# 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