Ordinary differential equations : basics and beyond /
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| Author / Creator: | Schaeffer, David G., author. |
|---|---|
| Imprint: | New York, NY : Springer, 2016. |
| Description: | 1 online resource (xxx, 542 pages) : illustrations (some color) |
| Language: | English |
| Series: | Texts in applied mathematics, 0939-2475 ; volume 65 Texts in applied mathematics ; v. 65. |
| Subject: | |
| Format: | E-Resource Book |
| URL for this record: | http://pi.lib.uchicago.edu/1001/cat/bib/11269208 |
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| 100 | 1 | |a Schaeffer, David G., |e author. | |
| 245 | 1 | 0 | |a Ordinary differential equations : |b basics and beyond / |c David G. Schaeffer, John W. Cain. |
| 264 | 1 | |a New York, NY : |b Springer, |c 2016. | |
| 300 | |a 1 online resource (xxx, 542 pages) : |b illustrations (some color) | ||
| 336 | |a text |b txt |2 rdacontent | ||
| 337 | |a computer |b c |2 rdamedia | ||
| 338 | |a online resource |b cr |2 rdacarrier | ||
| 347 | |a text file | ||
| 347 | |b PDF | ||
| 490 | 1 | |a Texts in applied mathematics, |x 0939-2475 ; |v volume 65 | |
| 504 | |a Includes bibliographical references and index. | ||
| 588 | 0 | |a Online resource; title from PDF title page (SpringerLink, viewed November 21, 2016). | |
| 505 | 0 | |a Introduction -- Linear Systems with Constant Coefficients -- Nonlinear Systems: Local Theory -- Nonlinear Systems: Global Theory -- Nondimensionalization and Scaling -- Trajectories Near Equilibria -- Oscillations in ODEs -- Bifurcation from Equilibria -- Examples of Global Bifurcation -- Epilogue -- Appendices. | |
| 520 | |a This book develops the theory of ordinary differential equations (ODEs), starting from an introductory level (with no prior experience in ODEs assumed) through to a graduate-level treatment of the qualitative theory, including bifurcation theory (but not chaos). While proofs are rigorous, the exposition is reader-friendly, aiming for the informality of face-to-face interactions. A unique feature of this book is the integration of rigorous theory with numerous applications of scientific interest. Besides providing motivation, this synthesis clarifies the theory and enhances scientific literacy. Other features include: (i) a wealth of exercises at various levels, along with commentary that explains why they matter; (ii) figures with consistent color conventions to identify nullclines, periodic orbits, stable and unstable manifolds; and (iii) a dedicated website with software templates, problem solutions, and other resources supporting the text. Given its many applications, the book may be used comfortably in science and engineering courses as well as in mathematics courses. Its level is accessible to upper-level undergraduates but still appropriate for graduate students. The thoughtful presentation, which anticipates many confusions of beginning students, makes the book suitable for a teaching environment that emphasizes self-directed, active learning (including the so-called inverted classroom). | ||
| 650 | 0 | |a Differential equations. |0 http://id.loc.gov/authorities/subjects/sh85037890 | |
| 650 | 7 | |a Mathematical physics. |2 bicssc | |
| 650 | 7 | |a Nonlinear science. |2 bicssc | |
| 650 | 7 | |a Differential calculus & equations. |2 bicssc | |
| 650 | 7 | |a Science |x Mathematical Physics. |2 bisacsh | |
| 650 | 7 | |a Mathematics |x Mathematical Analysis. |2 bisacsh | |
| 650 | 7 | |a Mathematics |x Differential Equations. |2 bisacsh | |
| 650 | 7 | |a Differential equations. |2 fast |0 (OCoLC)fst00893446 | |
| 655 | 4 | |a Electronic books. | |
| 700 | 1 | |a Cain, John W., |e author. | |
| 776 | 0 | 8 | |i Print version: |z 9781493963874 |
| 830 | 0 | |a Texts in applied mathematics ; |v v. 65. |x 0939-2475 |0 http://id.loc.gov/authorities/names/n86729581 | |
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| 928 | |t Library of Congress classification |a QA371 |l Online |c UC-FullText |u https://link.springer.com/10.1007/978-1-4939-6389-8 |z Springer Nature |g ebooks |i 12542081 | ||