Random walk and the heat equation (Record no. 4301)
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| 000 -LEADER | |
|---|---|
| fixed length control field | 02832nam a22003137a 4500 |
| 003 - CONTROL NUMBER IDENTIFIER | |
| control field | OSt |
| 005 - DATE AND TIME OF LATEST TRANSACTION | |
| control field | 20250801164235.0 |
| 008 - FIXED-LENGTH DATA ELEMENTS--GENERAL INFORMATION | |
| fixed length control field | 250801b |||||||| |||| 00| 0 eng d |
| 020 ## - INTERNATIONAL STANDARD BOOK NUMBER | |
| International Standard Book Number | 9780821848296 |
| 020 ## - INTERNATIONAL STANDARD BOOK NUMBER | |
| International Standard Book Number | 9789349750630 (pbk.) |
| Terms of availability | $ 59.00 |
| 040 ## - CATALOGING SOURCE | |
| Language of cataloging | ENG |
| Transcribing agency | IISER-BPR |
| Modifying agency | IISER-BPR |
| 041 ## - LANGUAGE CODE | |
| Language code of text/sound track or separate title | ENG |
| 082 ## - DEWEY DECIMAL CLASSIFICATION NUMBER | |
| Classification number | 519.282 |
| Item number | LAW |
| Edition number | 23rd |
| 100 ## - MAIN ENTRY--PERSONAL NAME | |
| Personal name | Lawler, Gregory F. |
| 9 (RLIN) | 5572 |
| 222 ## - KEY TITLE | |
| Key title | Mathematics |
| 245 ## - TITLE STATEMENT | |
| Title | Random walk and the heat equation |
| 250 ## - EDITION STATEMENT | |
| Edition statement | 1st Indian ed. |
| 260 ## - PUBLICATION, DISTRIBUTION, ETC. (IMPRINT) | |
| Place of publication, distribution, etc | Rhode Island : |
| Name of publisher, distributor, etc | American Mathematical Society, |
| Date of publication, distribution, etc | c2010. |
| 260 ## - PUBLICATION, DISTRIBUTION, ETC. (IMPRINT) | |
| Place of publication, distribution, etc | Hyderabad : |
| Name of publisher, distributor, etc | University Press (India) Pvt. Ltd., |
| Date of publication, distribution, etc | 2025. |
| 300 ## - PHYSICAL DESCRIPTION | |
| Extent | ix, 156 p. : |
| Other physical details | ill. ; |
| Dimensions | 22cm. |
| 440 ## - SERIES STATEMENT/ADDED ENTRY--TITLE | |
| Title | Student Mathematical Library |
| Volume number/sequential designation | Vol. 55 |
| 9 (RLIN) | 3204 |
| 504 ## - BIBLIOGRAPHY, ETC. NOTE | |
| Bibliography, etc | Includes illustrations. |
| 520 ## - SUMMARY, ETC. | |
| 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.<br/><br/>Readership: Undergraduate students interested in probability and connections between probability and classical analysis. |
| 650 ## - SUBJECT ADDED ENTRY--TOPICAL TERM | |
| Topical term or geographic name as entry element | Mathematics |
| 650 ## - SUBJECT ADDED ENTRY--TOPICAL TERM | |
| Topical term or geographic name as entry element | Probabilities |
| 9 (RLIN) | 2096 |
| 650 ## - SUBJECT ADDED ENTRY--TOPICAL TERM | |
| Topical term or geographic name as entry element | Random walks |
| 9 (RLIN) | 5573 |
| 650 ## - SUBJECT ADDED ENTRY--TOPICAL TERM | |
| Topical term or geographic name as entry element | Heat equation |
| 9 (RLIN) | 5574 |
| 942 ## - ADDED ENTRY ELEMENTS (KOHA) | |
| Source of classification or shelving scheme | Dewey Decimal Classification |
| Koha item type | Books |
| Withdrawn status | Lost status | Source of classification or shelving scheme | Damaged status | Not for loan | Home library | Current library | Date acquired | Source of acquisition | Cost, normal purchase price | Total Checkouts | Full call number | Barcode | Date last seen | Cost, replacement price | Price effective from | Koha item type | Public note |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Dewey Decimal Classification | Vigyanpuri Campus | Vigyanpuri Campus | 25/07/2025 | National Board for Higher Mathematics | 0.00 | 519.282 LAW | M00109 | 01/08/2025 | 5105.00 | 25/07/2025 | Books | Acquired through NBHM Library Grant 2025-2026. |
