Lecture Notes

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)