LEADER 04163nam 2200733 450 001 9910817891103321 005 20230803204633.0 010 $a3-11-037404-8 010 $a3-11-031667-6 024 7 $a10.1515/9783110316674 035 $a(CKB)3710000000229167 035 $a(EBL)1575466 035 $a(SSID)ssj0001332800 035 $a(PQKBManifestationID)11874708 035 $a(PQKBTitleCode)TC0001332800 035 $a(PQKBWorkID)11376976 035 $a(PQKB)10632806 035 $a(MiAaPQ)EBC1575466 035 $a(DE-B1597)209954 035 $a(OCoLC)900717257 035 $a(OCoLC)903960828 035 $a(DE-B1597)9783110316674 035 $a(Au-PeEL)EBL1575466 035 $a(CaPaEBR)ebr11010243 035 $a(CaONFJC)MIL783314 035 $a(OCoLC)890071012 035 $a(EXLCZ)993710000000229167 100 $a20150212h20142014 uy 0 101 0 $aeng 135 $aur|n|---||||| 181 $ctxt 182 $cc 183 $acr 200 10$aElements of partial differential equations /$fPavel Dra?bek, Gabriela Holubova? 205 $aSecond, revised and extended edition. 210 1$aBerlin, [Germany] ;$aBoston, [Massachusetts] :$cDe Gruyter,$d2014. 210 4$dİ2014 215 $a1 online resource (291 p.) 225 1 $aDe Gruyter Textbook 300 $aDescription based upon print version of record. 311 $a3-11-031665-X 320 $aIncludes bibliographical references and index. 327 $t Frontmatter -- $tPreface -- $tContents -- $tChapter 1. Motivation, Derivation of Basic Mathematical Models -- $tChapter 2. Classification, Types of Equations, Boundary and Initial Conditions -- $tChapter 3. Linear Partial Differential Equations of the First Order -- $tChapter 4. Wave Equation in One Spatial Variable - Cauchy Problem in R -- $tChapter 5. Diffusion Equation in One Spatial Variable - Cauchy Problem in R -- $tChapter 6. Laplace and Poisson Equations in Two Dimensions -- $tChapter 7. Solutions of Initial Boundary Value Problems for Evolution Equations -- $tChapter 8. Solutions of Boundary Value Problems for Stationary Equations -- $tChapter 9. Methods of Integral Transforms -- $tChapter 10. General Principles -- $tChapter 11. Laplace and Poisson equations in Higher Dimensions -- $tChapter 12. Diffusion Equation in Higher Dimensions -- $tChapter 13. Wave Equation in Higher Dimensions -- $tAppendix A. Sturm-Liouville Problem -- $tAppendix B. Bessel Functions -- $tSome Typical Problems Considered in this Book -- $tNotation -- $tBibliography -- $tIndex 330 $aThis textbook is an elementary introduction to the basic principles of partial differential equations. With many illustrations it introduces PDEs on an elementary level, enabling the reader to understand what partial differential equations are, where they come from and how they can be solved. The intention is that the reader understands the basic principles which are valid for particular types of PDEs, and to acquire some classical methods to solve them, thus the authors restrict their considerations to fundamental types of equations and basic methods. Only basic facts from calculus and linear ordinary differential equations of first and second order are needed as a prerequisite. The book is addressed to students who intend to specialize in mathematics as well as to students of physics, engineering, and economics. 410 0$aDe Gruyter textbook. 606 $aDifferential equations, Partial$vTextbooks 610 $aBoundary value problems for evolution and stationary equations. 610 $aDiffusion equation. 610 $aIntegral transforms. 610 $aLaplace and Poisson equation. 610 $aPartial differential equation. 610 $aWave equation. 615 0$aDifferential equations, Partial 676 $a515/.353 686 $aSK 540$2rvk 700 $aDra?bek$b Pavel$f1953-$042890 702 $aHolubova?$b Gabriela 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910817891103321 996 $aElements of partial differential equations$93950573 997 $aUNINA