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Course11110808140 lectures

Ordinary Differential Equations and Applications

A. K. Nandakumaran, P. S. Datti and Raju K. George · IISc Bangalore

Start with lecture 1 At NPTEL

Lectures

Motivation and Real Life Examples

  1. General Introduction Video
  2. Examples Video
  3. Examples Continued I Video
  4. Examples Continued II Video

Preliminaries

  1. Linear Algebra Video
  2. Linear Algebra Continued I Video
  3. Linear Algebra Continued II Video
  4. Analysis Video
  5. Analysis Continued Video

First and Second Order Linear equations

  1. First Order Linear Equations Video
  2. Exact Equations Video
  3. Second Order Linear Equations Video
  4. Second Order Linear Equations Continued I Video
  5. Second Order Linear Equations Continued II Video

General Existence and Uniqueness Theory

  1. Well-posedness and Examples of IVP Video
  2. Gronwall's Lemma Video
  3. Basic Lemma and Uniqueness Theorem Video
  4. Picard's Existence and Uniqueness Theorem Video
  5. Picard's Existence and Uniqueness Continued Video
  6. Cauchy Peano Existence Theorem Video
  7. Existence using Fixed Point Theorem Video
  8. Continuation of Solutions Video
  9. Series Solution Video

Linear Systems

  1. General System and Diagonalizability Video
  2. 2 by 2 systems and Phase Plane Analysis Video
  3. 2 by 2 systems and Phase Plane Analysis Continued Video
  4. General Systems Video
  5. General Systems Continued and Non-homogeneous Systems Video

Nonlinear Systems

  1. Basic Definitions and Examples Video
  2. Stability Equilibrium Points Video
  3. Stability Equilibrium Points Continued I Video
  4. Stability Equilibrium Points Continued II Video
  5. Second Order Linear Equations Continued III Video
  6. Lyapunov Function Video
  7. Lyapunov Function Continued Video
  8. Periodic Orbits and Poincare Bendixon Theory Video
  9. Periodic Orbits and Poincare Bendixon Theory Continued Video

Two-point Boundary Value Problems

  1. Linear Second Order Equations Video
  2. General Second Order Equations Video
  3. General Second Order Equations Continued Video

Syllabus and materials

At NPTEL, as the course publishes them.

Credits and licence

Institution
IISc Bangalore
Department
Mathematics
Taught by
A. K. Nandakumaran, P. S. Datti, Raju K. George
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
NPTEL states: "Distributed under Creative Commons Attribution-ShareAlike / CC BY - NC - SA", beside a BY-NC-SA badge.
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