###### Mathematics  Ordinary Differential Equations and Applications
 List Lectures   [ 1 ]  2  3  4
 # Lecture Name 1 General Introduction 2 Examples 3 Examples Continued I 4 Examples Continued II 5 Linear Algebra 6 Linear Algebra Continued I 7 Linear Algebra Continued II 8 Analysis 9 Analysis Continued 10 First Order Linear Equations

 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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