Differential Equations - Schedule

Differential Equations Schedule
  rev. 3/25/07        
week   topics… read… due in class  
1 22-Jan M What's a DE?  What's a solution?  Modeling.   1.1, pp. 1-8.
24-Jan W Separable equations 1.2, pp. 20-28. 1.1 ## 10, 11, 12
  26-Jan F Slope fields, software tools 1.3, pp. 36-43 mini-mini-exam
1.2 ## 2, 3, 35,
      6, 7,10, 26,
     plus any of 5-32
 
2 29-Jan M Euler's method for numerical solutions 1.4 1.3 ## 1,2,3,5 (with HPGSolver), 15,16,17 (for class); print interesting slope field
31-Jan W Existence and Uniqueness.  Extending solutions.  Continuous dependence on initial conditions and parameters. 1.5
  2-Feb F Autonomous equations.  Equlibria, attracting or otherwise.  Phase lines. 1.6 mini-exam  
3 5-Feb M First-order linear equations (formula handout).  Homogeneous equations 1.8
7-Feb W First-order linear equations: linear model with general and particular solutions; exact equations and integrating factors 1.8, 1.9; rest of 1.1, 1.2
  9-Feb F More modeling (logistic model) All of 1.1 thru 1.8 graded problem set  
4 12-Feb M Systems of equations 2.1
14-Feb W More logistic equation, more systems end of 1.1; 2.1 graded problem set due
  16-Feb F Vector fields in the phase plane: sources, sinks, periodic solutions, attractors 2.2    
5 19-Feb M Analytic methods: Decoupled and partly decoupled systems, substitutions in systems, conserved or monotone quantities 2.3
21-Feb W Euler's method for systems 2.4
  23-Feb F Linear systems Start chapter 3 (or Monday) exam about now  
6 26-Feb M Geometry and eigenvalues 3.1-3.2
28-Feb W Straight-line solutions 3.2
  2-Mar F More geometry of systems with two eigenvalues, hence straight-line solutions on two lines 3.3    
7 5-Mar M What if the eigenvalues are complex? 3.4
7-Mar W More complex eigenvalues
"undetermined coefficients"
 zero and identical eigenvalues
more 3.4
  9-Mar F Higher-order linear equations (not sytems) with constant coefficients 3.5, 3.6 mini-mini-exam  
Spring Break        
8 19-Mar M Traces and determinants again
Substitution in the spiral case
3.6, 3.7 graded problem set
21-Mar W Examples of linearization 3.7, 3.8 mini-exam
  23-Mar F Higher-dimensional systems; first example from chapter 4   graded problem set due  
9 26-Mar M Chapter 4: systems with forcing terms 4.1 Due: Sec. 3.8, ## 17, 18 (to turn in)
28-Mar W 4.2
  30-Mar F     exam about now  
10 2-Apr M
4-Apr W Chapter 5?  More likely, skip to Chapter 6, numerical methods Ch. 6
  6-Apr F        
11 9-Apr M
11-Apr W Laplace transforms: example of solving and equation; example involving convolutions Part of Ch. 7
  13-Apr F        
12 16-Apr M Dynamic systems: bifurcations and all that Ch. 8 and excursions
18-Apr W
  20-Apr F        
13 23-Apr M
25-Apr W Auction examples?
  27-Apr F Kepler orbits: solution of r''=r/(|r|^3)      
14 30-Apr M
2-May W
  4-May F Party / picture      
Final exam