Lecture Notes

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SES # TOPICS LECTURE NOTES MATLAB® SCRIPTS
1

Introduction to numerical methods in engineering

MATLAB® proficiency evaluation

First day of classes

(PDF) (ZIP) (The ZIP file contains: dudt.m, piv.m, and sph_drag_2.m.)
2

Number representations

Errors of numerical operations

Recursion

(PDF) (ZIP) (The ZIP file contains: heron.m, horner.m, radd.m, recur.m, sbfj.m, sbfj_3.m, sbfj_f.m, sbfy.m, and tsbfj.m.)
3

Error analysis

Error propagation

Condition numbers

(PDF)
4

Roots of non-linear equations

General/Bisection/Secant/Newton-Raphson methods

(PDF) (ZIP) (The ZIP file contains: bisect.m, cube.m, div.m, heron.m, and sqr.m.)
5

Linear systems

Gaussian elimination

(PDF) (ZIP) (The ZIP file contains: tbt.m, tbt2.m,tbt3.m, and tbt4.m.)
6

Linear systems

Multiple right-hand-sides

LU factorization

(PDF) (ZIP) (The ZIP file contains: tbt6.m, tbt7.m, and tbt8.m.)
7

Special matrices

Examples

(PDF) (ZIP) (The ZIP file contains: vib_string.m.)
8

Linear systems

Iterative techniques

Gauss-Seidel

(PDF - 1.0 MB) (Courtesy of Reza Karimi. Used with permission.)
9

Root finding and linear systems

Examples and applications

(PDF) (Courtesy of Dr. Yuming Liu. Used with permission.)
10

Optimization

Curve fitting

(PDF) (ZIP) (The ZIP file contains: cost.m, curve.m, lstsq.m, and salesman.m.)
11

Interpolation

Polynomial interpolation

Lagrange polynomials

Splines

(PDF) (ZIP) (The ZIP file contains: interp_test.m, lagrange.m, newton.m, and newton_coef.m.)
12

Fourier interpolation

Fourier transforms

(PDF) (ZIP) (The ZIP file contains: tpcoef.m, tpeval.m, tptest.m, trig_poly.m, and ts.m.)
13 Quiz 1
14

Numerical integration

Newton-Cotes

Gaussian quadratutre

(PDF)
15

Numerical differentiation

Finite differences

Ordinary differential equations

Initial value problems

Euler's method

(PDF) (ZIP) (The ZIP file contains: dudt.m, sph_drag_2.m, and sph_param.m.)
16

ODE-IVP

Runge-Kutta methods

(PDF) (ZIP) (The ZIP file contains: pcm.m, stiff.m, and stiff_imp.m.)
17

Higher order ODEs

Boundary value problems

(PDF) (ZIP) (The ZIP file contains: back_tri.m, dudy.m, forw_tri.m, lu_fact.m, lu_tri.m, plate_flow.m, and sou_flow.m.)
18

Partial differential equations

Introduction

Examples

(PDF) (ZIP) (The ZIP file contains: waveeq.m and wavei.m.)
19 PDE review
20

PDEs

Parabolic equations

(PDF) (ZIP) (The ZIP file contains: back_tri.m, forw_tri.m, heat_cn.m, heat_cn_sin.m, heat_fw.m, heat_fw_2.m, and lu_tri.m.)
21

PDEs

Elliptic equations

(PDF) (ZIP) (The ZIP file contains: duct.m, duct_fs.m, duct_oil.m, and heat_plate.m.)
22 Finite element methods (PDF) (ZIP) (The ZIP file contains: duct_galerkin.m, and exp_eq.m.)
23

Boundary element methods

Panel methods (1)

(PDF)# (Courtesy of Dr. Yuming Liu. Used with permission.) (ZIP) (The ZIP file contains: cpm_main.m, cylinder_geom.m, gxy.m, inflcoef.m, localize.m, matrices.m, setbcs.m, and setpanels.m.)
24

Boundary element methods

Panel methods (2)

25 Review (PDF - 1.0 MB)
26 Quiz 2