Phase portrait of undamped pendulum. You can see three critical points: A center at (0,0), a saddle point at (,0), a center at (2,0).

MATH 246, Fall 2003: Differential Equations for Scientists and Engineers

News

• Table for critical points of linear systems. The corresponding in the textbook is Table 9.3.1, p. 484.
  Note that in the two "sensitive cases" of (i) two equal eigenvalues and (ii) purely imaginary eigenvalues other types than in the table in the textbook may occur.
• Assignment 3: Read Using Matlab for Autonomous Systems.
  Problem 1: Use e.g. A = sym([1 2; 3 4]); [eigvect,eigval] = eig(A) to find exact, symbolic eigenvalues and eigenvectors (without sym you get numerical approximations).
• Matlab tutoring has started, see the Matlab Tutoring Schedule. The location is PG2, the tutors are at a workstation to the left on entering, marked by a sign.
• If you are not familiar with Matlab:
  • Attend the Peer Training class Introduction to Matlab on one of the following days: 9/8, 9/9, 9/12, 9/15, 9/18, 9/19 (see schedule). This class costs $10. It is recommended to register early (WAM account required). Take a look at the class notes.
  • Read the Matlab Primer (PDF file) and try out the commands on a computer. This explains basic Matlab commands (but not symbolic operations, differential equation commands which are also needed for this course.)

  Do this now. Matlab will be required for the projects, and I will not explain Matlab in class.

• Read chapters 2, 3, 4 in "Differential Equations with Matlab".
• Do Problem Set A in "Differential Equations with Matlab" until 9/10. This will not be collected, but I will assume that everybody knows this material after 9/10.

Syllabus

• (coming soon): Information about time & place, instructor, textbooks, syllabus, grading policy, Matlab assignments, final exam. This was handed out in the first class.
• Detailed Syllabus

Recommended Problems from the Textbook

How to Hand in Assignments

Read the section ``Presenting Your Results'' (p. 40-46) in Chapter 4 of the Matlab supplement. Printouts of interactive input at the Matlab prompt will not be accepted. Solutions must be prepared in the following format:

For each problem hand in

• a printout of the file problemX.m containing the Matlab commands, and comments answering the questions asked in the problem. Also include comments for each plot command indicating which of the attached graphics it produced.
• a printout of the file problemX.txt containing Matlab output (using the Matlab diary command). Use the command echo on to print out all Matlab commands together with the output.
• a printout of all graphics. Clearly label all graphs and put a comment in the file problemX.m so that it is clear which Matlab command produced which graphic.

  (On Glue, WAM typing print figXY.ps in Matlab produces a postscript file figXY.ps of the current figure which you can then send to the printer.)

• additional (possibly handwritten) pages containing answers to questions asked in the problem (unless they are contained in the comments of the file problemX.m).

Using Matlab for Differential Equations

You are expected to read these documents carefully and try out the explained commands and examples on the computer (you can copy and paste the commands from the browser into the Matlab window).

• Using Matlab for First Order ODEs: How to plot direction fields, solve ODEs numerically and symbolically, plot solutions
• Using Matlab for Higher Order ODEs and Systems of ODEs: Solving ODEs numerically and symbolically, plotting the solutions, phase plane plots, vector fields.
• Using the Euler Method in Matlab
• Solving ODEs using the Laplace Transform in Matlab
• Using Matlab for Autonomous Systems

General Matlab Information

• Read chapters 2, 3, 4, 8 in "Differential Equations with Matlab".
• For an introduction to standard Matlab commands read the Matlab Primer (PDF file).
  For an introduction to symbolic Matlab commands read in the Symbolic Math Toolbox Documentation the chapters ``Getting Started'' and ``Calculus'' (also available as PDF file which is better for printing: print pages 15-55).
• Common Problems with Matlab
• Matlab documentation, Symbolic Math Toolbox Documentation
  Matlab help:  
• Matlab Primer (PDF file): Explains basic Matlab commands (but not symbolic operations, differential equation commands)
• Matlab Peer Training: If you are new to Matlab you might consider attending the class Introduction to Matlab on one of the following days: 9/8, 9/9, 9/12, 9/15, 9/18, 9/19 (see schedule). This class costs $10. It is recommended to register early (WAM account required). Take a look at the class notes.

Matlab Tutoring

For time and location check Matlab Tutoring Schedule.. The tutor will not do the problem sets for you, but only help with technical questions about the computers and Matlab. The location is PG2, the tutors are at a workstation to the left on entering, marked by a sign.

Using Computers on Campus

• Computer labs where Matlab is available
• Currently available WAM/Glue Unix machines
• How to get a WAM/Glue account, Printing account
• Text editors available on WAM, Glue (for writing m-files): nedit, pico, vi, emacs
• How to use a PC, Unix workstation on campus
• How to print text files for free