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Ordinary Differential Equations

Prof. Kaushik Bal · IIT Kanpur

Start with lecture 1 At NPTEL

About

Differential Equations are one of the central topics which results when studying models arising out of physical systems. Most often than not the nonlinear nature of the equation forces us to study the qualitative and geometric theory of equations and dynamical systems. In this course we start by first studying about the various aspect of Linear Systems and then analyze local and global behavior of nonlinear systems using techniques from Linear theory.

Intended audience: Undergraduate students in Mathematics, Physics and Engineering, Graduate students in Mathematics.

Prerequisites: Linear Algebra and Several Variable Calculus.

Lectures

Week 1

  1. Lecture 1, Vector Spaces YouTube
  2. Lecture 2, Linear Transformations YouTube
  3. Lecture 3, Matrices YouTube
  4. Lecture 4, Derivatives YouTube
  5. Lecture 5, Lipschitz Continuity YouTube
  6. Lecture 6, Cauchy Schwartz Inequality YouTube

Week 2

  1. Lecture-7, Ordinary Differential Equations: Introduction YouTube
  2. Lecture-8, Differential Inequalities YouTube
  3. Lecture-9, 2nd Order ODEs YouTube

Week 3

  1. Lecture-10, Picard's Theorem YouTube
  2. Lecture-11, Linear Dependence and Independence YouTube

Week 4

  1. Lecture 12, Well-posedness of an ODE YouTube
  2. Lecture 13, Linear System 1 YouTube
  3. Lecture 14, Linear System 2 YouTube
  4. Extra Lecture YouTube

Week 5

  1. Lecture 15, Exponential matrix YouTube
  2. Lecture 16, Solution of linear system system of ODE YouTube
  3. Lecture 17, Eigen value and eigen vector YouTube
  4. Lecture 18, Canonical form YouTube

Week 6

  1. Lecture 19, Solution of system of equations using method of eigenvalue YouTube
  2. Lecture 20, Method of eigenvalue continued YouTube
  3. Lecture 21, Maximal interval of existence YouTube
  4. Lecture 22, Maximal interval of existence continued YouTube

Week 7

  1. Lecture 23, Periodic Linear system YouTube
  2. Lecture 24, Asymptotic behavior of solution YouTube
  3. Lecture 25, Asymptotic behavior of solution( continued ) YouTube

Week 8

  1. Lecture 26, Asymptotic Behavior of Linear System: Part 3 YouTube
  2. Lecture 27, Exact and Adjoint Equation YouTube
  3. Lecture 28, Theory of Oscillation YouTube

Week 9

  1. Lecture 29: Sturm-Picone's theorem, Leighton's theorem YouTube
  2. Lecture 30: Boundary Value Problems YouTube
  3. Lecture 31: Maximum Principle YouTube

Week 10

  1. Lecture 32, Strum-Liouville Theory YouTube
  2. Lecture 33, Strum-Liouville Theory 2 YouTube
  3. Lecture 34, Periodic Strum-Liouville Problem YouTube
  4. Lecture 35, Eigenfunction Expansion YouTube

Week 11

  1. Lecture 36, Stability of a system YouTube
  2. Lecture 37, Equilibrium points YouTube
  3. Lecture 38, Lyapunov function and its application YouTube

Week 12

  1. Lecture 39, Stability of Equilibria YouTube
  2. Lecture 40, Phase Portrait YouTube

Syllabus and materials

At NPTEL, as the course publishes them.

Credits and licence

Institution
IIT Kanpur
Department
Mathematics
Teacher
Prof. Kaushik Bal
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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