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. 1.6 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. 3.1-3.2 28-Feb Th Straight-line solutions. Geometry of systems with two eigenvalues. 3.3 7 4-Mar Tu What if the eigenvalues are complex? "Undetermined coefficients." Zero eigenvalues and repeated eigenvalues. 3.4 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