000 04382nam a22006255i 4500
001 978-3-031-51652-8
003 DE-He213
005 20251030112048.0
007 cr nn 008mamaa
008 240519s2024 sz | s |||| 0|eng d
020 _a9783031516528
_9978-3-031-51652-8
024 7 _a10.1007/978-3-031-51652-8
_2doi
050 4 _aQA299.6-433
050 4 _aQA299.6-433
072 7 _aPBK
_2bicssc
072 7 _aPBK
_2bicssc
072 7 _aMAT034000
_2bisacsh
072 7 _aPBK
_2thema
072 7 _aPBK
_2thema
100 1 _aChicone, Carmen.
_eauthor.
_4aut
_4http://id.loc.gov/vocabulary/relators/aut
_977035
245 1 0 _aOrdinary Differential Equations with Applications
_h[electronic resource] /
_cby Carmen Chicone.
250 _a3rd ed. 2024.
264 1 _aCham :
_bSpringer International Publishing :
_bImprint: Springer,
_c2024.
300 _aXXII, 729 p. 76 illus.
_bonline resource.
336 _atext
_btxt
_2rdacontent
337 _acomputer
_bc
_2rdamedia
338 _aonline resource
_bcr
_2rdacarrier
347 _atext file
_bPDF
_2rda
490 1 _aTexts in Applied Mathematics,
_x2196-9949 ;
_v34
505 0 _aOrdinary Differential Equations -- Linear Systems and Stability of Nonlinear Systems -- Applications -- Hyperbolic Theory -- Continuation of Periodic Solutions -- Homoclinic Orbits, Melnikov’s Method, and Chaos -- Averaging -- Local Bifurcation.
520 _aThis book, developed during 20 years of the author teaching differential equations courses at his home university, is designed to serve as a text for a graduate level course focused on the central theory of the subject with attention paid to applications and connections to other advanced topics in mathematics. Core theory includes local existence and uniqueness, the phase plane, Poincaré–Bendixson theory, Lyapunov and linearized stability, linear systems, Floquet theory, the Grobman–Hartman theorem, persistence of rest points and periodic orbits, the stable and center manifold theorems, and bifurcation theory. This edition includes expanded treatment of deterministic chaos, perturbation theory for periodic solutions, boundary value problems, optimization, and a wide range of their applications. In addition, it contains a formulation and new proof of a theorem on instability of rest points in the presence of an eigenvalue with positive real part, and new proofs of differential inequalities and Lyapunov’s center theorem. New sections present discussions of global bifurcation, the Crandall–Rabinowitz theorem, and Alekseev’s formula. Of particular note is a new chapter on basic control theory, a discussion of optimal control, and a proof of a useful special case of the maximum principle. A key feature of earlier editions, a wide selection of original exercises, is respected in this edition with the inclusion of a wealth of new exercises. Reviews of the first edition: “As an applied mathematics text on linear and nonlinear equations, the book by Chicone is written with stimulating enthusiasm. It will certainly appeal to many students and researchers.”—F. Verhulst, SIAM Review “The author writes lucidly and in an engaging conversational style. His book is wide-ranging in its subject matter, thorough in its presentation, and written at a generally high level of generality, detail, and rigor.” —D. S. Shafer, Mathematical Reviews.
650 0 _aMathematical analysis.
_964178
650 0 _aDynamical systems.
650 0 _aSystem theory.
_966519
650 0 _aMathematical physics.
650 1 4 _aAnalysis.
650 2 4 _aDynamical Systems.
650 2 4 _aComplex Systems.
_966520
650 2 4 _aAnalysis.
650 2 4 _aTheoretical, Mathematical and Computational Physics.
_965563
710 2 _aSpringerLink (Online service)
773 0 _tSpringer Nature eBook
776 0 8 _iPrinted edition:
_z9783031516511
776 0 8 _iPrinted edition:
_z9783031516535
776 0 8 _iPrinted edition:
_z9783031516542
830 0 _aTexts in Applied Mathematics,
_x2196-9949 ;
_v34
_976354
856 4 0 _uhttps://doi.org/10.1007/978-3-031-51652-8
912 _aZDB-2-SMA
912 _aZDB-2-SXMS
999 _c59960
_d59960