This text presents, for the first time at an elementary level, current topics in applied mathematics such as singular perturbation, nonlinear wave propagation, bifurcation, similarity methods and the numerical solution of partial differential equations. It emphasizes the interdependency of mathematics and its application to physical phenomena, and is written in a style accessible to readers with a wide range of interests and backgrounds.
The book provides a self-contained and accessible introduction to the subject. It starts with an introduction to integrability of ordinary and partial differential equations.
Nonlinear Partial Differential Equations for Scientists and Engineers, 2 Ed
"An exceptionally complete overview. There are numerous examples and the emphasis is on applications to almost all areas of science and engineering. There is truly something for everyone here.this reviewer feels that it is a very hard act to follow, and recommends it strongly. [This book] is a jewel."-Applied Mechanics Review
Monotone Operators in Banach Space and Nonlinear Partial Differential EquationsThe objectives of this monograph are to present some topics from the theory of monotone operators and nonlinear semigroup theory which are directly applicable to the existence and uniqueness theory of initial-boundary-value problems for partial differential equations and to construct such operators as realizations of those problems in appropriate function spaces.
Partial Differential Equations: Sources and Solutions
Offering a welcome balance between rigor and ease of comprehension, this book presents full coverage of the analytic (and accurate) method for solving PDEs -- in a manner that is both decipherable to engineers and physically insightful for mathematicians. By exploring the eigenfunction expansion method based on physical principles instead of abstract analyses, it makes the analytic approach understandable, visualizable, and straightforward to implement. Contains tabulations and derivations of all known eigenfunction expansions.
