News

• Note change in list of suggested problems from section 2.10.
• Numerical Methods (PS, 16 p.), the Matlab version of Chapter 7 in ``Differential Equations with Maple'' is now available. Contents: Numerical solution ODEs using ode45 in Matlab; Euler, improved Euler and Runge-Kutta methods; controlling the eror in ode45, reliability of numerical methods.
• Exam 1 will be on Tue, Oct. 7. It will cover the material about first order ODEs, but not numerical methods. The corresponding sections in the textbook are BD 1.1, 2.1-2.6, 2.8 and the theoretical material in chapters 5 and 6 in ``Differential Equations with Maple'' (I will not ask about any Matlab commands).
• Read the remarks about Assignment 1
• There is a page about Common Problems with Matlab. If you have trouble check this page before asking the tutor.
• Warning: the command close all sometimes causes Matlab to crash.

Course Outline

Information about time & place, instructor, textbooks, syllabus, grading policy, Matlab assignments, final exam. This was handed out in the first class.

Assignments

• Problem Set A (PS, 3 p.): Problem set for practicing Matlab. Will not be collected or graded. Must be completed by each student by Thu, Sept. 11.
  Solutions for Problem Set A: You should study this to see how to hand in homework problems (printouts of file prob.m, prob.txt and graphics for each problem).
• Assignment 1 was handed out on Sept. 18 and is due on Sept. 30.
  Note: Problems 3. (B-10.(a)) and 4.(e) mention the fsolve command. You can use the fzero command instead (which was explained in ``Getting started with Matlab (PS)''). The fsolve command is more versatile, but is not included in the student version of Matlab. Note that the first argument of fsolve or fzero can be a string like 'exp(-x)-sin(x)', but the variable must be x in this case. The first argument can also be an inline function of one variable.

  Problem 2 (B-8 in ``Differential Equations with Maple''): Matlab may not be able to solve all the given differential equations (a)-(f). Either Matlab returns a solution, or it returns ``Explicit solution could not be found''.

  Problem 4(b), (c): I recommend to make the contour plot for t in [-3,3] and y in [-3,3] (instead of y in [-2,2] as stated in the problem).

  Problem 4(a): Here is an example which shows how to interpret the Matlab output.

  Problem 4(b), (c): Problem 5 of Problem Set A (PS) explains how to make contour plots. Use t, T instead of x, X and use in contour the formula in T, Y resulting from (a) (remember to use ``.*'' instead of ``*'').

  Problem 4(d): Write the problem in the form g(y)=0 where y is the unknown function value at t=1. Define an inline function g(y). Then use fzero(g,guess).