# InfoCoBuild

## Ordinary Differential Equations and Applications

Ordinary Differential Equations and Applications. Instructors: A. K. Nandakumaran, IISc Bangalore; P. S. Datti, TIFR-CAM, Bangalore; Raju K. George, IIST,Trivandrum.

Motivation and real life examples: an introduction about differential equations and examples.
Preliminaries: basic concepts from linear algebra and some important preliminaries from analysis like uniform convergence, Arzela-Ascoli theorem, fixed point theorems 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.
General existence and uniqueness theory: Picard's iteration, Peano's existence 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.
Qualitative analysis: examples of nonlinear systems, Stability analysis, Lyapunov stability, phase portrait of 2D systems, Poincare-Bendixson theory.
Introduction to two-point boundary value problems: linear equations, Green's function, nonlinear equations, existence and uniqueness. (from nptel.ac.in)

 Introduction

 Motivation and Real Life Examples Lecture 01 - General Introduction Lecture 02 - Examples Lecture 03 - Examples Continued I Lecture 04 - Examples Continued II Preliminaries Lecture 05 - Linear Algebra Lecture 06 - Linear Algebra Continued I Lecture 07 - Linear Algebra Continued II Lecture 08 - Analysis Lecture 09 - Analysis Continued First and Second Order Linear Equations Lecture 10 - First Order Linear Equations Lecture 11 - Exact Equations Lecture 12 - Second Order Linear Equations Lecture 13 - Second Order Linear Equations Continued I Lecture 14 - Second Order Linear Equations Continued II General Existence and Uniqueness Theory Lecture 15 - Well-posedness and Examples of IVP Lecture 16 - Gronwall's Lemma Lecture 17 - Basic Lemma and Uniqueness Theorem Lecture 18 - Picard's Existence and Uniqueness Theorem Lecture 19 - Picard's Existence and Uniqueness Theorem Continued Lecture 20 - Cauchy Peano Existence Theorem Lecture 21 - Existence using Fixed Point Theorem Lecture 22 - Continuation of Solutions Lecture 23 - Series Solution Linear Systems Lecture 24 - General System and Diagonalizability Lecture 25 - 2 by 2 Systems and Phase Plane Analysis Lecture 26 - 2 by 2 Systems and Phase Plane Analysis Continued Lecture 27 - General Systems Lecture 28 - General Systems Continued and Non-homogeneous Systems Nonlinear Systems Lecture 29 - Basic Definitions and Examples Lecture 30 - Stability Equilibrium Points Lecture 31 - Stability Equilibrium Points Continued I Lecture 32 - Stability Equilibrium Points Continued II Lecture 33 - Stability Equilibrium Points Continued III Lecture 34 - Lyapunov Function Lecture 35 - Lyapunov Function Continued Lecture 36 - Periodic Orbits and Poincare-Bendixson Theory Lecture 37 - Periodic Orbits and Poincare-Bendixson Theory Continued Two-point Boundary Value Problems Lecture 38 - Linear Second Order Equations Lecture 39 - General Second Order Equations Lecture 40 - General Second Order Equations Continued

 References Ordinary Differential Equations and Applications Instructors: A. K. Nandakumaran, IISc Bangalore; P. S. Datti, TIFR-CAM, Bangalore; Raju K. George, IIST,Trivandrum. an introduction about differential equations and examples.