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)
| 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) |