Ordinary differential equations and dynamical systems (Record no. 67018)
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| 000 -LEADER | |
|---|---|
| fixed length control field | 02322nam a2200217 4500 |
| 020 ## - INTERNATIONAL STANDARD BOOK NUMBER | |
| ISBN | 9781470425869 |
| 082 00 - DEWEY DECIMAL CLASSIFICATION NUMBER | |
| Classification number | 515.352 |
| Item number | TES/O |
| 100 1# - MAIN ENTRY--AUTHOR NAME | |
| Personal name | Teschl, Gerald |
| 245 10 - TITLE STATEMENT | |
| Title | Ordinary differential equations and dynamical systems |
| 260 ## - PUBLICATION, DISTRIBUTION, ETC. (IMPRINT) | |
| Place of publication | Rhode Island |
| Name of publisher | American Mathematical Society |
| Year of publication | 2012. |
| 300 ## - PHYSICAL DESCRIPTION | |
| Number of Pages | xi, 356 p. |
| Other physical details | ill. ; |
| 490 0# - SERIES STATEMENT | |
| Series statement | Graduate studies in mathematics ; |
| 520 ## - SUMMARY, ETC. | |
| Summary, etc | This book provides a self-contained introduction to ordinary differential equations and dynamical systems suitable for beginning graduate students. The first part begins with some simple examples of explicitly solvable equations and a first glance at qualitative methods. Then the fundamental results concerning the initial value problem are proved: existence, uniqueness, extensibility, dependence on initial conditions. Furthermore, linear equations are considered, including the Floquet theorem, and some perturbation results. As somewhat independent topics, the Frobenius method for linear equations in the complex domain is established and Sturm- Liouville boundary value problems, including oscillation theory, are investigated. The second part introduces the concept of a dynamical system. The Poincaré–Bendixson theorem is proved, and several examples of planar systems from classical mechanics, ecology, and electrical engineering are investigated. Moreover, attractors, Hamiltonian systems, the KAM theorem, and periodic solutions are discussed. Finally, stability is studied, including the stable manifold and the Hartman–Grobman theorem for both continuous and discrete systems. The third part introduces chaos, beginning with the basics for iterated interval maps and ending with the Smale–Birkhoff theorem and the Melnikov method for homoclinic orbits. The text contains almost three hundred exercises. Additionally, the use of mathematical software systems is incorporated throughout, showing how they can help in the study of differential equations. |
| 650 #0 - SUBJECT ADDED ENTRY--TOPICAL TERM | |
| Topical Term | Differential equations |
| 650 #0 - SUBJECT ADDED ENTRY--TOPICAL TERM | |
| Topical Term | Dynamics |
| 650 #7 - SUBJECT ADDED ENTRY--TOPICAL TERM | |
| Topical Term | Ordinary differential equations -- Instructional exposition (textbooks, tutorial papers, etc.). |
| 650 #7 - SUBJECT ADDED ENTRY--TOPICAL TERM | |
| Topical Term | Dynamical systems and ergodic theory -- Instructional exposition (textbooks, tutorial papers, etc.). |
| 942 ## - ADDED ENTRY ELEMENTS (KOHA) | |
| Koha item type | BK |
| 001 - CONTROL NUMBER | |
| control field | 17313382 |
| 010 ## - LIBRARY OF CONGRESS CONTROL NUMBER | |
| LC control number | 2012015024 |
| 952 ## - LOCATION AND ITEM INFORMATION (KOHA) | |
| Withdrawn status | |
| Lost status | |
| Damaged status | Collection code | Home library | Shelving location | Date acquired | Full call number | Accession Number | Koha item type |
|---|---|---|---|---|---|---|---|
| Stack | Kannur University Central Library | Stack | 22/06/2023 | 515.352 TES/O | 59774 | BK |