Math 319 Homework -- Spring 2000

These are the ASSIGNED exercises. You must hand them in by the specified due date.

• Due Thu Feb 10, 2000 10 Problems
  B&DP: 2.2.22, 23, 38; 2.3.23; 2.4.10, 14; 2.5.10, 27; 2.6.18; Extra problem (electric circuit)
• Due Tue Feb 22, 2000
  
  1. B&DP: 2.7.13, 2.8.14, 2.9.13, 2.10.30, 2.10.42, 2.10.45
  2. Use Euler's method to solve y'= y, y(0)=1. Use time steps h=1, 1/2, 1/4, 1/8, ... Make a relevant plot of error ( i.e. | y(1)-y_n |) vs. time step.
     ["relevant": what is the best way to display (x,y) data where y ~ x^a? lin-lin, lin-log, log-lin, log-log?] (Ideally, program a computer so you can use any step size effortlessly, but otherwise try at least a few step sizes with a calculator).
  3. If you have written a computer program, use it to solve y'= cos(t y), y(0)=1. What do you think is the asymptotic behavior of y(t) when t is very large?
  4. B&DP 3.1.9 + solve y''+5y'=0, y(0)=-2, y'(0)=3.

• Due Tue Apr 4, 2000
  
  • B&DP: 3.8.17, 3.9.6 + 8, 3.9.17, 5.2.21, 5.4.2, 5.5.17, 6.3.9, 6.3.17, 6.3.23, 6.4.2, 6.4.15

• Due Tue Apr 25, 2000
  
  Solve 10 of the following 11 problems:
  • B&DP: 7.1.19, 7.1.21, 7.2.18, 7.3.3, 7.5.18, 7.5.24, 7.5.30, 7.6.25, 7.7.7, 7.8.6, 7.9.1