Math 305, Spring 2015

• Mondays: 14:00-15:30
• Wednesdays: 14:00-15:30

The Festival of Scholars is a campus-wide celebration of student work. It is an opportunity to discuss research, to exhibit, perform, or appreciate art, and to cross disciplinary boundaries. The Festival will be held on Friday, April 17, 2015. Classes will be cancelled on that day, but you are still required to participate in the Festival, either by presenting your work or attending presentations by your fellow students.

• Notes about the calculus of variations
• Calculus of Variations Exercises (section 2.3), updated

• Please turn in the following exercises by Friday 13 February:
  2.2.2, 2.2.3, 2.2.5, 2.2.7, 2.2.8
  2.3.1, 2.3.2
• You were also supposed to complete Exercise 2.2.9. Please do this, but do not turn it in yet. You’ll need it to do the next homework set.
• Once you’re done with those problems, the next batch of homework will be:
  2.2.9, 2.3.12, 2.3.13
  These are due Wednesday 18 February.

u[t_, x_] := 
 Sum[(8/((2 k + 1)^2 Pi^2)) Cos[(2 k + 1)*.5*Pi*x]*
   Cos[(2 k + 1)*.5*Pi*t], {k, 0, 5}]
u0[t_, x_] := (8/((2*0 + 1)^2 Pi^2)) Cos[(2*0 + 1)*.5*Pi*x]*
  Cos[(2*0 + 1)*.5*Pi*t]
u1[t_, x_] := (8/((2*1 + 1)^2 Pi^2)) Cos[(2*1 + 1)*.5*Pi*x]*
  Cos[(2*1 + 1)*.5*Pi*t]
u2[t_, x_] := (8/((2*2 + 1)^2 Pi^2)) Cos[(2*2 + 1)*.5*Pi*x]*
  Cos[(2*2 + 1)*.5*Pi*t]
u3[t_, x_] := (8/((2*3 + 1)^2 Pi^2)) Cos[(2*3 + 1)*.5*Pi*x]*
  Cos[(2*3 + 1)*.5*Pi*t]
Manipulate[
 Plot[{u[t, x], u0[t, x], u1[t, x]}, {x, -1, 1}, PlotRange -> 1], {t, 
  0, 12}]