Warriors B2G1 Free
 
 

Special Offers see all

Enter to WIN a $100 Credit

Subscribe to PowellsBooks.news
for a chance to win.
Privacy Policy

Visit our stores


    Recently Viewed clear list


    Q&A | May 11, 2015

    Heidi Pitlor: IMG Powell’s Q&A: Heidi Pitlor



    Describe your latest book. My novel, The Daylight Marriage, is about a wife and mother who goes missing one day. The narrative alternates between... Continue »
    1. $17.47 Sale Hardcover add to wish list

      The Daylight Marriage

      Heidi Pitlor 9781616203689

    spacer

This item may be
out of stock.

Click on the button below to search for this title in other formats.


Check for Availability
Add to Wishlist

Random Walk and the Heat Equation

Random Walk and the Heat Equation Cover

 

Synopses & Reviews

Publisher Comments:

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 and 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 equations 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. This 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.

Book News Annotation:

Written primarily for advanced undergraduates intending to pursue graduate studies, this book presents the study of heat equations from a probabilistic perspective. Lawler (mathematics, U. of Chicago) aims to merge the more common deterministic equations with probabilistic models based on individual random particles. Propositions and proofs make up each chapter, followed by exercises. The work contains no index or references, but does have a list of suggested further reading. Annotation ©2011 Book News, Inc., Portland, OR (booknews.com)

Synopsis:

Written primarily for advanced undergraduates intending to pursue graduate studies, this book presents the study of heat equations from a probabilistic perspective. Lawler (mathematics, U. of Chicago) aims to merge the more common deterministic equations with probabilistic models based on individual random particles. Propositions and proofs make up each chapter, followed by exercises. The work contains no index or references, but does have a list of suggested further reading. Annotation ©2011 Book News, Inc., Portland, OR (booknews.com)

Product Details

ISBN:
9780821848296
Publisher:
Amer Mathematical Society
Subject:
Heat equation.
Publication Date:
2010-12-09
Binding:
Paperback
Grade Level:
SG
Language:
English

Related Subjects


Science and Mathematics » Mathematics » Geometry » Geometry and Trigonometry
Science and Mathematics » Mathematics » Probability and Statistics » General
Science and Mathematics » Mathematics » Probability and Statistics » Probability Theory
Science and Mathematics » Mathematics » Probability and Statistics » Statistics

Random Walk and the Heat Equation
0 stars - 0 reviews
$ In Stock
Product details pages Amer Mathematical Society - English 9780821848296 Reviews:
"Synopsis" by , Written primarily for advanced undergraduates intending to pursue graduate studies, this book presents the study of heat equations from a probabilistic perspective. Lawler (mathematics, U. of Chicago) aims to merge the more common deterministic equations with probabilistic models based on individual random particles. Propositions and proofs make up each chapter, followed by exercises. The work contains no index or references, but does have a list of suggested further reading. Annotation ©2011 Book News, Inc., Portland, OR (booknews.com)
spacer
spacer
  • back to top

FOLLOW US ON...

     
Powell's City of Books is an independent bookstore in Portland, Oregon, that fills a whole city block with more than a million new, used, and out of print books. Shop those shelves — plus literally millions more books, DVDs, and gifts — here at Powells.com.