000 03891nam a22005775i 4500
001 978-94-017-9816-7
003 DE-He213
005 20200420220222.0
007 cr nn 008mamaa
008 150226s2015 ne | s |||| 0|eng d
020 _a9789401798167
_9978-94-017-9816-7
024 7 _a10.1007/978-94-017-9816-7
_2doi
050 4 _aQA76.87
072 7 _aPBWH
_2bicssc
072 7 _aMAT003000
_2bisacsh
082 0 4 _a519
_223
100 1 _aYadav, Neha.
_eauthor.
245 1 3 _aAn Introduction to Neural Network Methods for Differential Equations
_h[electronic resource] /
_cby Neha Yadav, Anupam Yadav, Manoj Kumar.
264 1 _aDordrecht :
_bSpringer Netherlands :
_bImprint: Springer,
_c2015.
300 _aXIII, 114 p. 21 illus.
_bonline resource.
336 _atext
_btxt
_2rdacontent
337 _acomputer
_bc
_2rdamedia
338 _aonline resource
_bcr
_2rdacarrier
347 _atext file
_bPDF
_2rda
490 1 _aSpringerBriefs in Applied Sciences and Technology,
_x2191-530X
505 0 _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.
520 _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.
650 0 _aMathematics.
650 0 _aDifferential equations.
650 0 _aNeural networks (Computer science).
650 0 _aComputer mathematics.
650 0 _aPhysics.
650 0 _aApplied mathematics.
650 0 _aEngineering mathematics.
650 1 4 _aMathematics.
650 2 4 _aMathematical Models of Cognitive Processes and Neural Networks.
650 2 4 _aOrdinary Differential Equations.
650 2 4 _aNumerical and Computational Physics.
650 2 4 _aAppl.Mathematics/Computational Methods of Engineering.
650 2 4 _aComputational Mathematics and Numerical Analysis.
700 1 _aYadav, Anupam.
_eauthor.
700 1 _aKumar, Manoj.
_eauthor.
710 2 _aSpringerLink (Online service)
773 0 _tSpringer eBooks
776 0 8 _iPrinted edition:
_z9789401798150
830 0 _aSpringerBriefs in Applied Sciences and Technology,
_x2191-530X
856 4 0 _uhttp://dx.doi.org/10.1007/978-94-017-9816-7
912 _aZDB-2-ENG
942 _cEBK
999 _c51958
_d51958