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...)