Bill Goodwine's Courses

In this class we will solve various forms of the wave equation, which describe the motion of vibrating strings, drum heads, etc. Movies of the solution to the wave equation in various forms are as follows. If the movies are jittery in a browser, save them to your computer and play them in a video viewer.

1. The one-dimensional wave equation:
   1. The first mode of the plucked string (guitar),
   2. The first five modes of the plucked string plotted separately,
   3. The sum of the first five modes of the plucked string,
   4. The sum of the first fifty modes of the plucked string,
   5. The sum of the first fifty modes of the plucked string with dispursion,
   6. The sum of the first ten modes of the impacted string (piano), and
   7. The sum of the first fifty modes of the impacted string (piano).
2. The one-dimensional heat conduction equation:
   1. Solution with inhomogeneous boundary conditions, and
   2. Solution with an insulated end.
3. The two-dimensional wave equation
   1. in rectangular coordinates:
      1. 1-1 mode of a rectangular drum,
      2. 2-1 mode of a rectangular drum,
      3. 2-2 mode of a rectangular drum,
      4. Rectangular drum impacted,
   2. in polar coordinates:
      1. 1-1 mode of a circular drum,
      2. 1-2 mode of a circular drum,
      3. 1-3 mode of a circular drum,
      4. 1-4 mode of a circular drum,
      5. 2-1 mode of a circular drum,
      6. 2-2 mode of a circular drum,
      7. 4-4 mode of a circular drum,
      8. Circular drum impacted, and
      9. Circular drum impacted in the center.
   3. Two-dimensional heat equation in rectangular coordinates (boring).

Real world applications of the wave equation are as follows:

1. Jimmy Page guitar solo
2. Led Zeppelin, Over the Hills and Far Away
3. Guns n' Roses, Paradise City
4. Guns n' Roses, Welcome to the Jungle
5. Guns n' Roses, Welcome to the Jungle
6. Electric Light Orchestra, Don't Bring Me Down
7. Ozzy Osbourne, Crazy Train
8. Pink Floyd, Wish You Were Here
9. Pink Floyd, Comfortably Numb
10. Pink Floyd, Money
11. Bob Dylan, Subterranian Homesick Blues
12. The Police, Invisible Sun
13. The Police, Synchronicity II
14. The Clash, Should I Stay or Should I Go?
15. The Clash, Train in Vain
16. The Clash, The Magnificent Seven
17. The Clash, Police on My Back
18. Peter Gabriel, Shock the Monkey
19. Slade, Run Runaway
20. Talking Heads, Once in a Lifetime
21. Talking Heads, Burning Down the House
22. AC/DC, Back in Black
23. The Who, Magic Bus
24. Run DMC, It's Tricky
25. Gary Newman, Cars
26. Frankie Goes to Hollywood, Relax
27. U2, Where the Streets Have No Name
28. REM, It's the End of the World as We Know It (And I Feel Fine)
29. REM, Stand
30. Rush, Closer to the Heart
31. Thomas Dolby, She Blinded Me with Science
32. The Ramones, I wanna be Sedated
33. Cheap Trick, Dream Police
34. Duran Duran, Hungry Like the Wolf
35. Billy Idol, Rebel Yell
36. Billy Idol, Dancing with Myself
37. Metallica, Master of Puppets
38. Dead or Alive, You Spin Me Round (Like a Record)
39. Wall of Voodoo, Mexican Radio
40. Falco, Rock me Amadeus
41. Falco, Der Kommissar
42. John Lennon, Instant Karma
43. John Lennon, Nobody Told Me
44. David Bowie, Modern Love
45. Buddy Rich Quartet
46. Weather Report, Birdland
47. Simon and Garfunkel, Me and Julio Down by the Schoolyard