Math 4325: Homework & Exams


Handouts and notes


Homework assignments

AssignmentDescription Problems Due Date
1 Taylor series and Matlab Problems, Solutions: page1, page2 Tue, Sep 3
2 Phase Line 2.2.1, 2.2.4, 2.2.5, 2.2.8, 2.3.2 Tue, Sep 10
3 Phase Line with Linear Stability 2.4.4, 2.4.5, 2.4.6, 2.4.7 Tue, Sep 17
Exam 1 Solutions Tue, Sep 24
4 Bifurcations in Scaler Systems, 3.1.3, 3.3.2, 3.4.4, 3.7.4 (pssst....)
3.3.2 long solution
Tue, Oct 1
5 General 2-D systems Problems, Solutions Tue, Oct 8
6 Linear 2D systems 5.2.1, 5.2.2, 5.2.3, 5.2.4,5.2.5, 5.2.7, 5.2.8, (pssst....) Thu, Oct 17
7 Phase Plane Problems & Solutions Thu, Oct 24
Exam 2 Solutions Tue, Oct 29
8 Limit Cycles 7.1.2, 7.1.3, 7.3.1, 7.3.2 ,
Tue, Nov 5.
9 Bifurcations in Planer Systems 8.1.6, 8.1.10, one other Tue, Nov 12
10 Hopf Bifurcations Problems Tue, Nov 19
12 Maps and bifurcations Problems, Cobweb templates, Solutions Thu, Dec 5
Exam 3 Solutions TBD

ODE Software for Matlab

John C. Polking, Department of Mathematics, Rice University, has developed some very nice routines to analyze first and second order differential equations that run inside of MATLAB. They are dfield*.m, pplane*.m. The * differentiates routines that run on Matlab version *. The most recent versions to use with current versions of matlab are: Older versions can be found at the dfield homepage, which provides the m-files for all versions of MATLAB. There are also a JAVA versions available that run using your browser. Use whichever version is convenient for you; before deciding, double check that you can print plots as you will need to turn results in as part of homework assignments.

Save these files to your MATLAB working directory, start up MATLAB, and type "dfield*" at the MATLAB prompt. dfield* and pplane* are very easy to use - just play and experiment. I give some brief comments regarding their capabilities below.

dfield*

pplane*