MATLAB® software is required to run the .m and .mat files in this section.
Lecture notes are listed by week in the table below. A complete set of lecture notes is also available and is included above the table.
Complete Lecture Notes - "Computational Methods in Aerospace Engineering" (PDF - 2.5 MB)
Lecture Notes Files
| LEC # |
TOPICS |
LECTURE NOTES |
| Ordinary Differential Equations |
| 1 |
Numerical Integration of Ordinary Differential Equations: An Introduction |
(PDF)
drop_fe.m (M)
drop_mp.m (M)
drop_rhs.m (M) |
| 2 |
Convergence and Accuracy |
(PDF)
ga_fe.m (M)
ga_mp.m (M) |
| 3 |
Convergence of Multi-Step Methods |
(PDF)
ga_ma2.m (M) |
| 4 |
Systems of ODE's and Eigenvalue Stability |
(PDF)
fe_stab.m (M)
nonpen_fe.m (M)
nonpen_mp.m (M) |
| 5 |
Stiffness and Implicit Methods |
(PDF)
dif1d.m (M)
dif1d_fun.m (M)
dif1d_main.m (M)
eig_dif1d.m (M)
mstepstab.m (M)
stiff_err.m (M)
stiff_forced.m (M) |
| 6 |
Runge-Kutta Methods |
(PDF)
rkstab.m (M) |
| Finite Volume/Difference Methods |
| 7 |
Conservation Laws and Finite Volume Methods |
(PDF)
convect1d.m (M)
convect2d.m (M) |
| 8 |
Finite Difference Methods for Convection-Diffusion |
(PDF)
convect1d_ftcs.m (M) |
| 9 |
Matrix Stability Analysis |
(PDF)
condif1d_ftcs_eig.m (M)
convect1d_ftcs_eig.m (M) |
|
Midterm Exam |
|
| 10 |
Fourier Stability Analysis |
(PDF) |
| Finite Element Methods |
| 11 |
Method of Weighted Residuals |
(PDF)
MWR_dif1d.m (M) |
| 12 |
Finite Element Method for 1-D Diffusion |
(PDF)
fem_dif1d.m (M)
fem_dif1d_gq.m (M) |
| 13 |
Finite Element Method for 2-D Diffusion |
(PDF) |
| 14 |
Higher-order FEM |
(PDF)
fem1D_hier.m (M)
fem1D_quad.m (M) |
| Probabilistic Methods |
| 15 |
Introduction to Monte Carlo Method |
(PDF)
blade1D.m (M)
bladedet.m (M)
bladeLtbc.m (M)
bladeuni.m (M) |
| 16 |
Error Estimates for Monte Carlo Method |
(PDF) |