IISc Bangalore Course , Prof. A. K. Nandakumaran

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IISc Bangalore Course , Prof. A. K. Nandakumaran

Motivation and real life examples:An introduction about differential equations and why this course - Present various examples like population growth, spring-mass-dashpot system and other nonlinear system. These examples will be recalled as and when necessary - Preliminaries:Basic concepts from linear algebra - Some important preliminaries from analysis like uniform convergence, Arzela-Ascoli theorem, fixed point theorems etc - First and second order linear equations:First order linear differential equations, Exact differential equations and integrating factors - Second order linear differential equations (homogeneous and non-homogeneous. Equation with constant coefficients, analysis of spring-mass-dashpot system.

General Existence and Uniqueness theory:Examples of non-uniqueness, non-existence, importance of existence uniqueness theory, Picard's iteration, Peano's existence theory, Existence via Arzela Ascoli theorem, continuous dependence:Methods of solving (series solution) - Linear systems:Understanding linear system via linear algebra, stability of Linear systems, Explicit phase portrait of 2D linear systems with constant coefficients, General case, Non-homogeneous Systems - 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:

General Existence and Uniqueness theory:Examples of non-uniqueness, non-existence, importance of existence uniqueness theory, Picard's iteration, Peano's existence theory, Existence via Arzela Ascoli theorem, continuous dependence:Methods of solving (series solution) - Linear systems:Understanding linear system via linear algebra, stability of Linear systems, Explicit phase portrait of 2D linear systems with constant coefficients, General case, Non-homogeneous Systems - 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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Ordinary Differential Equations and Applications by A. K. Nandakumaran,P. S. Datti & Raju K. George,Department of Mathematics,IISc Bangalore.For more details on NPTEL visit httpnptel.ac.in.

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- 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 I
- 10.First Order Linear Equations
- 11.Exact Equations
- 12.Second Order Linear Equations
- 13.Second Order Linear Equations Continued I
- 14.Second Order Linear Equations Continued II
- 15.Well-posedness and Examples of IVP
- 16.Gronwalls Lemma
- 17.Basic Lemma and Uniqueness Theorem
- 18.Picards Existence and Uniqueness Theorem
- 19.Picards Existence and Uniqueness I
- 20.Cauchy Peano Existence Theorem
- 21.Existence using Fixed Point Theorem
- 22.Continuation of Solutions
- 23.Series Solution
- 24.General System and Diagonalizability
- 25.2 by 2 systems and Phase Plane Analysis
- 26.2 by 2 systems and Phase Plane Analysis Continued I
- 27.General Systems
- 28.General Systems Continued and Non-homogeneous Systems I
- 29.Basic Definitions and Examples
- 30.Stability Equilibrium Points
- 31.Stability Equilibrium Points Continued I
- 32.Stability Equilibrium Points Continued II
- 33.Second Order Linear Equations Continued III
- 34.Lyapunov Function
- 35.Lyapunov Function I
- 36.Periodic Orbits and Poincare Bendixon Theory
- 37.Periodic Orbits and Poincare Bendixon Theory I
- 38.Linear Second Order Equations
- 39.General Second Order Equations
- 40.General Second Order Equations Continued I

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