NOC:Advanced Theory of Ordinary Differential Equations

Lecture 1 - Introduction to ODEs

Lecture 2 - Introduction to ODEs (Continued...)

Lecture 3 - Existence of local solution. Theorems and Examples

Lecture 4 - Continuation of solutions upto the boundary. Global existence of Solution

Lecture 5 - Continuation of solution and dependence on initital data

Lecture 6 - Dependence on Initial data : Examples

Lecture 7 - Regular Perturbations and linearisation

Lecture 8 - Linear System of equations and their stability

Lecture 9 - Linear System of equations and their stability (Continued...)

Lecture 10 - Stability Analysis

Lecture 11 - Stability Analysis (Continued...)

Lecture 12 - Stability of linear systems with constant and periodic co-efficient Matrix

Lecture 13 - Stability of linear systems with constant and periodic co-efficient Matrix (Continued...)

Lecture 14 - Stability of nonlinear system, linearization and Lyapunov functions

Lecture 15 - Stability and Lyapunov functions

Lecture 16 - Stability and Lyapunov functions (Continued...)

Lecture 17 - Chaotic Theory - Introduction

Lecture 18 - Chaotic Theory - Introduction (Continued...)

Lecture 19 - Lorenz equation, attractor, Lyapunov exponent

Lecture 20 - Lorenz equation, attractor, Lyapunov exponent (Continued...)

Lecture 21 - Local divergence, Lyapunov exponents and related topics

Lecture 22 - Local divergence, Lyapunov exponents and related topics (Continued...)

Lecture 23 - Strange and Chaotic attractors

Lecture 24 - Strange and Chaotic attractors

Lecture 25 - Fractal Dimension and Reconstruction

Lecture 26 - Fractal Dimension and Reconstruction (Continued...)

Lecture 27 - Stiff Differential Equations: Introduction

Lecture 28 - Stiff Differential Equations: Slow and fast time scales

Lecture 29 - Stiff differential equations: Introduction

Lecture 30 - Increment function, A-stable

Lecture 31 - BDF methods and their implementation, Bifurcation Theory: Introduction

Lecture 32 - Bifurcation Theory

Lecture 33 - One dimensional bifurcation for scalar equations

Lecture 34 - One dimensional bifurcations for planar systems

Lecture 35 - Few definitions related to Hopf bifurcation

Lecture 36 - Few definitions related to Hopf bifurcation (Continued...)

Lecture 37 - Mathematical models with second order equations - Undamped free oscillations

Lecture 38 - Damped free oscillations

Lecture 39 - Undamped and Damped Forced Oscillations

Lecture 40 - Undamped and Damped Forced Oscillations (Continued...)

Lecture 41 - Higher order linear ODEs

Lecture 42 - Higher order linear ODEs (Continued...)

Lecture 43 - Linear Differential Equations of Higher Order with Constant Coefficients

Lecture 44 - Linear Differential Equations of Higher Order with Constant Coefficients (Continued...)

Lecture 45 - Higher order linear ODEs - Particular Integrals

Lecture 46 - Higher order linear ODEs - Particular Integrals (Continued...)

Lecture 47 - Higher order linear ODEs - Variable Coefficients

Lecture 48 - Higher order linear ODEs - Variation of Parameters

Lecture 49 - Series Solution

Lecture 50 - Series Solution (Continued...)

Lecture 51 - Series Solution - Frobenius Method

Lecture 52 - Series Solution - Frobenius method (Continued...)

Lecture 53 - Special functions

Lecture 54 - Special functions (Continued...)

Lecture 55 - Sturm-Liouville Problem - Eigenvalues and Eigenfunctions

Lecture 56 - Sturm-Liouville Problem - Eigenvalues and Eigenfunctions (Continued...)

Lecture 57 - Laplace Transform and Its Applications (Continued...)

Lecture 58 - Laplace Transform

Lecture 59 - Laplace Transform and Its Applications

Lecture 60 - Laplace Transform and Its Applications (Continued...)