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BL
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| Record Number
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809848
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| Doc. No
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b623864
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| Main Entry
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Logan, J. David, (John David)
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| Title & Author
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Applied partial differential equations /\ J. David Logan.
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| Edition Statement
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Third edition.
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| Series Statement
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Undergraduate texts in mathematics
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| Page. NO
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1 online resource (x, 289 pages) :: illustrations
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| ISBN
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9783319124933
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: 3319124935
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: 3319124927
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: 9783319124926
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9783319124926
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| Bibliographies/Indexes
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Includes bibliographical references and index.
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| Contents
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Intro; Contents; Preface to the Third Edition; To Students; 1 The Physical Origins of Partial Differential Equations; 1.1 PDE Models; 1.2 Conservation Laws; 1.3 Diffusion; 1.4 Diffusion and Randomness; 1.5 Vibrations and Acoustics; 1.6 Quantum Mechanics*; 1.7 Heat Conduction in Higher Dimensions; 1.8 Laplace's Equation; 1.9 Classification of PDEs; 2 Partial Differential Equations on Unbounded Domains; 2.1 Cauchy Problem for the Heat Equation; 2.2 Cauchy Problem for the Wave Equation; 2.3 Well-Posed Problems; 2.4 Semi-Infinite Domains; 2.5 Sources and Duhamel's Principle
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2.6 Laplace Transforms2.7 Fourier Transforms; 3 Orthogonal Expansions; 3.1 The Fourier Method; 3.2 Orthogonal Expansions; 3.3 Classical Fourier Series; 4 Partial Differential Equations on Bounded Domains; 4.1 Overview of Separation of Variables; 4.2 Sturm-Liouville Problems; 4.3 Generalization and Singular Problems; 4.4 Laplace's Equation; 4.5 Cooling of a Sphere; 4.6 Diffusion in a Disk; 4.7 Sources on Bounded Domains; 4.8 Poisson's Equation*; 5 Applications in the Life Sciences; 5.1 Age-Structured Models; 5.2 Traveling Waves Fronts; 5.3 Equilibria and Stability
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6 Numerical Computation of Solutions6.1 Finite Difference Approximations; 6.2 Explicit Scheme for the Heat Equation; 6.3 Laplace's Equation; 6.4 Implicit Scheme for the Heat Equation; A Differential Equations; References; Index
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| Abstract
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This text presents the standard material usually covered in a one-semester, undergraduate course on boundary value problems and PDEs.
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Emphasis is placed on motivation, concepts, methods, and interpretation, rather than on formal theory.
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The concise treatment of the subject is maintained in this third edition covering all the major ideas: the wave equation, the diffusion equation, the Laplace equation, and the advection equation on bounded and unbounded domains.
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Methods include eigenfunction expansions, integral transforms, and characteristics.
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In this third edition, text remains intimately tied to applications in heat transfer, wave motion, biological systems, and a variety other topics in pure and applied science.
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The text offers flexibility to instructors who, for example, may wish to insert topics from biology or numerical methods at any time in the course.
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The exposition is presented in a friendly, easy-to-read, style, with mathematical ideas motivated from physical problems.
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Many exercises and worked examples have been added to this edition.
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Prerequisites include calculus and ordinary differential equations.
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A student who reads this book and works many of the exercises will have a sound knowledge for a second course in partial differential equations or for courses in advanced engineering and science.
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Two additional chapters include short introductions to applications of PDEs in biology and a new chapter to the computation of solutions.
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A brief appendix reviews techniques from ordinary differential equations.
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From the reviews of the second edition: "This second edition of the short undergraduate text provides a fist course in PDE aimed at students in mathematics, engineering and the sciences.
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The material is standard ... Strong emphasis is put on modeling and applications throughout; the main text is supplied with many examples and exercises." -R.
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Steinbauer, Monatshefte für Mathematik, Vol.
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150 (4), 2007 "This is a unique book in the sense that it provides a coverage of the main topics of the subject in a concise style which is accessible to science and engineering students.
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... Reading this book and solving the problems, the students will have a solid base for a course in partial differential equations ... ." -Tibor Krisztin, Acta Scientiarum Mathematicarum, Vol.
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74, 2008.
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| Subject
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Differential equations, Partial.
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| Subject
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Mathematics.
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| Subject
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Differential equations, Partial.
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| Dewey Classification
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515/.353
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| LC Classification
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QA377
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