MARC details
| 000 -LEADER |
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| fixed length control field |
02938nam a22002657a 4500 |
| 003 - CONTROL NUMBER IDENTIFIER |
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| control field |
OSt |
| 005 - DATE AND TIME OF LATEST TRANSACTION |
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| control field |
20250617095231.0 |
| 008 - FIXED-LENGTH DATA ELEMENTS--GENERAL INFORMATION |
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| fixed length control field |
250616b |||||||| |||| 00| 0 hin d |
| 020 ## - INTERNATIONAL STANDARD BOOK NUMBER |
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| International Standard Book Number |
9789349750630 |
| 040 ## - CATALOGING SOURCE |
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| Original cataloging agency |
NISER LIBRARY |
| Language of cataloging |
eng |
| Transcribing agency |
NISER LIBRARY |
| 082 ## - DEWEY DECIMAL CLASSIFICATION NUMBER |
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| Classification number |
519.2 |
| Item number |
LAW-R |
| 100 ## - MAIN ENTRY--PERSONAL NAME |
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| Personal name |
Lawler, Gregory F. |
| 245 ## - TITLE STATEMENT |
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| Title |
Random walk and the heat equation |
| 260 ## - PUBLICATION, DISTRIBUTION, ETC. (IMPRINT) |
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| Place of publication, distribution, etc. |
India : |
| Name of publisher, distributor, etc. |
Universities Press, |
| Date of publication, distribution, etc. |
2025. |
| 300 ## - PHYSICAL DESCRIPTION |
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| Extent |
ix, 156 p. : |
| Other physical details |
ill. ; |
| Dimensions |
22 cm. |
| 490 ## - SERIES STATEMENT |
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| Series statement |
Student mathematical library ; |
| Volume/sequential designation |
v. 55 |
| 504 ## - BIBLIOGRAPHY, ETC. NOTE |
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| Bibliography, etc |
Includes bibliographical references. |
| 520 ## - SUMMARY, ETC. |
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| Summary, etc. |
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.<br/><br/>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.<br/><br/>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. |
| 521 ## - TARGET AUDIENCE NOTE |
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| Target audience note |
Readership: Undergraduate students interested in probability and connections between probability and classical analysis. |
| 650 ## - SUBJECT ADDED ENTRY--TOPICAL TERM |
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| Topical term or geographic name as entry element |
Random walks (Mathematics) |
| 650 ## - SUBJECT ADDED ENTRY--TOPICAL TERM |
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| Topical term or geographic name as entry element |
Heat equation |
| 856 ## - ELECTRONIC LOCATION AND ACCESS |
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| Materials specified |
Table of Contents |
| Uniform Resource Identifier |
<a href="https://www.ams.org/bookstore/pspdf/stml-55-toc.pdf?_gl=1*ygvj0b*_ga*NzkyMDE0ODczLjE3NTAwNDYzMjU.*_ga_26G4XFTR63*czE3NTAxMzI2MzckbzIkZzEkdDE3NTAxMzM3MjEkajUyJGwwJGgw">https://www.ams.org/bookstore/pspdf/stml-55-toc.pdf?_gl=1*ygvj0b*_ga*NzkyMDE0ODczLjE3NTAwNDYzMjU.*_ga_26G4XFTR63*czE3NTAxMzI2MzckbzIkZzEkdDE3NTAxMzM3MjEkajUyJGwwJGgw</a> |
| 856 ## - ELECTRONIC LOCATION AND ACCESS |
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| Materials specified |
Reviews |
| Uniform Resource Identifier |
<a href="https://www.goodreads.com/book/show/11261817-random-walk-and-the-heat-equation-student-mathematical-library?ref=nav_sb_ss_1_33#CommunityReviews">https://www.goodreads.com/book/show/11261817-random-walk-and-the-heat-equation-student-mathematical-library?ref=nav_sb_ss_1_33#CommunityReviews</a> |
| 942 ## - ADDED ENTRY ELEMENTS (KOHA) |
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| Source of classification or shelving scheme |
Universal Decimal Classification |
| Koha item type |
NBHM Books |
