Differential Equations

This text provides an introductory understanding of stochastic evolution equations for those with minimal formal training in mathematics. It develops all necessary prerequisite material in real analysis, probability theory, and functional analysis. The author presents examples of 20 different models..

This is both an introductory survey on the theory and techniques of discrete dynamical systems and difference equations and a users' manual for the software package Dynamica, developed by the authors. The Dynamica package is based on the Mathematica software and is designed as a collection of tools ..

The second edition of this popular text continues to treat dynamical systems from a mathematical perspective centering on multidimensional systems of real variables. At a level accessible to beginning graduate students, it addresses the dynamics of both the iteration of functions and solutions of o..

In the 19th century, the Fourier transformation was introduced to study various problems of partial differential equations. Since 1960, this old tool has been developed into a well-organized theory called microlocal analysis that is based on the concept of the pseudo-differential operator. This book..

The index theorem is a central result of modern mathematics and all students of global analysis need to be familiar with it. This edition preserves the brevity of the first edition, but includes new material and reworkings of some of the more difficult arguments...

The index theorem continues to stand as a central result of modern mathematics. In a concise presentation that offers streamlined analyses and coverage of important examples and applications, this book introduces the ideas surrounding the heat equation proof of the Atiyah-Singer index theorem. It as..

First of three volumes containing the proceedings of the International Colloquium on Free Boundary Problems: Theory and Applications, held in Canada in June 1990. Topics covered in this volume range from combustion in porous media to controlled release of drugs by osmosis...

Presents a practical, elementary introduction to fractal geometry and chaotic dynamics - subjects that have attracted immense interest in the scientific and engineering disciplines. This book uses many illustrations to convey the concepts required for comprehension of the subject. It provides plenty..

Free Boundary Problems Involving Solids..

The second edition of this bestselling text goes even further toward a treatment that is at once gentle but rigorous, atypical yet logical, and ultimately an ideal introduction to a subject important to careers both within and outside of mathematics. The author's style remains informal and his appro..

"Provides a thorough introduction to the algebraic theory of systems of differential equations, as developed by the Japanese school of M. Sato and his colleagues. Features a complete review of hyperfunction-microfunction theory and the theory of D-modules. Strikes the perfect balance between analyti..

Employing a closed set-theoretic foundation for interval computations, Global Optimization Using Interval Analysis simplifies algorithm construction and increases generality of interval arithmetic. This Second Edition contains an up-to-date discussion of interval methods for solving systems of nonli..