The One-Dimensional Heat Equation PDF Download
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Author: John Rozier Cannon
Publisher: Cambridge University Press
ISBN: 9780521302432
Category : Mathematics
Languages : en
Pages : 522
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Book Description
This is a version of Gevrey's classical treatise on the heat equations. Included in this volume are discussions of initial and/or boundary value problems, numerical methods, free boundary problems and parameter determination problems. The material is presented as a monograph and/or information source book. After the first six chapters of standard classical material, each chapter is written as a self-contained unit except for an occasional reference to elementary definitions, theorems and lemmas in previous chapters.
Author: John Rozier Cannon
Publisher: Cambridge University Press
ISBN: 9780521302432
Category : Mathematics
Languages : en
Pages : 522
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Book Description
This is a version of Gevrey's classical treatise on the heat equations. Included in this volume are discussions of initial and/or boundary value problems, numerical methods, free boundary problems and parameter determination problems. The material is presented as a monograph and/or information source book. After the first six chapters of standard classical material, each chapter is written as a self-contained unit except for an occasional reference to elementary definitions, theorems and lemmas in previous chapters.
Author: D. V. Widder
Publisher: Academic Press
ISBN: 0080873839
Category : Science
Languages : en
Pages : 285
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Book Description
The Heat Equation
Author: Jiri Lebl
Publisher:
ISBN: 9781706230236
Category :
Languages : en
Pages : 468
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Book Description
Version 6.0. An introductory course on differential equations aimed at engineers. The book covers first order ODEs, higher order linear ODEs, systems of ODEs, Fourier series and PDEs, eigenvalue problems, the Laplace transform, and power series methods. It has a detailed appendix on linear algebra. The book was developed and used to teach Math 286/285 at the University of Illinois at Urbana-Champaign, and in the decade since, it has been used in many classrooms, ranging from small community colleges to large public research universities. See https: //www.jirka.org/diffyqs/ for more information, updates, errata, and a list of classroom adoptions.
Author: Gregory F. Lawler
Publisher: American Mathematical Soc.
ISBN: 0821848291
Category : Mathematics
Languages : en
Pages : 170
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Book Description
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.
Author: Bill Goodwine
Publisher: Springer Science & Business Media
ISBN: 1441979190
Category : Mathematics
Languages : en
Pages : 762
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Book Description
This book is a comprehensive treatment of engineering undergraduate differential equations as well as linear vibrations and feedback control. While this material has traditionally been separated into different courses in undergraduate engineering curricula. This text provides a streamlined and efficient treatment of material normally covered in three courses. Ultimately, engineering students study mathematics in order to be able to solve problems within the engineering realm. Engineering Differential Equations: Theory and Applications guides students to approach the mathematical theory with much greater interest and enthusiasm by teaching the theory together with applications. Additionally, it includes an abundance of detailed examples. Appendices include numerous C and FORTRAN example programs. This book is intended for engineering undergraduate students, particularly aerospace and mechanical engineers and students in other disciplines concerned with mechanical systems analysis and control. Prerequisites include basic and advanced calculus with an introduction to linear algebra.
Author: Walter Gander
Publisher: Springer Science & Business Media
ISBN: 364297533X
Category : Mathematics
Languages : en
Pages : 268
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Book Description
Modern computing tools like Maple (symbolic computation) and Matlab (a numeric computation and visualization program) make it possible to easily solve realistic nontrivial problems in scientific computing. In education, traditionally, complicated problems were avoided, since the amount of work for obtaining the solutions was not feasible for the students. This situation has changed now, and the students can be taught real-life problems that they can actually solve using the new powerful software. The reader will improve his knowledge through learning by examples and he will learn how both systems, MATLAB and MAPLE, may be used to solve problems interactively in an elegant way. Readers will learn to solve similar problems by understanding and applying the techniques presented in the book. All programs used in the book are available to the reader in electronic form.
