LEADER 04082nam 22005655 450 001 9911007357203321 005 20250522130257.0 010 $a3-662-70890-6 024 7 $a10.1007/978-3-662-70890-3 035 $a(MiAaPQ)EBC32128683 035 $a(Au-PeEL)EBL32128683 035 $a(CKB)38874967000041 035 $a(DE-He213)978-3-662-70890-3 035 $a(EXLCZ)9938874967000041 100 $a20250522d2025 u| 0 101 0 $aeng 135 $aurcnu|||||||| 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 10$aNumerical Mathematics 3x9 $eThree subject areas in 27 short chapters /$fby Sören Bartels 205 $a1st ed. 2025. 210 1$aBerlin, Heidelberg :$cSpringer Berlin Heidelberg :$cImprint: Springer,$d2025. 215 $a1 online resource (734 pages) 225 1 $aLa Matematica per il 3+2,$x2038-5757 ;$v160 311 08$a3-662-70889-2 327 $aPrologue ? Why Numerics? -- Part I Numerical Linear Algebra -- Part II Numerical Analysis -- Part III Numerics for Differential Equations -- Part IV Problems and Projects -- Part V Supplementary Material. 330 $aNumerical Mathematics 3x9 This book provides an introduction to methods for practically solving mathematical problems, such as solving systems of linear equations, determining eigenvalues, approximating and integrating functions, solving nonlinear equations, and the approximate solution of ordinary differential equations. It consists of three parts: ? Systems of linear equations, eigenvalue problems and optimisation ? Interpolation, quadrature and nonlinear equations ? Initial value problems and Hamiltonian systems Each of these parts is divided into nine short chapters and corresponds approximately to the scope of a two-hour lecture over one semester. Basic knowledge of linear algebra and analysis as well as elementary programming experience are assumed. Results of analysis are only used in the second and third part of the book. Learning objectives, self-assessment tests and exemplary applications at the end of each chapter are intended to deepen the understanding of the presented material. The last chapters of the book contain extensive collections of exercises, detailed descriptions for programming projects, introductions to the programming languages MATLAB, C++ and Python, compilations of the most important results from linear algebra and analysis, some example programs, a list of further topics as well as detailed literature references. The book is aimed at undergraduate students of mathematics as well as engineering and natural sciences. The Author Sören Bartels is Professor of Applied Mathematics at the Albert-Ludwigs Universität in Freiburg, Germany. His primary research interest is in the development and analysis of approximation schemes for nonlinear partial differential equations with applications in the simulation of modern materials. Professor Bartels has published the Springer textbook ?Numerical approximation of partial differential equations? and the monograph ?Numerical methods for nonlinear partial differential equations? in the Springer Series in Computational Mathematics. The translation of this book was done with the help of artificial intelligence. A subsequent human revision was done primarily in terms of content. 410 0$aLa Matematica per il 3+2,$x2038-5757 ;$v160 606 $aNumerical analysis 606 $aAlgebras, Linear 606 $aDifferential equations 606 $aNumerical Analysis 606 $aLinear Algebra 606 $aDifferential Equations 615 0$aNumerical analysis. 615 0$aAlgebras, Linear. 615 0$aDifferential equations. 615 14$aNumerical Analysis. 615 24$aLinear Algebra. 615 24$aDifferential Equations. 676 $a518 700 $aBartels$b Sören$0755547 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9911007357203321 996 $aNumerical Mathematics 3x9$94390474 997 $aUNINA