Ordinary Differential Equations and Applications

Lecture 1 - General Introduction

Lecture 2 - Examples

Lecture 3 - Examples (Continued - I)

Lecture 4 - Examples (Continued - II)

Lecture 5 - Linear Algebra

Lecture 6 - Linear Algebra (Continued - I)

Lecture 7 - Linear Algebra (Continued - II)

Lecture 8 - Analysis

Lecture 9 - Analysis (Continued...)

Lecture 10 - First Order Linear Equations

Lecture 11 - Exact Equations

Lecture 12 - Second Order Linear Equations

Lecture 13 - Second Order Linear Equations (Continued - I)

Lecture 14 - Second Order Linear Equations (Continued - II)

Lecture 15 - Well-posedness and Examples of IVP

Lecture 16 - Gronwall's Lemma

Lecture 17 - Basic Lemma and Uniqueness Theorem

Lecture 18 - Picard's Existence and Uniqueness Theorem

Lecture 19 - Picard's Existence and Uniqueness (Continued...)

Lecture 20 - Cauchy Peano Existence Theorem

Lecture 21 - Existence using Fixed Point Theorem

Lecture 22 - Continuation of Solutions

Lecture 23 - Series Solution

Lecture 24 - General System and Diagonalizability

Lecture 25 - 2 by 2 systems and Phase Plane Analysis

Lecture 26 - 2 by 2 systems and Phase Plane Analysis (Continued...)

Lecture 27 - General Systems

Lecture 28 - General Systems (Continued...) and Non-homogeneous Systems

Lecture 29 - Basic Definitions and Examples

Lecture 30 - Stability Equilibrium Points

Lecture 31 - Stability Equilibrium Points (Continued - I)

Lecture 32 - Stability Equilibrium Points (Continued - II)

Lecture 33 - Second Order Linear Equations (Continued - III)

Lecture 34 - Lyapunov Function

Lecture 35 - Lyapunov Function (Continued...)

Lecture 36 - Periodic Orbits and Poincare Bendixon Theory

Lecture 37 - Periodic Orbits and Poincare Bendixon Theory (Continued...)

Lecture 38 - Linear Second Order Equations

Lecture 39 - General Second Order Equations

Lecture 40 - General Second Order Equations (Continued...)