# Lecture Notes

Class 01 - Introduction (08/22/18)

Class 02 - Approximate solutions of first order equations (08/24/18)

Class 03 - Separable equations (08/27/18)

Class 04 - Linear equations, I (08/29/18)

Class 05 - Linear equations, II (08/31/18)

Class 06 - Models of motion (09/03/18)

Class 07 - Mixing problems (09/05/18)

Class 08 - Exact solutions, I (09/07/18)

Class 09 - Exact solutions, II (09/10/18)

Class 10 - Existence of Solutions (09/12/18)

Class 11 - Uniqueness of Solutions; Dependence of solutions on initial conditions (09/14/18)

Class 12 - Autonomous equations and stability (09/17/18)

Class 13 - Modeling population growth (09/19/18)

Class 14 - Financial models (09/21/18)

Class 15 - The catenary (09/24/18)

Recap Pre Exam 1 (09/26/18)

Class 16 - Introduction to systems (10/01/18)

Class 17 - Geometric interpretation of systems (10/03/18)

Class 18 - Existence and Uniqueness of solutions (10/05/18)

Class 19 - Equilibrium points, and introducing linear systems of ODE’s (10/08/18)

Class 20 - Properties of solutions of homogeneous systems (10/10/18)

Class 21 - Homogeneous systems with constant coefficients (10/12/18)

Class 22 - Planar systems, I (10/22/18)

Class 23 - Planar systems, II (10/24/18)

Class 24 - Phase plane portraits (10/26/18)

Class 25 - The Trace-Determinant plane (10/29/18)

Class 26 - Higher dimensional systems, I (10/31/18)

Recap Pre Exam 2 (11/02/18)

Class 27 - Hgher dimensional systems, II (11/07/18)

Class 28 - Stability of solutions of homogeneous systems (11/09/18)

Class 29 - Higher order homogeneous ODE’s, I (11/12/18)

Class 30 - Higher order homogeneous ODE’s, II (11/14/18)

Class 31 - Higher order homogeneous ODE’s, III (11/16/18)

Class 32 - Inhomogeneous linear systems of ODE’s (11/19/18)

Class 33 - Linearization of nonlinear systems (11/26/18)

Class 34 - Linearization of nonlinear systems, II (11/28/18)

Class 35 - Stability of equilibrium solutions (11/30/18)

Class 36 - The method of Lyapunov (12/03/18)

Recap Pre Final (12/05/18)