INTERNET SPECIAL, Spring Semester 2002

Recall from calculus that y'(t) is roughly (y(t+h)-y(t))/h for small h, and consider the IVP y'=y, y(0)=1

  1. First of all, plot the solution of the above IVP for t between 0 and 1.

  2. Let h=1, replace y'(0) by the above expression, calculate y(1) from the condition y(0)=1 and y'=y, and plot y(0) and y(1) in a coordinate system.

  3. Now let h=0.5 and calculate y(0.5) and y(1) as above, also plot them in a coordinate system.

  4. Do all of the above for h=0.25 and for h=0.1.

  5. Use a computer to do all of the above for h=0.01 and for h=0.00001. Explain what is happening as h is tending to 0.

If you want to work on this extra credit internet special, which is worth 30 points (only if all parts of the problem are addressed), you have to turn it in no later than February 28, 2002, absolutely no later than 3:30 pm in either my office SH-311 or in my mailbox in the second floor of the Crawford building.