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Random Walk and the Heat Equation
Gregory F. Lawler
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Description for Random Walk and the Heat Equation
Paperback. Introducing the heat equation and the closely related notion of harmonic functions from a probabilistic perspective, this book includes chapters on: the discrete case, random walk and the heat equation on the integer lattice; the continuous case, Brownian motion and the usual heat equation; and martingales and fractal dimension. Series: Student Mathematical Library. Num Pages: 156 pages, Illustrations. BIC Classification: PBT. Category: (P) Professional & Vocational. Dimension: 222 x 143 x 13. Weight in Grams: 212.
The heat equation can be derived by averaging over a very large number of particles. Traditionally, the resulting PDE is studied as a deterministic equation, an approach that has brought many significant results and a deep understanding of the equation and its solutions. By studying the heat equation by considering the individual random particles, however, one gains further intuition into the problem. While this is now standard for many researchers, this approach is generally not presented at the undergraduate level. In this book, Lawler introduces the heat equation and the closely related notion of harmonic functions from a probabilistic perspective. ... Read more
The heat equation can be derived by averaging over a very large number of particles. Traditionally, the resulting PDE is studied as a deterministic equation, an approach that has brought many significant results and a deep understanding of the equation and its solutions. By studying the heat equation by considering the individual random particles, however, one gains further intuition into the problem. While this is now standard for many researchers, this approach is generally not presented at the undergraduate level. In this book, Lawler introduces the heat equation and the closely related notion of harmonic functions from a probabilistic perspective. ... Read more
Product Details
Format
Paperback
Publication date
2010
Publisher
American Mathematical Society United States
Number of pages
156
Condition
New
Series
Student Mathematical Library
Number of Pages
156
Place of Publication
Providence, United States
ISBN
9780821848296
SKU
V9780821848296
Shipping Time
Usually ships in 7 to 11 working days
Ref
99-1
About Gregory F. Lawler
Gregory F. Lawler, University of Chicago, Chicago, IL, USA
Reviews for Random Walk and the Heat Equation
This beautiful little book is an introduction to some of the key ideas of probability written at an advanced undergraduate level. ... This book is very well-written, self-contained up to material from elementary calculus and basic linear algebra, and has plenty of interesting exercises. It is well suited for an advanced undergraduate course, a student seminar or as material for ... Read more