Marco Radeschi

Fall 2019 Math 20750 Syllabus


Syllabus

 

Date Section Topic Assignment
August 28 1.1 Introduction
30 2.1 Approximate solutions of first order equations Assignment 1
September 2 2.2 Separable equations
4 2.4 Linear equations
6 2.4 Linear Equations Assignment 1 due
Assignment 2
9 2.3 Models of motion (only air resistance proportional to velocity)
11 2.5 Mixing problems Assigment 2 due
13 2.6 Exact solutions, I Assignment 3
16 2.6 Exact solutions, II
18 2.7 Existence of Solutions Assignment 3 due
20 2.7 - 2.8 Uniqueness of Solutions; Dependence of solutions on initial conditions Assignment 4
23 2.9 Autonomous equations and stability
25 3.1 Modeling population growth Assignment 4 due
27 3.3 Financial models Assignment 5
30 Equation of a hanging rope: the catenary
October 2 Review
4 Exam 1 (in class)
7 8.1 Introducing systems of ODE's
9 8.2 Geometric Interpretation of systems of ODE's Assignment 5 due
11 8.3 Existence and Uniqueness of solutions; Equilibrium points Assignment 6
14 8.4 Introducing linear systems
16 8.5 Properties of solutions to homogeneous systems Assignment 6 due
18 9.1 Homogeneous systems with constant coefficients Assignment 7
19-27 Fall Break
28 9.2 Planar Systems, I
30 9.2 Planar Systems, II Assignment 7 due
November 1 9.3 Phase plane portraits Assignment 8
4 9.4 The trace-determinant plane
6 9.5 Higher dimensional systems, I
8 Review
11 Exam 2 (in class)
13 9.5 Higher dimensional systems, II Assignment 8 due
15 9.7 Stability of higher order linear systems Assignment 9
18 9.8 Higher Order Homogeneous ODE's, I
20 9.8 Higher Order Homogeneous ODE's, II Assignment 9 due
22 9.9 Higher Order Homogeneous ODE's, III Assignment 10
25 9.9 Inhomogeneous linear systems
27-1 Thanksgiving Break
December 2 10.1 Linearization of nonlinear systems
4 10.1 Linearization of nonlinear systems, II Assignment 10 due
6 10.2 Stability of equilibrium solutions to nonlinear autonomous systems Assignment 11
December 9 10.7 The method of Lyapunov
11 Review Assignment 11 due
17 Final Exam (8-10am)