InfoCoBuild

Ordinary Differential Equations

Ordinary Differential Equations. Instructor: Prof. Kaushik Bal, Department of Mathematics and Statistics, IIT Kanpur. 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 aspects of Linear Systems and then analyze local and global behavior of nonlinear systems using techniques from Linear theory. (from nptel.ac.in)

Introduction


Lecture 01 - Vector Spaces
Lecture 02 - Linear Transformation
Lecture 03 - Matrices
Lecture 04 - Calculus in Several Variable
Lecture 05 - Lipschitz Continuity
Lecture 06 - Cauchy-Schwarz and Gronwall Inequality
Lecture 07 - Ordinary Differential Equations: Introduction
Lecture 08 - Differential Inequalities
Lecture 09 - 2nd Order Constant Coefficient Linear Equations
Lecture 10 - Picard Existence and Uniqueness Theorem
Lecture 11 - Linear System
Lecture 12 - Well-posedness of an ODE
Lecture 13 - Linear System 1
Lecture 14 - Linear System 2
Lecture 14-1 - Fundamental Matrix - W4P3
Lecture 15 - Exponential of a Linear Operator
Lecture 16 - Fundamental Theorem of Linear Systems
Lecture 17 - Higher Dimensional Matrix Exponential
Lecture 18 - Higher Dimensional Matrix Exponential (cont.)
Lecture 19 - Method of Eigenvalue
Lecture 20 - Method of Eigenvalue (cont.)
Lecture 21 - Maximal Interval of Existence
Lecture 22 - Maximal Interval of Existence: Worked Out Examples
Lecture 23 - Periodic Linear System
Lecture 24 - Asymptotic Behavior of Solution to Linear System 1
Lecture 25 - Asymptotic Behavior of Solution to Linear System 2
Lecture 26 - Asymptotic Behavior of Solution to Linear System 3
Lecture 27 - Exact and Adjoint Equations
Lecture 28 - Sturm Comparison Theory
Lecture 29 - Oscillation Theory
Lecture 30 - Linear Boundary Value Problem
Lecture 31 - Maximum Principle
Lecture 32 - Sturm Liouville Theory
Lecture 33 - Sturm Liouville Theory (cont.)
Lecture 34 - Periodic Sturm Liouville Theory Problem
Lecture 35 - Eigenfunction Expansion
Lecture 36 - Stability in the Sense of Lyapunov I
Lecture 37 - Stability in the Sense of Lyapunov II
Lecture 38 - Lyapunov Direct Method
Lecture 39 - Linear Two-dimensional Phase Space Dynamics
Lecture 40 - Phase Portrait for Planar Systems

References
Ordinary Differential Equations
Instructor: Prof. Kaushik Bal, Department of Mathematics and Statistics, IIT Kanpur. Differential Equations are one of the central topics which results when studying models arising out of physical systems.