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Course11110552260 lectures

Advanced Theory of Ordinary Differential Equations

Prof. Hari Shankar Mahato · IIT Kharagpur

Start with lecture 1 At NPTEL

About

Differential equations play an important role in applied mathematics. They provide the modelling tools to depict and simulate real world (physical) problems. This course is intended for all undergraduate students such as students from any BTech, BSc and MSc level courses. It will offer a detailed introduction and tools necessary to model, analyze and solve numerically the differential equations (DEs). We will cover both first order and second order ODEs & their subsequent theories.

Intended audience: UG students including all BTech, BSc and MSc students.

Prerequisites: Differential calculus of one and several variables, Integral calculus, Ordinary differential equations.

Lectures

Week 1

  1. Lecture 01 : Introduction to ODEs YouTube
  2. Lecture 02 : Introduction to ODEs (Contd.) YouTube
  3. Lecture 03 : Existence of local solution. Theorems and Examples YouTube
  4. Lecture 04 : Continuation of solutions upto the boundary. Global existence of Solution YouTube
  5. Lecture 05 : Continuation of solution and dependence on initital data YouTube

Week 2

  1. Lecture 06 : Dependence on Initial data : Examples YouTube
  2. Lecture 07 : Regular Perturbations and linearisation YouTube
  3. Lecture 08 : Linear System of equations and their stability YouTube
  4. Lecture 09 : Linear System of equations and their stability (Contd.) YouTube
  5. Lecture 10 : Stability Analysis YouTube

Week 3

  1. Lecture 11 : Stability Analysis (Contd.) YouTube
  2. Lecture 12 : Stability of linear systems with constant and periodic coefficient matrix YouTube
  3. Lecture 13 : Stability of linear systems with constant and periodic co-efficient Matrix (Contd.) YouTube
  4. Lecture 14 : Stability of nonlinear system, linearization and Lyapunov functions YouTube
  5. Lecture 15 : Stability and Lyapunov functions YouTube

Week 4

  1. Lecture 16 : Stability and Lyapunov functions (Contd.) YouTube
  2. Lecture 17: Chaotic Theory - Introduction YouTube
  3. Lecture 18 : Chaotic Theory - Introduction(Contd.) YouTube
  4. Lecture 19 : Lorenz equation, attractor, Lyapunov exponent YouTube
  5. Lecture 20 : Lorenz equation, attractor, Lyapunov exponent (Contd.) YouTube

Week 5

  1. Lecture 21: Local divergence, Lyapunov exponents and related topics YouTube
  2. Lecture 22: Local divergence, Lyapunov exponents and related topics contd.. YouTube
  3. Lecture 23: Strange and Chaotic attractors YouTube
  4. Lecture 24: Strange and Chaotic attractors YouTube
  5. Lecture 25: Fractal Dimension and Reconstruction YouTube

Week 6

  1. Lecture 26 : Fractal Dimension and Reconstruction (Contd.) YouTube
  2. Lecture 27 : Stiff Differential Equations: Introduction YouTube
  3. Lecture 28 : Stiff Differential Equations: Slow and fast time scales YouTube
  4. Lecture 29 : Stiff differential equations: Introduction YouTube
  5. Lecture 30 : Increment function, A-stable YouTube

Week 7

  1. Lecture 31 : BDF methods and their implementation, Bifurcation Theory: Introduction YouTube
  2. Lecture 32: Bifurcation Theory YouTube
  3. Lecture 33: One dimensional bifurcation for scalar equations YouTube
  4. Lecture 34: One dimensional bifurcations for planar systems YouTube
  5. Lecture 35 : Few definitions related to Hopf bifurcation YouTube

Week 8

  1. Lecture 36 : Few definitions related to Hopf bifurcation (Contd.) YouTube
  2. Lecture 37 : Mathematical models with second order equations – Undamped free oscillations YouTube
  3. Lecture 38 : Damped free oscillations YouTube
  4. Lecture 39 : Undamped and Damped Forced Oscillations YouTube
  5. Lecture 40 : Undamped and Damped Forced Oscillations (Contd.) YouTube

Week 9

  1. Lecture 41 : Higher order linear ODEs YouTube
  2. Lecture 42 : Higher order linear ODEs (Contd.) YouTube
  3. Lecture 43 : Linear Differential Equations of Higher Order with Constant Coefficients YouTube
  4. Lecture 44 : Linear Differential Equations of Higher Order with Constant Coefficients (Contd.) YouTube
  5. Lecture 45 : Higher order linear ODEs – Particular Integrals YouTube

Week 10

  1. Lecture 46 : Higher order linear ODEs – Particular Integrals (Contd.) YouTube
  2. Lecture 47 : Higher order linear ODEs – Variable Coefficients YouTube
  3. Lecture 48 : Higher order linear ODEs – Variation of Parameters YouTube
  4. Lecture 49 : Series Solution YouTube
  5. Lecture 50 : Series Solution (Contd.) YouTube

Week 11

  1. Lecture 51 : Series Solution – Frobenius Method YouTube
  2. Lecture 52 : Series Solution – Frobenius method (Contd.) YouTube
  3. Lecture 53 : Special functions YouTube
  4. Lecture 54 : Special functions (contd.) YouTube
  5. Lecture 55 : Sturm-Liouville Problem – Eigenvalues and Eigenfunctions YouTube

Week 12

  1. Lecture 56 : Sturm-Liouville Problem – Eigenvalues and Eigenfunctions (Contd.) YouTube
  2. Lecture 57 : Sturm-Liouville Problem – Eigenvalues and Eigenfunctions (Contd.) YouTube
  3. Lecture 58 : Laplace Transform YouTube
  4. Lecture 59 : Laplace Transform and Its Applications YouTube
  5. Lecture 60 : Laplace Transform and Its Applications (Contd.) YouTube

Syllabus and materials

At NPTEL, as the course publishes them.

Credits and licence

Institution
IIT Kharagpur
Department
Mathematics
Teacher
Prof. Hari Shankar Mahato
Level
Undergraduate
Language
English
Subjects
Mathematics
Source
NPTEL
Licence
CC BY-NC-SA, as NPTEL states it. Non-commercial use only. NPTEL's terms
Attribution
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