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Applied partial differential equations

Logan, J. David.

Applied partial differential equations

紀錄類型:	書目-電子資源 : Monograph/item
正題名/作者:	Applied partial differential equationsby J. David Logan.
作者:	Logan, J. David.
出版者:	Cham :Springer International Publishing :2015.
面頁冊數:	xi, 289 p. :ill., digital ;24 cm.
Contained By:	Springer eBooks
標題:	Differential equations, Partial.
電子資源:	http://dx.doi.org/10.1007/978-3-319-12493-3
ISBN:	9783319124933 (electronic bk.)

Applied partial differential equations
Logan, J. David.

Applied partial differential equations[electronic resource] /by J. David Logan. - 3rd ed. - Cham :Springer International Publishing :2015. - xi, 289 p. :ill., digital ;24 cm. - Undergraduate texts in mathematics,0172-6056. - Undergraduate texts in mathematics..

Preface to the Third Edition -- To the 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 -- 2.6 Laplace Transforms -- 2.7 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 inb 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 -- References -- Appendix A. Ordinary Differential Equations -- Index.

This text presents the standard material usually covered in a one-semester, undergraduate course on boundary value problems and PDEs. Emphasis is placed on motivation, concepts, methods, and interpretation, rather than on formal theory. 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. Methods include eigenfunction expansions, integral transforms, and characteristics. 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. 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. The exposition is presented in a friendly, easy-to-read, style, with mathematical ideas motivated from physical problems. Many exercises and worked examples have been added to this edition. Prerequisites include calculus and ordinary differential equations. 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. Two additional chapters include short introductions to applications of PDEs in biology and a new chapter to the computation of solutions. A brief appendix reviews techniques from ordinary differential equations. 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. The material is standard Strong emphasis is put on modeling and applications throughout; the main text is supplied with many examples and exercises. R. Steinbauer, Monatshefte fur Mathematik, Vol. 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. 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. 74, 2008

ISBN: 9783319124933 (electronic bk.)

Standard No.: 10.1007/978-3-319-12493-3doiSubjects--Topical Terms:

189753
Differential equations, Partial.

LC Class. No.: QA377

Dewey Class. No.: 515.353

Applied partial differential equations
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