Marco Radeschi

Math 20750 Syllabus


Syllabus

 

Date Section Topic Assignment
August 22 1.1 Introduction
24 2.1 Approximate solutions of first order equations Assignment 1
27 2.2 Separable equations
29 2.4 Linear equations
31 2.4 Linear Equations Assignment 1 due
Assignment 2
September 3 2.3 Models of motion (only air resistance proportional to velocity)
5 2.5 Mixing problems Assigment 2 due
7 2.6 Exact solutions, I Assignment 3
10 2.6 Exact solutions, II
12 2.7 Existence of Solutions Assignment 3 due
14 2.7 - 2.8 Uniqueness of Solutions; Dependence of solutions on initial conditions Assignment 4
17 2.9 Autonomous equations and stability
19 3.1 Modeling population growth
21 3.3 Financial models Assignment 4 due; Assignment 5
24 Equation of a hanging rope: the catenary
26 Review
28 Exam 1 (in class)
October 1 8.1 Introducing systems of ODE's
3 8.2 Geometric Interpretation of systems of ODE's Assignment 5 due
5 8.3 Existence and Uniqueness of solutions; Equilibrium points Assignment 6
8 8.4 Introducing linear systems
10 8.5 Properties of solutions to homogeneous systems Assignment 6 due
12 9.1 Homogeneous systems with constant coefficients Assignment 7
15-19 Fall Break
22 9.2 Planar Systems, I
24 9.2 Planar Systems, II Assignment 7 due
26 9.3 Phase plane portraits Assignment 8
29 9.4 The trace-determinant plane
31 9.5 Higher dimensional systems, I
November 2 Review
5 Exam 2 (in class)
7 9.5 Higher dimensional systems, II Assignment 8 due
9 9.7 Stability of higher order linear systems Assignment 9
12 9.8 Higher Order Homogeneous ODE's, I
14 9.8 Higher Order Homogeneous ODE's, II Assignment 9 due
16 9.9 Higher Order Homogeneous ODE's, III Assignment 10
19 9.9 Inhomogeneous linear systems
21 - 25 Thanksgiving Break
26 10.1 Linearization of nonlinear systems
28 10.1 Linearization of nonlinear systems, II Assignment 10 due
30 10.2 Stability of equilibrium solutions to nonlinear autonomous systems Assignment 11
December 3 10.7 The method of Lyapunov
5 Review Assignment 11 due
10 Final Exam (8-10am)