LEADER 05462nam 22005775 450 001 9910299780603321 005 20230803165118.0 010 $a3-319-12493-5 024 7 $a10.1007/978-3-319-12493-3 035 $a(CKB)3710000000325004 035 $a(SSID)ssj0001408177 035 $a(PQKBManifestationID)11901241 035 $a(PQKBTitleCode)TC0001408177 035 $a(PQKBWorkID)11346378 035 $a(PQKB)11444538 035 $a(DE-He213)978-3-319-12493-3 035 $a(MiAaPQ)EBC6314062 035 $a(MiAaPQ)EBC5587359 035 $a(Au-PeEL)EBL5587359 035 $a(OCoLC)898276719 035 $a(PPN)183153170 035 $a(EXLCZ)993710000000325004 100 $a20141205d2015 u| 0 101 0 $aeng 135 $aurnn#008mamaa 181 $ctxt 182 $cc 183 $acr 200 10$aApplied Partial Differential Equations$b[electronic resource] /$fby J. David Logan 205 $a3rd ed. 2015. 210 1$aCham :$cSpringer International Publishing :$cImprint: Springer,$d2015. 215 $a1 online resource (XI, 289 p. 51 illus., 6 illus. in color.) 225 1 $aUndergraduate Texts in Mathematics,$x0172-6056 300 $aBibliographic Level Mode of Issuance: Monograph 311 08$a3-319-12492-7 327 $aPreface 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. . 330 $aThis 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 für 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. 410 0$aUndergraduate Texts in Mathematics,$x0172-6056 606 $aDifferential equations, Partial 606 $aMathematics 615 0$aDifferential equations, Partial. 615 0$aMathematics. 676 $a515.353 700 $aLogan$b J. David$g(John David),$4aut$4http://id.loc.gov/vocabulary/relators/aut$048876 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910299780603321 996 $aApplied partial differential equations$9319414 997 $aUNINA