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Random Walk and the Heat Equation (Student Mathematical Library) (Student Mathem
US $14.44
ApproximatelyS$ 18.63
Condition:
“Paperback. Cover and spine in good condition. Spine is tight. Pages are clean, no markings, notes ”... Read moreabout condition
Good
A book that has been read but is in good condition. Very minimal damage to the cover including scuff marks, but no holes or tears. The dust jacket for hard covers may not be included. Binding has minimal wear. The majority of pages are undamaged with minimal creasing or tearing, minimal pencil underlining of text, no highlighting of text, no writing in margins. No missing pages.
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Located in: Beaverton, Oregon, United States
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Estimated between Fri, 3 Oct and Mon, 6 Oct to 94104
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eBay item number:167821068377
Item specifics
- Condition
- Good
- Seller Notes
- Book Title
- Random Walk and the Heat Equation (Student Mathematical Librar
- ISBN
- 9780821848296
About this product
Product Identifiers
Publisher
American Mathematical Society
ISBN-10
0821848291
ISBN-13
9780821848296
eBay Product ID (ePID)
99596682
Product Key Features
Number of Pages
156 Pages
Publication Name
Random Walk and the Heat Equation
Language
English
Publication Year
2010
Subject
Differential Equations / General, Probability & Statistics / Stochastic Processes
Type
Textbook
Subject Area
Mathematics
Series
Student Mathematical Library
Format
Trade Paperback
Dimensions
Item Height
0.4 in
Item Weight
7.6 Oz
Item Length
8.5 in
Item Width
5.5 in
Additional Product Features
Intended Audience
Scholarly & Professional
LCCN
2010-031593
Dewey Edition
22
Reviews
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 an undergraduate project." - Mathematical Reviews "This is a very readable introductory course resource on topics...that have more than their fair share of unreadable textbooks...Its reader-friendly style makes it an ideal choice for a reading course or self-study. ...Given the paucity of quality books in this area, the work will be a critical resource for mathematics collections... Essential." - M. Bona, Choice
Series Volume Number
55
Illustrated
Yes
Dewey Decimal
519.2/82
Table Of Content
Preface Random walk and discrete heat equation Brownian motion and the heat equation Martingales Fractal dimension Suggestions for further reading
Synopsis
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., 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. The theme of the first two chapters of the book is the relationship between random walks and the heat equation. The first chapter discusses the discrete case, random walk and the heat equation on the integer lattice; and the second chapter discusses the continuous case, Brownian motion and the usual heat equation. Relationships are shown between the two. For example, solving the heat equation in the discrete setting becomes a problem of diagonalization of symmetric matrices, which becomes a problem in Fourier series in the continuous case. Random walk and Brownian motion are introduced and developed from first principles. The latter two chapters discuss different topics: martingales and fractal dimension, with the chapters tied together by one example, a random Cantor set. The idea of this book is to merge probabilistic and deterministic approaches to heat flow. It is also intended as a bridge from undergraduate analysis to graduate and research perspectives. The book is suitable for advanced undergraduates, particularly those considering graduate work in mathematics or related areas.
LC Classification Number
QA274.73.L385 2010
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- l***d (1162)- Feedback left by buyer.Past monthVerified purchaseA+
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