Math 2.0

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Advanced Theory of Ordinary Differential Equations 87MPWJ2SE6

URIm2://res/87MPWJ2SE6
Kindcourse
CreatorsHari Shankar Mahato (instructor)
Date2024-07-08
MSC34-XX
Scopein
Idscourse 03w5sq511:111105522

Expressions

e1: edition

Languageen
Date2024-07-08
Contents
  • part 1: Week 1
  • session 1: Lecture 01 : Introduction to ODEs
  • session 2: Lecture 02 : Introduction to ODEs (Contd.)
  • session 3: Lecture 03 : Existence of local solution. Theorems and Examples
  • session 4: Lecture 04 : Continuation of solutions upto the boundary. Global existence of Solution
  • session 5: Lecture 05 : Continuation of solution and dependence on initital data
  • part 2: Week 2
  • session 6: Lecture 06 : Dependence on Initial data : Examples
  • session 7: Lecture 07 : Regular Perturbations and linearisation
  • session 8: Lecture 08 : Linear System of equations and their stability
  • session 9: Lecture 09 : Linear System of equations and their stability (Contd.)
  • session 10: Lecture 10 : Stability Analysis
  • part 3: Week 3
  • session 11: Lecture 11 : Stability Analysis (Contd.)
  • session 12: Lecture 12 : Stability of linear systems with constant and periodic coefficient matrix
  • session 13: Lecture 13 : Stability of linear systems with constant and periodic co-efficient Matrix (Contd.)
  • session 14: Lecture 14 : Stability of nonlinear system, linearization and Lyapunov functions
  • session 15: Lecture 15 : Stability and Lyapunov functions
  • part 4: Week 4
  • session 16: Lecture 16 : Stability and Lyapunov functions (Contd.)
  • session 17: Lecture 17: Chaotic Theory - Introduction
  • session 18: Lecture 18 : Chaotic Theory - Introduction(Contd.)
  • session 19: Lecture 19 : Lorenz equation, attractor, Lyapunov exponent
  • session 20: Lecture 20 : Lorenz equation, attractor, Lyapunov exponent (Contd.)
  • part 5: Week 5
  • session 21: Lecture 21: Local divergence, Lyapunov exponents and related topics
  • session 22: Lecture 22: Local divergence, Lyapunov exponents and related topics contd..
  • session 23: Lecture 23: Strange and Chaotic attractors
  • session 24: Lecture 24: Strange and Chaotic attractors
  • session 25: Lecture 25: Fractal Dimension and Reconstruction
  • part 6: Week 6
  • session 26: Lecture 26 : Fractal Dimension and Reconstruction (Contd.)
  • session 27: Lecture 27 : Stiff Differential Equations: Introduction
  • session 28: Lecture 28 : Stiff Differential Equations: Slow and fast time scales
  • session 29: Lecture 29 : Stiff differential equations: Introduction
  • session 30: Lecture 30 : Increment function, A-stable
  • part 7: Week 7
  • session 31: Lecture 31 : BDF methods and their implementation, Bifurcation Theory: Introduction
  • session 32: Lecture 32: Bifurcation Theory
  • session 33: Lecture 33: One dimensional bifurcation for scalar equations
  • session 34: Lecture 34: One dimensional bifurcations for planar systems
  • session 35: Lecture 35 : Few definitions related to Hopf bifurcation
  • part 8: Week 8
  • session 36: Lecture 36 : Few definitions related to Hopf bifurcation (Contd.)
  • session 37: Lecture 37 : Mathematical models with second order equations – Undamped free oscillations
  • session 38: Lecture 38 : Damped free oscillations
  • session 39: Lecture 39 : Undamped and Damped Forced Oscillations
  • session 40: Lecture 40 : Undamped and Damped Forced Oscillations (Contd.)
  • part 9: Week 9
  • session 41: Lecture 41 : Higher order linear ODEs
  • session 42: Lecture 42 : Higher order linear ODEs (Contd.)
  • session 43: Lecture 43 : Linear Differential Equations of Higher Order with Constant Coefficients
  • session 44: Lecture 44 : Linear Differential Equations of Higher Order with Constant Coefficients (Contd.)
  • session 45: Lecture 45 : Higher order linear ODEs – Particular Integrals
  • part 10: Week 10
  • session 46: Lecture 46 : Higher order linear ODEs – Particular Integrals (Contd.)
  • session 47: Lecture 47 : Higher order linear ODEs – Variable Coefficients
  • session 48: Lecture 48 : Higher order linear ODEs – Variation of Parameters
  • session 49: Lecture 49 : Series Solution
  • session 50: Lecture 50 : Series Solution (Contd.)
  • part 11: Week 11
  • session 51: Lecture 51 : Series Solution – Frobenius Method
  • session 52: Lecture 52 : Series Solution – Frobenius method (Contd.)
  • session 53: Lecture 53 : Special functions
  • session 54: Lecture 54 : Special functions (contd.)
  • session 55: Lecture 55 : Sturm-Liouville Problem – Eigenvalues and Eigenfunctions
  • part 12: Week 12
  • session 56: Lecture 56 : Sturm-Liouville Problem – Eigenvalues and Eigenfunctions (Contd.)
  • session 57: Lecture 57 : Sturm-Liouville Problem – Eigenvalues and Eigenfunctions (Contd.)
  • session 58: Lecture 58 : Laplace Transform
  • session 59: Lecture 59 : Laplace Transform and Its Applications
  • session 60: Lecture 60 : Laplace Transform and Its Applications (Contd.)

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