Math 307: homework

• For Wednesday, 2 October: Read Section 2.1, and answer these questions: What does "first order linear differential equation" mean? How do you solve one? (Don't hand anything in for this assignment; just come to class with the answers in mind.)
• Due Wednesday, 9 October. Solutions.
  • Section 2.1: 13, 17, 29
  • Section 2.2: 2, 4, 25
  • Section 2.3: 1, 18, 26
• Due Wednesday, 16 October. Solutions.
  • Section 2.5: 3, 5, 22
• Practice problems on Euler's method. Don't turn these in. Solutions.
  • Section 2.7: 1, 2, 11, 19
• Practice problems on complex numbers and Euler's formula. Don't turn these in. Solutions.
  • Section 3.4: 1-6, 29.
• No homework due Wednesday, 23 October.
• Due Monday, 28 October: exam revisions. Solutions.
• Due Wednesday, 30 October. Solutions.
  • Section 3.1: 4, 5, 15, 21
  • Section 3.4: 9, 10, 21, 41
  • Suggestion for 41: to make the substitution x=lnt, also use the chain rule to rewrite dy/dt as

      dy/dt = dy/dx  dx/dt
            = dy/dx  1/t
    	    

    Find a similar formula for y'' -- problem 34 might help.
• Due Wednesday, 6 November. Solutions.
  • Section 3.5: 4, 14, 25
  • Section 3.6: 1, 8, 17, 28
  • Section 3.7: 5, 18
• Due Wednesday, 13 November. Solutions.
  • Section 3.8: 3, 6, 11, 17
  • Also do this problem: imagine a train which goes in a straight line through a tunnel between two points on the surface of the earth (for example, between Seattle and Rio de Janeiro). Suppose that there is no friction, and the train just operates under gravity, so if you start it at one end of the tunnel, at rest, it will fall into the tunnel, accelerate until it reaches the midpoint of its trip, decelerate as it nears the other end, stop at the other end, and then return. Show that the time required for a complete round trip is the same for all such tunnels (it doesn't matter whether it ends at Rio de Janeiro or Beijing or Baltimore), and estimate its value.
    You may need to know some facts about gravity to do this problem.
• Do these before the exam on Wednesday, November 20. Don't hand them in. Solutions.
  • Section 3.9: 1, 5, 7, 17, 18.
• Due Wednesday, 27 November: exam revisions. Solutions.
• Due Wednesday, 27 November. Solutions.
  • Section 6.1: 7, 13, 27abc. Also read problem 26.
  • Section 6.2: 1, 8, 16, 22
• Due Wednesday, 4 December. Solutions.
  • Section 6.3: 9, 18, 27
  • Section 6.4: 2, 4, 5, 15
• Practice problems on impulse functions and formulas for Laplace transforms. This material will be on the final exam, so make sure you do these. Don't hand in. Solutions.
  • Section 6.5: 1, 2, 6, 13
  • Section 6.2: 28-30
  • Section 6.3: 19-21

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Last modified: Wed Dec 11 15:11:53 PST 2002