LEADER 05564nam 22008775 450 001 9910300159103321 005 20200704192410.0 010 $a81-322-1835-3 024 7 $a10.1007/978-81-322-1835-7 035 $a(CKB)3710000000106803 035 $a(Springer)9788132218357 035 $a(MH)014020920-4 035 $a(SSID)ssj0001204899 035 $a(PQKBManifestationID)11696675 035 $a(PQKBTitleCode)TC0001204899 035 $a(PQKBWorkID)11191614 035 $a(PQKB)10626641 035 $a(DE-He213)978-81-322-1835-7 035 $a(MiAaPQ)EBC6312104 035 $a(MiAaPQ)EBC1731508 035 $a(Au-PeEL)EBL1731508 035 $a(CaPaEBR)ebr10969006 035 $a(OCoLC)878949741 035 $a(PPN)17831787X 035 $a(EXLCZ)993710000000106803 100 $a20140422d2014 u| 0 101 0 $aeng 135 $aurnn|008mamaa 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 12$aA First Course in Ordinary Differential Equations$b[electronic resource] $eAnalytical and Numerical Methods /$fby Martin Hermann, Masoud Saravi 205 $a1st ed. 2014. 210 1$aNew Delhi :$cSpringer India :$cImprint: Springer,$d2014. 215 $a1 online resource (XIV, 288 p. 10 illus.)$conline resource 300 $aIncludes index. 311 $a81-322-1834-5 327 $aChapter 1. Basic Concepts of Differential Equations -- Chapter 2. First-Order Differential Equations -- Chapter 3. Second-Order Differential Equations -- Chapter 4. Laplace Transforms -- Chapter 5. System of Linear Differential Equations -- Chapter 6. Power Series Solutions -- Chapter 7. Numerical Methods for Initial Value Problems -- Chapter 8. Shooting Methods for Linear Boundary -- Appendix A. Power Series -- Appendix B. Some elementary integration formulae -- Appendix C. Table of Laplace    transforms.             . 330 $aThis book presents a modern introduction to analytical and numerical techniques for solving ordinary differential equations (ODEs). Contrary to the traditional format?the theorem-and-proof format?the book is focusing on analytical and numerical methods. The book supplies a variety of problems and examples, ranging from the elementary to the advanced level, to introduce and study the mathematics of ODEs. The analytical part of the book deals with solution techniques for scalar first-order and second-order linear ODEs, and systems of linear ODEs?with a special focus on the Laplace transform, operator techniques and power series solutions. In the numerical part, theoretical and practical aspects of Runge-Kutta methods for solving initial-value problems and shooting methods for linear two-point boundary-value problems are considered. The book is intended as a primary text for courses on the theory of ODEs and numerical treatment of ODEs for advanced undergraduate and early graduate students. It is assumed that the reader has a basic grasp of elementary calculus, in particular methods of integration, and of numerical analysis. Physicists, chemists, biologists, computer scientists and engineers whose work involves solving ODEs will also find the book useful as a reference work and tool for independent study. The book has been prepared within the framework of a German?Iranian research project on mathematical methods for ODEs, which was started in early 2012. 606 $aDifferential equations 606 $aNumerical analysis 606 $aApplied mathematics 606 $aEngineering mathematics 606 $aMathematical physics 606 $aMechanics 606 $aMechanics, Applied 606 $aOrdinary Differential Equations$3https://scigraph.springernature.com/ontologies/product-market-codes/M12147 606 $aNumerical Analysis$3https://scigraph.springernature.com/ontologies/product-market-codes/M14050 606 $aApplications of Mathematics$3https://scigraph.springernature.com/ontologies/product-market-codes/M13003 606 $aMathematical Applications in the Physical Sciences$3https://scigraph.springernature.com/ontologies/product-market-codes/M13120 606 $aSolid Mechanics$3https://scigraph.springernature.com/ontologies/product-market-codes/T15010 606 $aMathematical Physics$3https://scigraph.springernature.com/ontologies/product-market-codes/M35000 615 0$aDifferential equations. 615 0$aNumerical analysis. 615 0$aApplied mathematics. 615 0$aEngineering mathematics. 615 0$aMathematical physics. 615 0$aMechanics. 615 0$aMechanics, Applied. 615 14$aOrdinary Differential Equations. 615 24$aNumerical Analysis. 615 24$aApplications of Mathematics. 615 24$aMathematical Applications in the Physical Sciences. 615 24$aSolid Mechanics. 615 24$aMathematical Physics. 676 $a515.352 700 $aHermann$b Martin$4aut$4http://id.loc.gov/vocabulary/relators/aut$0721182 702 $aSaravi$b Masoud$4aut$4http://id.loc.gov/vocabulary/relators/aut 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910300159103321 996 $aA First Course in Ordinary Differential Equations$92509321 997 $aUNINA 999 $aThis Record contains information from the Harvard Library Bibliographic Dataset, which is provided by the Harvard Library under its Bibliographic Dataset Use Terms and includes data made available by, among others the Library of Congress