LEADER 05197nam 22008175 450 001 9910299676803321 005 20200707014258.0 010 $a94-017-9816-8 024 7 $a10.1007/978-94-017-9816-7 035 $a(CKB)3710000000360463 035 $a(EBL)1998188 035 $a(OCoLC)904248956 035 $a(SSID)ssj0001452104 035 $a(PQKBManifestationID)11890637 035 $a(PQKBTitleCode)TC0001452104 035 $a(PQKBWorkID)11479644 035 $a(PQKB)10407921 035 $a(DE-He213)978-94-017-9816-7 035 $a(MiAaPQ)EBC1998188 035 $a(PPN)184495423 035 $a(EXLCZ)993710000000360463 100 $a20150226d2015 u| 0 101 0 $aeng 135 $aur|n|---||||| 181 $ctxt 182 $cc 183 $acr 200 13$aAn Introduction to Neural Network Methods for Differential Equations /$fby Neha Yadav, Anupam Yadav, Manoj Kumar 205 $a1st ed. 2015. 210 1$aDordrecht :$cSpringer Netherlands :$cImprint: Springer,$d2015. 215 $a1 online resource (124 p.) 225 1 $aSpringerBriefs in Computational Intelligence,$x2625-3704 300 $aDescription based upon print version of record. 311 $a94-017-9815-X 320 $aIncludes bibliographical references and index. 327 $aPreface -- Introduction -- 1 Overview of Differential Equations -- 2 History of Neural Networks -- 3 Preliminaries of Neural Networks -- 4 Neural Network Methods for Solving Differential Equations -- Conclusion -- Appendix -- References -- Index. 330 $aThis book introduces a variety of neural network methods for solving differential equations arising in science and engineering. The emphasis is placed on a deep understanding of the neural network techniques, which has been presented in a mostly heuristic and intuitive manner. This approach will enable the reader to understand the working, efficiency and shortcomings of each neural network technique for solving differential equations. The objective of this book is to provide the reader with a sound understanding of the foundations of neural networks, and a comprehensive introduction to neural network methods for solving differential equations together with recent developments in the techniques and their applications. The book comprises four major sections. Section I consists of a brief overview of differential equations and the relevant physical problems arising in science and engineering. Section II illustrates the history of neural networks starting from their beginnings in the 1940s through to the renewed interest of the 1980s. A general introduction to neural networks and learning technologies is presented in Section III. This section also includes the description of the multilayer perceptron and its learning methods. In Section IV, the different neural network methods for solving differential equations are introduced, including discussion of the most recent developments in the field. Advanced students and researchers in mathematics, computer science and various disciplines in science and engineering will find this book a valuable reference source. 410 0$aSpringerBriefs in Computational Intelligence,$x2625-3704 606 $aNeural networks (Computer science) 606 $aDifferential equations 606 $aPhysics 606 $aApplied mathematics 606 $aEngineering mathematics 606 $aComputer science$xMathematics 606 $aMathematical Models of Cognitive Processes and Neural Networks$3https://scigraph.springernature.com/ontologies/product-market-codes/M13100 606 $aOrdinary Differential Equations$3https://scigraph.springernature.com/ontologies/product-market-codes/M12147 606 $aNumerical and Computational Physics, Simulation$3https://scigraph.springernature.com/ontologies/product-market-codes/P19021 606 $aMathematical and Computational Engineering$3https://scigraph.springernature.com/ontologies/product-market-codes/T11006 606 $aComputational Mathematics and Numerical Analysis$3https://scigraph.springernature.com/ontologies/product-market-codes/M1400X 615 0$aNeural networks (Computer science) 615 0$aDifferential equations. 615 0$aPhysics. 615 0$aApplied mathematics. 615 0$aEngineering mathematics. 615 0$aComputer science$xMathematics. 615 14$aMathematical Models of Cognitive Processes and Neural Networks. 615 24$aOrdinary Differential Equations. 615 24$aNumerical and Computational Physics, Simulation. 615 24$aMathematical and Computational Engineering. 615 24$aComputational Mathematics and Numerical Analysis. 676 $a006.32 700 $aYadav$b Neha$4aut$4http://id.loc.gov/vocabulary/relators/aut$0720897 702 $aYadav$b Anupam$4aut$4http://id.loc.gov/vocabulary/relators/aut 702 $aKumar$b Manoj$4aut$4http://id.loc.gov/vocabulary/relators/aut 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910299676803321 996 $aAn Introduction to Neural Network Methods for Differential Equations$92497650 997 $aUNINA