## Mathematics 210 - Spring term 2003 - seventh assignment

This assignment requires you to submit several spreadsheets concerned with solving differential equations. This lab and the re-done mid-terms are due Wednesday, March 19, by class time. I repeat the instructions from the first lab:
• Question 1. Use the spread sheet to solve the differential equation dy/dt = -y + cos(2t) and initial condition y(0) = 1 with step size dx = 0.1 for the range t=0 to 20. Do this by each of the three methods explained in class: Euler's, Improved Euler's, Runge-Kutta of order 4. Do all of these on one sheet. Graph the solutions you get.

Save this sheet as m210.7.1.ms.

• Question 2. Use the spread sheet to solve the differential equation dy/dt = -y + t and initial condition y(0) = 1. Use Improved Euler over the range 0 to 6. Find roughly the largest step size you can that will give you an answer at the end correct to 4 decimals. Graph your solution.

Save this sheet as m210.7.2.ms.

• Question 3. An object at the surface of the Earth accelerates at 9.8 m/s2. The radius of the Earth is 6370 kilometers. If you drop an object from rest at a distance of 10,000 kilometers from the centre of the Earth, how long does it take for it to hit the Earth? Answer correct to 1%. Ignore air friction. Explain your accuracy.

Save this sheet as m210.7.3.ms.

That's it!

If you find these questions confusing, please write me.