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Mathematics  Ordinary Differential Equations and Applications
   
 
Title: Ordinary Differential Equations and Applications
Department: Mathematics
Author: A. K. Nandakumaran Raju K. George P. S. Datti
University: IISc Bangalore
Type: WebLink
Abstract: Motivation and real life examples:
Preliminaries; Basics from linear algebra and real analysis like concepts of dependence, independence, basis, Rank-Nullity theorem, determinants and eigenvalues, remarks on Jordan decomposition theorem - convergence, uniform convergence, fixed point theorems, Lipschitz continuity etc.:
First and second order linear equations; Examples, A systematic procedure to solve first order and development of the concept integrating factor, Second order homogeneous and non-homogeneous equations, Wronskian, methods of solving:
General Existence and Uniqueness theory; Picard s iteration, Peano s exisentce theory, Existence via Arzela Ascoli theorem, non-uniqueness, continuous dependence:
Linear systems; Understanding linear system via linear algebra, stability of Linear systems, Explicit phase portrait in 2D linear with constant coefficients :
Periodic Solutions; Stability, Floquet theory, particular case o second order equations-Hill s equation:
Sturm-Liouville theory; Oscillation theorems:
Qualitative Analysis; Examples of nonlinear systems, Stability analysis, Liapunov stability, phase portrait of 2D systems, Poincare Bendixon theory, Leinard s theorem:
Introduction to two-point Boundary value problems; Linear equations, Green s function, nonlinear equations, existence and uniqueness:
 
   
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