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 Inhomogeneous linear systems Assignment 10
19 10.1 Linearization of nonlinear systems
21 - 25 Thanksgiving Break
26 10.2 Long term behaviour of solutions
28 Assignment 10 due
30 Assignment 11
December 3
5 Assignment 11 due
Review
10 Final Exam (8-10am)