Author: David W. Hahn
Publisher: John Wiley & Sons
ISBN: 1118330110
Category : Science
Languages : en
Pages : 754
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Book Description
HEAT CONDUCTION Mechanical Engineering THE LONG-AWAITED REVISION OF THE BESTSELLER ON HEAT CONDUCTION Heat Conduction, Third Edition is an update of the classic text on heat conduction, replacing some of the coverage of numerical methods with content on micro- and nanoscale heat transfer. With an emphasis on the mathematics and underlying physics, this new edition has considerable depth and analytical rigor, providing a systematic framework for each solution scheme with attention to boundary conditions and energy conservation. Chapter coverage includes: Heat conduction fundamentals Orthogonal functions, boundary value problems, and the Fourier Series The separation of variables in the rectangular coordinate system The separation of variables in the cylindrical coordinate system The separation of variables in the spherical coordinate system Solution of the heat equation for semi-infinite and infinite domains The use of Duhamel’s theorem The use of Green’s function for solution of heat conduction The use of the Laplace transform One-dimensional composite medium Moving heat source problems Phase-change problems Approximate analytic methods Integral-transform technique Heat conduction in anisotropic solids Introduction to microscale heat conduction In addition, new capstone examples are included in this edition and extensive problems, cases, and examples have been thoroughly updated. A solutions manual is also available. Heat Conduction is appropriate reading for students in mainstream courses of conduction heat transfer, students in mechanical engineering, and engineers in research and design functions throughout industry.
Author: Walter A. Strauss
Publisher: John Wiley & Sons
ISBN: 0470054565
Category : Mathematics
Languages : en
Pages : 467
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Book Description
Our understanding of the fundamental processes of the natural world is based to a large extent on partial differential equations (PDEs). The second edition of Partial Differential Equations provides an introduction to the basic properties of PDEs and the ideas and techniques that have proven useful in analyzing them. It provides the student a broad perspective on the subject, illustrates the incredibly rich variety of phenomena encompassed by it, and imparts a working knowledge of the most important techniques of analysis of the solutions of the equations. In this book mathematical jargon is minimized. Our focus is on the three most classical PDEs: the wave, heat and Laplace equations. Advanced concepts are introduced frequently but with the least possible technicalities. The book is flexibly designed for juniors, seniors or beginning graduate students in science, engineering or mathematics.
Author: Svein Linge
Publisher: Springer
ISBN: 3319324284
Category : Computers
Languages : en
Pages : 244
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Book Description
This book presents computer programming as a key method for solving mathematical problems. There are two versions of the book, one for MATLAB and one for Python. The book was inspired by the Springer book TCSE 6: A Primer on Scientific Programming with Python (by Langtangen), but the style is more accessible and concise, in keeping with the needs of engineering students. The book outlines the shortest possible path from no previous experience with programming to a set of skills that allows the students to write simple programs for solving common mathematical problems with numerical methods in engineering and science courses. The emphasis is on generic algorithms, clean design of programs, use of functions, and automatic tests for verification.
Author: Denis Maillet
Publisher:
ISBN:
Category : Mathematics
Languages : en
Pages : 392
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Book Description
This superb text describes a novel and powerful method for allowing design engineers to firstly model a linear problem in heat conduction, then build a solution in an explicit form and finally obtain a numerical solution. It constitutes a modelling and calculation tool based on a very efficient and systemic methodological approach. Solving the heat equations through integral transforms does not constitute a new subject. However, finding a solution generally constitutes only one part of the problem. In design problems, an initial thermal design has to be tested through the calculation of the temperature or flux field, followed by an analysis of this field in terms of constraints. A modified design is then proposed, followed by a new thermal field calculation, and so on until the right design is found. The thermal quadrupole method allows this often painful iterative procedure to be removed by allowing only one calculation. The chapters in this book increase in complexity from a rapid presentation of the method for one dimensional transient problems in chapter one, to non uniform boundary conditions or inhomogeneous media in chapter six. In addition, a wide range of corrected problems of contemporary interest are presented mainly in chapters three and six with their numerical implementation in MATLAB (r) language. This book covers the whole scope of linear problems and presents a wide range of concrete issues of contemporary interest such as harmonic excitations of buildings, transfer in composite media, thermal contact resistance and moving material heat transfer. Extensions of this method to coupled transfers in a semi-transparent medium and to mass transfer in porous media are considered respectively in chapters seven and eight. Chapter nine is devoted to practical numerical methods that can be used to inverse the Laplace transform. Written from an engineering perspective, with applications to real engineering problems, this book will be of significant interest not only to researchers, lecturers and graduate students in mechanical engineering (thermodynamics) and process engineers needing to model a heat transfer problem to obtain optimized operating conditions, but also to researchers interested in the simulation or design of experiments where heat transfer play a significant role.
