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Boundary-Value Problems and Solution Methods in Rectangular Coordinates

Explore numerical methods for boundary-value problems in rectangular coordinates, including heat flow, string vibrations, and steady-state temperatures in plates. Learn concepts through visual aids and examples.

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Boundary-Value Problems and Solution Methods in Rectangular Coordinates

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  1. Chapter 12 Boundary-Value Problems in Rectangular Coordinates

  2. FIGURE 12.2.1 One-dimensional flow of heat

  3. FIGURE 12.2.2Flexible string anchored at x =0 and x = L

  4. FIGURE 12.2.3 Steady-state temperatures in a rectangular plate

  5. FIGURE 12.2.4 Plucked string

  6. FIGURE 12.3.1 Temperatures in a rod of length L

  7. FIGURE 12.3.2 Graphs of (17) when one variable is held fixed

  8. FIGURE 12.3.3Rod losing heat in Problem 5

  9. FIGURE 12.4.1 Frames of a CAS “movie”

  10. FIGURE 12.4.2 First three standing waves

  11. FIGURE 12.4.3Initial displacement in Problem 7

  12. FIGURE 12.4.4Initial displacement in Problem 8

  13. FIGURE 12.4.5Initial displacement in Problem 9

  14. FIGURE 12.4.6 Initial displacement in Problem 10

  15. FIGURE 12.4.7Vibrating bar in Problem 11

  16. FIGURE 12.4.8Vibrating string in Problem 12

  17. FIGURE 12.4.9 Simply supported beam in Problem 17

  18. FIGURE 12.5.1 Steady-state temperatures in a rectangular plate

  19. FIGURE 12.5.2 Surface is graph of partial sums when f(x) = 100 and a = b = 1 in (10)

  20. FIGURE 12.5.3Solution u = Solution u1 of Problem 1 + Solution u2 of Problem 2

  21. FIGURE12.5.4 Plate in Problem 11

  22. FIGURE 12.5.5 Plate in Problem 12

  23. FIGURE 12.6.1Plate in Problem 11

  24. FIGURE 12.7.1 Twisted shaft in Example 2

  25. FIGURE 12.7.2 Surface is the graph of a partial sum of (17) in Example 2

  26. FIGURE 12.7.3 Angular displacementsas a function of time at various cross sections of the rod in Example 2

  27. FIGURE 12.7.4 Vibrating cantilever beam in Problem 11

  28. FIGURE 12.8.1(a) Rectangular plate and (b) rectangular membrane

  29. FIGURE 12.8.2Rectangular parallelepiped in Problems 5 and 6

  30. FIGURE 12.R.1Initial velocity g(x) in Problem 5

  31. FIGURE 12.R.2 Square plate in Problem 7

  32. FIGURE 12.R.3 Semi-infinite plate in Problem 8

  33. FIGURE 12.R.4Infinite plate in Problem 10

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