Introduction to Numerical Methods in MSE2094

• Taylor series used to approximate analytic functions: Class notes.

• Taylor series used to create approximations of first and higher order derivatives: Class notes

• Reducing differential equations to simultaneous equations (Temperature Gradient): Class notes

• Solving simultaneous equations using Gauss-Elimination (Theory of LU Decomposition): Class notes
  • Simple Fortran programs: Review
    • README file summarizes procedures for working with F90 and F77 files.

    • F90 programs:
      • test1.f / test1.out (main program)
      • test2.f / test2.out (main program with interface and a subroutine)
      • test3.f / test3.out (main program with no interface and a subroutine)
      • gauss.dat / gauss.f / gauss.out (arbitrary N equations, all solutions = 1.0)

    • F77 programs:
      • test1.for / test1.out (main program)
      • test3.for / test3.out (main program with interface and a subroutine)
      • gauss.dat / gauss.for / gauss.out (arbitrary N equations, all solutions = 1.0)

  • Simple Gauss Elimination programs: Temperature Gradient Examples
    • F90: gauss.f / gauss.out
    • F77: gauss.for / gauss.out

• Solving the non-homogeneous Laplace's equation: Class notes

• Solving simultaneous equations using Successive Over Relaxation (SOR)
  • Simple Fortran programs: Diffusion problem
    • F90: diff90.f / diff90.out
    • F77: diff77.for / diff77.out