NOC:Ordinary Differential Equations

Lecture 1 - Vector Spaces

Lecture 2 - Linear Transformation

Lecture 3 - Matrices

Lecture 4 - Calculus in Several Variable

Lecture 5 - Lipchitz Continuity

Lecture 6 - Cauchy-Schwatz and Gronwall Inequality

Lecture 7 - Ordinary Differential Equations: Introduction

Lecture 8 - Differential Inequalities

Lecture 9 - 2nd Order Constant coefficient linear equations

Lecture 10 - Picard Existence and Uniqueness Theorem

Lecture 11 - Linear System

Lecture 12 - Well-Posedness of a ODE

Lecture 13 - Linear System - 1

Lecture 14 - Linear System - 2

Lecture 15 - Fundamental Matrix

Lecture 16 - Exponential of a Linear Operator

Lecture 17 - Fundamental theorem of linear Systems

Lecture 18 - Higher Dimensional Matrix Exponential - 1

Lecture 19 - Higher Dimensional Matrix Exponential - 2

Lecture 20 - Method of Eigenvalue

Lecture 21 - Method of Eigenvalue (Continued...)

Lecture 22 - Maximal Interval of Existence

Lecture 23 - Maximal Interval of Existence: Worked out examples

Lecture 24 - Periodic Linear System

Lecture 25 - Asymptotic behavior of solution to linear system - I

Lecture 26 - Asymptotic behavior of solution to linear system - II

Lecture 27 - Asymptotic Behavior of Linear Systems - III

Lecture 28 - Exact and Adjoint equations

Lecture 29 - Sturm Comparison Theory

Lecture 30 - Oscillation Theory - 2

Lecture 31 - Linear Boundary Value Problem

Lecture 32 - Maximum Principle

Lecture 33 - Sturm Liouville Theory - 1

Lecture 34 - Sturm Liouville Theory - 2

Lecture 35 - Periodic Sturm Liouville Problem

Lecture 36 - Eigenfunction Expansion

Lecture 37 - Stability in the sense of Lyapunov - I

Lecture 38 - Stability in the sense of Lyapunov - II

Lecture 39 - Lyapunov Direct method

Lecture 40 - Linear two-dimensional phase space dynamics (Continued...)

Lecture 41 - Phase Portrait for Planar Systems