This course covers general second-order equations, linear second-order equations, periodic orbits, stability equilibrium points, series solutions, existence theorems, uniqueness theorems, and well-posedness in the context of ordinary differential equations. Students will learn to analyze 2 by 2 systems using phase plane analysis, understand Picard's existence and uniqueness theorem, and apply Gronwall's Lemma. The teaching method includes theoretical explanations, examples, and problem-solving sessions. This course is intended for individuals interested in gaining a deeper understanding of ordinary differential equations and their applications.
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
