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＜電子ブック＞
Perturbation Methods, Bifurcation Theory and Computer Algebra / by Richard H. Rand, Dieter Armbruster
(Applied Mathematical Sciences. ISSN:2196968X ; 65)

版	1st ed. 1987.
出版者	New York, NY : Springer New York : Imprint: Springer
出版年	1987
本文言語	英語
大きさ	IX, 251 p. 1 illus : online resource
冊子体	Perturbation methods, bifurcation theory and computer algebra / Richard H. Rand, Dieter Armbruster ; : us,: gw
著者標目	*Rand, Richard H author Armbruster, Dieter author SpringerLink (Online service)
件　名	LCSH:Mathematical analysis LCSH:Mathematical physics FREE:Analysis FREE:Theoretical, Mathematical and Computational Physics
一般注記	1 Lindstedt’s Method -- 2 Center Manifolds -- 3 Normal Forms -- 4 Two Variable Expansion Method -- 5 Averaging -- 6 Lie Transforms -- 7 Liapunov-Schmidt Reduction -- Appendix Introduction to MACSYMA -- References Perturbation methods have always been an important tool for treating nonlinear differential equations. Now the drudgery associated with them has been eliminated! This book offers computer algebra (MACSYMA) programs which implement the most popular perturbation methods. Not only does this avoid the errors associated with hand computation, but the increase in efficiency permits more complicated problems to be tackled. This book is useful both for the beginner learning perturbation methods for the first time, as well as for the researcher. Methods covered include: Lindstedt's method, center manifolds, normal forms, two variable expansion method (method of multiple scales), averaging, Lie transforms and Liapunov-Schmidt reduction. For each method the book includes an introduction and some example problems solved both by hand and by machine. The examples feature common bifurcations such as the pitchfork and the Hopf. The MACSYMA code for each method is given and suggested exercises are provided at the end of each Chapter. An Appendix offers a brief introduction to MACSYMA Accessibility summary: This PDF is not accessible. It is based on scanned pages and does not support features such as screen reader compatibility or described non-text content (images, graphs etc). However, it likely supports searchable and selectable text based on OCR (Optical Character Recognition). Users with accessibility needs may not be able to use this content effectively. Please contact us at accessibilitysupport@springernature.com if you require assistance or an alternative format Inaccessible, or known limited accessibility No reading system accessibility options actively disabled Publisher contact for further accessibility information: accessibilitysupport@springernature.com HTTP:URL=https://doi.org/10.1007/978-1-4612-1060-3

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