LAB # 1

The goal of this exercise is to help you (re)gain confidence with EXCEL, Maple etc... Not much materials content here.

Exercise 0. The link below illustrates some limitations of our computers with respect to numerical errors. There is a java program that simulates the problem of hard colliding spheres - a model system in many physical systems.  If this simulation is not working properly on your computer, try this one or this one

1. Read the background information.
2. Go to to the java program: Select the number of particles (start with 10) and run the program for a (small) number of time steps. Then stop it and reverse it. If the number of steps is large then the "reverse" simulation will not return to the original position. Find the maximum number of steps that produce a "reversible"
3. Produce a plot of maximum number of steps that produce a reversible solution versus the number of particles.
4.  Discuss the implications of this problem.
   

Exercise 1.   What is the maximum and minimum numbers that your computer can handle?  Click here

Exercise 2.   What is the precision of your computer?  Click here

Exercise 3.   Numerical Integration?  Click here