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  
1927  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 tracedeterminant 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  
271  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 (810am) 