Class Notes & Reading Materials :1998 Winter

Instead of using a textbook, I have suggested references to this course. However, you may get class notes ( which are originally prepared by using MAC version Microsoft Words5.1 with MathType, but filed in PostScript files by LaserWriter 8, and then compressed into pdf file format by Adobe Acrobat 3.0 so that you can read them by using Adobe's public software for reading. Software should be available in the internet. If you do not have it, please down load the soft from Adobe. ) These notes are prepared just for my own sake, and they are not quite perfect as a course pack. For example, there are many spelling mistakes, and insufficient explanation. Please read them with patience, especially for mistakes, and please send me your comments and mistakes you find. My address is mailto:kikuchi@engin.umich.edu ).

These reading material is reproduced from Avner Friedman, Mathematics in Industrial Problems, Part 8, The IMA Volumes in Mathematics and its Applications, Vol. 83, Spriger, New York, 1997. I strongly recommend you to look at this monograph if you are intersting in knowing how mathematicians consider engineering problems. I am planning to use these material to show examples how mathematics is used in engineering.

  • Class Note #1 (01/08/98) : Variational Methods
  • Class Note #2 (01/09/98) : Approximation Methods
  • Class Note #3 (01/09/98) : Domain Decomposition and FEM
  • Class Note #4 (01/09/98) : Homohenization 1D
  • Class Note #5 (01/09/98) : Caluculus of Variation
  • Class Note #6 (01/09/98) : Fourier Transform and Function Spaces
  • Class Note #7 (01/09/98) : Lagrange Multiplier Methods
  • Class Note #8 (01/09/98) : Penatlty Methos
  • Class Note #9 : Mathematical Physics and PDE
  • Homework : 1998 Winter

  • Homework #1 : Ritz, FDM, and FEM for a Nonlinear 1-D Problem (01/21/98 posted, 2 weeks)
  • Solution of Homework #1 : (03/27/98 posted)
  • Homework #2 : 4-th Order PDE for Plate Bending Problems (02/02/98 posted, 2 weeks)
  • Homework #3 : Image Processing, Wavelet, Element Galerkin Method(03/17/98 posted, 2 weeks)
  • HW3_1_98W : Image Data File ( jpeg file created by Photoshop 3 )
  • Homework #4 : Homogenization Method (03/17/98 posted, 2 weeks)