LEADER 02993nam 2200577 450 001 9910483039803321 005 20220321135920.0 010 $a3-030-50284-8 024 7 $a10.1007/978-3-030-50284-3 035 $a(CKB)4100000011515651 035 $a(DE-He213)978-3-030-50284-3 035 $a(MiAaPQ)EBC6380788 035 $a(MiAaPQ)EBC6647507 035 $a(Au-PeEL)EBL6380788 035 $a(OCoLC)1202760573 035 $a(Au-PeEL)EBL6647507 035 $a(PPN)255226861 035 $a(EXLCZ)994100000011515651 100 $a20220321d2020 uy 0 101 0 $aeng 135 $aurnn|008mamaa 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 10$aTools and problems in partial differential equations /$fThomas Alazard and Claude Zuily 205 $a1st ed. 2020. 210 1$aCham, Switzerland :$cSpringer,$d[2020] 210 4$d©2020 215 $a1 online resource (XII, 357 p. 1 illus.) 225 1 $aUniversitext,$x0172-5939 311 $a3-030-50283-X 320 $aIncludes bibliographical references and index. 327 $aPart I Tools and Problems -- 1 Elements of functional analysis and distributions -- 2 Statements of the problems of Chapter 1 -- 3 Functional spaces -- 4 Statements of the problems of Chapter 3 -- 5 Microlocal analysis -- 6 Statements of the problems of Chapter 5 -- 7 The classical equations -- 8 Statements of the problems of Chapter 7 -- Part II Solutions of the Problems. A Classical results. Index. 330 $aThis textbook offers a unique learning-by-doing introduction to the modern theory of partial differential equations. Through 65 fully solved problems, the book offers readers a fast but in-depth introduction to the field, covering advanced topics in microlocal analysis, including pseudo- and para-differential calculus, and the key classical equations, such as the Laplace, Schrödinger or Navier-Stokes equations. Essentially self-contained, the book begins with problems on the necessary tools from functional analysis, distributions, and the theory of functional spaces, and in each chapter the problems are preceded by a summary of the relevant results of the theory. Informed by the authors' extensive research experience and years of teaching, this book is for graduate students and researchers who wish to gain real working knowledge of the subject. 410 0$aUniversitext,$x0172-5939 606 $aMathematical analysis 606 $aDifferential equations, Partial 606 $aFunctional analysis 615 0$aMathematical analysis. 615 0$aDifferential equations, Partial. 615 0$aFunctional analysis. 676 $a515.353 700 $aAlazard$b Thomas$0845497 702 $aZuily$b Claude$f1945- 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910483039803321 996 $aTools and Problems in Partial Differential Equations$91887570 997 $aUNINA