Differential Equations With Maple

Measure and integration wereonceconsidered,especially by many ofthe more practically inclined, to be an esoteric area ofabstract mathematics best left to pure mathematicians. However,it has become increasingly obvious in recent years that this area is now an indispensable, even unavoidable, language and provides a fundamental methodology for modern probability theory, stochas­ tic analysis and their applications, especially in financial mathematics. Our aim in writing this book is to provide a smooth and fast introduction to the language and basic results ofmodern probability theory and stochastic differential equations with help ofthe computer manipulator software package MAPLE. It is intended for advanced undergraduate students or graduates, not necessarily in mathematics, to provide an overviewand intuitive background for more advanced studies as wellas somepractical skillsin the use of MAPLE software in the context of probability and its applications. This book is not a conventional mathematics book. Like such books it provides precise definitions and mathematical statements, particularly those based on measure and integration theory, but instead ofmathematical proofs it uses numerous MAPLE experiments and examples to help the reader un­ derstand intuitively the ideas under discussion. The pace increases from ex­ tensive and detailed explanations in the first chapters to a more advanced presentation in the latter part of the book. The MAPLE is handled in a sim­ ilar way, at first with simple commands, then some simple procedures are gardually developed and, finally, the stochastic package is introduced.

The emphasis of this work is on constructing different types of solutions (exact, approximate analytical, numerical, graphical) of numerous nonlinear PDEs correctly, easily, and quickly. The reader can learn a wide variety of techniques and solve numerous nonlinear PDEs included and many other differential equations, simplifying and transforming the equations and solutions, arbitrary functions and parameters, presented in the book).