, 2006)