000			02951nam a2200349 4500
001			OTLid0000525
003			MnU
005			20201105133336.0
006			m o d s
008			180907s2017 mnu o 0 0 eng d
040			_aMnU _beng _cMnU
050		4	_aQA1
050		4	_aQA37.3
100	1		_aWiggins, Stephen _eauthor
245	0	0	_aOrdinary Differential Equations _cStephen Wiggins
264		2	_bOpen Textbook Library
264		1	_bStephen Wiggins
300			_a1 online resource
490	0		_aOpen textbook library.
505	0		_aPreface -- 1 Getting Started: The Language of ODEs -- 2 Special Structure and Solutions of ODEs -- 3 Behavior Near Trajectories and Invariant Sets: Stability -- 4 Behavior Near Trajectories: Linearization -- 5 Behavior Near Equilbria: Linearization -- 6 Stable and Unstable Manifolds of Equilibria -- 7 Lyapunov's Method and the LaSalle Invariance Principle -- 8 Bifurcation of Equilibria, I -- 9 Bifurcation of Equilibria, II -- 10 Center Manifold Theory -- A Jacobians, Inverses of Matrices, and Eigenvalues -- B Integration of Some Basic Linear ODEs -- C Finding Lyapunov Functions -- D Center Manifolds Depending on Parameters -- E Dynamics of Hamilton's Equations -- F A Brief Introduction to the Characteristics of Chaos -- Bibliography -- Index
520	0		_aThis book consists of ten weeks of material given as a course on ordinary differential equations (ODEs) for second year mathematics majors at the University of Bristol. It is the first course devoted solely to differential equations that these students will take. This book consists of 10 chapters, and the course is 12 weeks long. Each chapter is covered in a week, and in the remaining two weeks I summarize the entire course, answer lots of questions, and prepare the students for the exam. I do not cover the material in the appendices in the lectures. Some of it is basic material that the students have already seen that I include for completeness and other topics are "tasters" for more advanced material that students will encounter in later courses or in their project work. Students are very curious about the notion of chaos, and I have included some material in an appendix on that concept. The focus in that appendix is only to connect it with ideas that have been developed in this course related to ODEs and to prepare them for more advanced courses in dynamical systems and ergodic theory that are available in their third and fourth years.
542	1		_fAttribution
546			_aIn English.
588	0		_aDescription based on online resource
650		0	_aMathematics _vTextbooks
710	2		_aOpen Textbook Library _edistributor
856	4	0	_uhttps://open.umn.edu/opentextbooks/textbooks/525 _zAccess online version
999			_c19905 _d19905