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Books > Science & Mathematics > Mathematics > Calculus & mathematical analysis > Differential equations
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An Introduction to Fronts in Random Media (Paperback, 2009 ed.)
Loot Price: R1,417
Discovery Miles 14 170
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An Introduction to Fronts in Random Media (Paperback, 2009 ed.)
Series: Surveys and Tutorials in the Applied Mathematical Sciences, 5
Expected to ship within 10 - 15 working days
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This book aims to give a user friendly tutorial of an
interdisciplinary research topic (fronts or interfaces in random
media) to senior undergraduates and beginning grad uate students
with basic knowledge of partial differential equations (PDE) and
prob ability. The approach taken is semiformal, using elementary
methods to introduce ideas and motivate results as much as
possible, then outlining how to pursue rigor ous theorems, with
details to be found in the references section. Since the topic
concerns both differential equations and probability, and proba
bility is traditionally a quite technical subject with a heavy
measure theoretic com ponent, the book strives to develop a
simplistic approach so that students can grasp the essentials of
fronts and random media and their applications in a self contained
tutorial. The book introduces three fundamental PDEs (the Burgers
equation, Hamilton- Jacobi equations, and reaction-diffusion
equations), analysis of their formulas and front solutions, and
related stochastic processes. It builds up tools gradually, so that
students are brought to the frontiers of research at a steady pace.
A moderate number of exercises are provided to consolidate the
concepts and ideas. The main methods are representation formulas of
solutions, Laplace meth ods, homogenization, ergodic theory,
central limit theorems, large deviation princi ples, variational
principles, maximum principles, and Harnack inequalities, among
others. These methods are normally covered in separate books on
either differential equations or probability. It is my hope that
this tutorial will help to illustrate how to combine these tools in
solving concrete problems.
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