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  
1519  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 tracedeterminant 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 (810am) 