Lectures:

In this page we'll post useful information about the lectures: source codes, data, references, etc...

Matlab:

• A practical introduction to Matlab (HTML [PDF], PDF)
• Matlab Help
• Matlab GUI for differential equations: dfield and pplane.

Maple:

• Maple Workshop notes

Chap 3: Linear eqs, Vectors, Matrices, & Determinants:

• Determinant in Matlab (Ex 3.3.4): determinant.m
• Linear systems of eqs in Maple (Ex 3.3.5 & 3.3.6): linear_syst.mws
• Rotation using a matrix: rotate_pic.m
  

  Original GIF picture before rotation	After 30o rotation

  
  
• Inverse of a matrix using Matlab: inverse.m
• Applications of linear spaces:
  • Eigenface decomposition: CDSST @ UBC:
    
    
  • POD or Karhunen-Loève of flame patterns: paper1, paper2, movie of the reconstruction.
    Sample image reconstruction:
    
    
• Vibrational modes:
  • Some vibrational modes of the Benzene molecule: link1, link2.
  • Vibrational modes of the Buckyball (buckminsterfullerene C₆₀) molecule: link.
  • Eigenvalues for systems of connected oscillators: link.

Chap 4: Partial Differentiation:

• Finding extrema of a constraint function: Lagrange Multipliers: extrema_Lagrange.mws
• Changing coordinates in a PDE: change_coord_PDE.mws

Chap 5: Integrals:

• Miscellaneous integrals using Maple: integrals.mws

Chap 6: Vector Analysis:

• Aplication of gradient: normal vector: surf_gradient
  

Chap 8: Differential Equations:

• Resonance in forced-damped oscillators: resonance.m, DampedForced.mw
• Solving and ploting for differential equations: deq.mws
• Fitting data to a real pendulum (or the experiement please click here: PENDULUM)
  • Data extracted for experiment: pendulumCR.dat
  • fitting program: fit_pendulum.m
  • fucntion to be fitted: damped_oscill.m
  • If Matlab gives you problems with undefined functions please go HERE to download any optimization subroutine that you need.
  • You shopuld obtain the following picture:
    
• Solving Nth order linear differential equations: NthOrderDeq.mw