Sections (d) and (e) will also be explored by computer implementation using MATLAB or other software. (f) Sturm-Liouville Boundary Value Problems: Sturm-Liouville problem for 2 nd order equations, Green's function, Sturm comparison theorems and oscillations, eigenvalue problems. (e)* Asymptotic Behavior: Stability (linearized stability and Lyapunov methods). (d)* Two Dimensional Autonomous Systems and Phase Space Analysis: critical points, proper and improper nodes, spiral points, saddle points, Limit cycles, and periodic solutions. (c) Higher Order Linear Equations and Linear Systems: fundamental solutions, Wronskian, variation of constants, matrix exponential solution, behaviour of solutions. (b) Existence and Uniqueness of Initial Value Problems: Lipschitz and Gronwall's inequality, Picard’s Theorem, dependence on initial conditions, continuation of solutions and maximal interval of existence. (a) Review of Solution Methods for first order and second order linear equations. ![]() Prerequisites: MAT 230/430 ODE (for undergraduates) ![]() Credits : 4 (3 lectures and 1 tutorial weekly)
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