Learn · Advanced Theory of Ordinary Differential Equations
Lecture 11 of 60Week 3
Lecture 11 : Stability Analysis (Contd.)
Prof. Hari Shankar Mahato · IIT Kharagpur
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All the lectures
- Lecture 01 : Introduction to ODEs
- Lecture 02 : Introduction to ODEs (Contd.)
- Lecture 03 : Existence of local solution. Theorems and Examples
- Lecture 04 : Continuation of solutions upto the boundary. Global existence of Solution
- Lecture 05 : Continuation of solution and dependence on initital data
- Lecture 06 : Dependence on Initial data : Examples
- Lecture 07 : Regular Perturbations and linearisation
- Lecture 08 : Linear System of equations and their stability
- Lecture 09 : Linear System of equations and their stability (Contd.)
- Lecture 10 : Stability Analysis
- Lecture 11 : Stability Analysis (Contd.)
- Lecture 12 : Stability of linear systems with constant and periodic coefficient matrix
- Lecture 13 : Stability of linear systems with constant and periodic co-efficient Matrix (Contd.)
- Lecture 14 : Stability of nonlinear system, linearization and Lyapunov functions
- Lecture 15 : Stability and Lyapunov functions
- Lecture 16 : Stability and Lyapunov functions (Contd.)
- Lecture 17: Chaotic Theory - Introduction
- Lecture 18 : Chaotic Theory - Introduction(Contd.)
- Lecture 19 : Lorenz equation, attractor, Lyapunov exponent
- Lecture 20 : Lorenz equation, attractor, Lyapunov exponent (Contd.)
- Lecture 21: Local divergence, Lyapunov exponents and related topics
- Lecture 22: Local divergence, Lyapunov exponents and related topics contd..
- Lecture 23: Strange and Chaotic attractors
- Lecture 24: Strange and Chaotic attractors
- Lecture 25: Fractal Dimension and Reconstruction
- Lecture 26 : Fractal Dimension and Reconstruction (Contd.)
- 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 (Contd.)
- 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 (Contd.)
- Lecture 41 : Higher order linear ODEs
- Lecture 42 : Higher order linear ODEs (Contd.)
- Lecture 43 : Linear Differential Equations of Higher Order with Constant Coefficients
- Lecture 44 : Linear Differential Equations of Higher Order with Constant Coefficients (Contd.)
- Lecture 45 : Higher order linear ODEs – Particular Integrals
- Lecture 46 : Higher order linear ODEs – Particular Integrals (Contd.)
- 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 (Contd.)
- Lecture 51 : Series Solution – Frobenius Method
- Lecture 52 : Series Solution – Frobenius method (Contd.)
- Lecture 53 : Special functions
- Lecture 54 : Special functions (contd.)
- Lecture 55 : Sturm-Liouville Problem – Eigenvalues and Eigenfunctions
- Lecture 56 : Sturm-Liouville Problem – Eigenvalues and Eigenfunctions (Contd.)
- Lecture 57 : Sturm-Liouville Problem – Eigenvalues and Eigenfunctions (Contd.)
- Lecture 58 : Laplace Transform
- Lecture 59 : Laplace Transform and Its Applications
- Lecture 60 : Laplace Transform and Its Applications (Contd.)