Explore a comprehensive course on ordinary differential equations and their applications. Delve into topics such as general and linear second-order equations, periodic orbits, Poincare-Bendixon theory, stability of equilibrium points, and phase plane analysis. Learn about Picard's existence and uniqueness theorem, Gronwall's Lemma, and well-posedness of initial value problems. Study series solutions, continuation of solutions, and various types of systems including 2x2 and general systems. Gain a deep understanding of first and second-order linear equations, diagonalizability, and the application of fixed point theorems in existence proofs.
Overview
Syllabus
General Second Order Equations - Continued.
General Second Order Equations.
Linear Second Order Equations.
Periodic orbits and Poincare Bendixon Theory Continued.
Periodic orbits and Poincare Bendixon Theory.
Second Order Linear Equations Continued - III.
Stability Equilibrium points continued II.
Stability Equilibrium points continued I.
Stability Equilibrium points.
Basic Definitions and Examples.
General Systems Continued and Non-homogeneous systems.
General systems.
2 by 2 Systems and Phase Plane Analysis Continued.
2 by 2 Systems Phase Plane Analysis.
General System and Diagonalizability.
Series solution.
Continuation of solutions.
Existence using fixed point theorem.
Basic Lemma and Uniqueness Theorem.
Picard's existence and uniqueness theorem.
Picard's existence and uniqueness continued.
Gronwall's Lemma.
Well-posedness and examples of IVP.
Second order linear equations Continued II.
Second order linear equations Continued I.
Second order linear equations.
First order linear equations.
Taught by
Ch 30 NIOS: Gyanamrit
