LEADER 03078nam 22004935 450 001 9911003592603321 005 20250521124730.0 010 $a3-031-86532-4 024 7 $a10.1007/978-3-031-86532-9 035 $a(CKB)38859286400041 035 $a(MiAaPQ)EBC32125985 035 $a(Au-PeEL)EBL32125985 035 $a(DE-He213)978-3-031-86532-9 035 $a(EXLCZ)9938859286400041 100 $a20250521d2025 u| 0 101 0 $aeng 135 $aur||||||||||| 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 10$aFundamentals of Ordinary Differential Equations /$fby Uri Elias 205 $a1st ed. 2025. 210 1$aCham :$cSpringer Nature Switzerland :$cImprint: Birkhäuser,$d2025. 215 $a1 online resource (499 pages) 311 08$a3-031-86531-6 327 $aWhat is an ordinary differential equation? -- First-order differential equations -- Existence and uniqueness theorems -- Linear equations of higher order -- Systems of differential equations -- The qualitative theory and the phase plane -- Solution of differential equations by power series -- The Laplace transform -- Appendix: The orbits of the planets -- Appendix: Historical notes. 330 $aThis textbook offers an introduction to ODEs that focuses on the qualitative behavior of differential equations rather than specialized methods for solving them. The book is organized around this approach with important topics, such as existence, uniqueness, qualitative behaviour, and stability, appearing in early chapters and explicit solution methods covered later. Proofs are included in an approachable manner, which are first motivated by describing the main ideas in a general sense before being written out in detail. A clear and accessible writing style is used, containing numerous examples and calculations throughout the text. Two appendices offer readers further material to explore, with the first using the orbits of the planets as an illustrative example and the second providing insightful historical notes. After reading this book, students will have a strong foundation for a course in PDEs or mathematical modeling. Fundamentals of Ordinary Differential Equations is suitable for an undergraduate course for students who have taken basic calculus and linear algebra courses, and who are able to read and write basic proofs. Because of its detailed approach, it is also conducive to self-study. 606 $aDifferential equations 606 $aMathematical analysis 606 $aDifferential Equations 606 $aIntegral Transforms and Operational Calculus 615 0$aDifferential equations. 615 0$aMathematical analysis. 615 14$aDifferential Equations. 615 24$aIntegral Transforms and Operational Calculus. 676 $a515.35 700 $aElias$b Uri$01820014 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9911003592603321 996 $aFundamentals of Ordinary Differential Equations$94381090 997 $aUNINA