Differential Equations Schedule
  rev. 1/22/2008        
week   topics… read… due in class  
1 22-Jan Tu What's a DE?  What's a solution?
Some Modeling.
Separable Equations.
1.1, pp. 1-8
1.2, pp. 10-28
  24-Jan Th More separable equations.
Slope fields.
Software tools.
1.3, pp. 36-43 1.2 ## 2, 3, 6, 7, 10, 26
Also, "problem 1"
2 29-Jan Tu Euler's method for numerical solutions.
Existence and Uniqueness.
1.4, 1.5
  31-Jan Th More existence and uniqueness: extending solutions; continuous dependence on initial conditions and parameters.
Autonomous equations.  Equlibria, attracting or otherwise.  Phase lines.
3 5-Feb Tu First-order linear equations (formula handout).  Homogeneous equations. 1.8
  7-Feb Th First-order linear equations: linear model with general and particular solutions; exact equations and integrating factors.
More modeling (logistic model).
1.9; rest of 1.1, 1.2    
4 12-Feb Tu Systems of equations 2.1
  14-Feb Th Vector fields in the phase plane: sources, sinks, periodic solutions, attractors 2.2    
5 19-Feb Tu Analytic methods: Decoupled and partly decoupled systems, substitutions in systems, conserved or monotone quantities 2.3
  21-Feb Th Euler's method for systems 2.4 exam about now  
6 26-Feb Tu Linear systems.
Geometry and eigenvalues.
  28-Feb Th Straight-line solutions.
Geometry of systems with two eigenvalues.
7 4-Mar Tu What if the eigenvalues are complex?
"Undetermined coefficients."
Zero eigenvalues and repeated eigenvalues.
  6-Mar Th Higher-order linear equations (not sytems) with constant coefficients 3.5, 3.6    
Spring Break        
8 18-Mar Tu (Schedule from here on is speculative)
Traces and determinants again.
Examples of linearization.
3.6, 3.7, 3.8
  20-Mar Th Higher-dimensional systems; first example from chapter 4      
9 25-Mar Tu Chapter 4: systems with forcing terms 4.1
  27-Mar Th More systems with forcing terms 4.2 exam about now  
10 1-Apr Tu Chapter 5?  More likely, skip to Chapter 6, numerical methods Ch. 6
  3-Apr Th        
11 8-Apr Tu Laplace transforms: example of solving and equation; example involving convolutions Part of Ch. 7
  10-Apr Th        
12 15-Apr Tu Dynamic systems: bifurcations and all that Ch. 8 and excursions
  17-Apr Th        
13 22-Apr Tu Auction examples?
  24-Apr Th Kepler orbits: solution of r''=r/(|r|^3)      
14 29-Apr Tu
  1-May Th Party / picture      
Final exam