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

Problem set 1 (PDF)

(PDF - 1.5 MB)

(ZIP) (The ZIP file contains: 16 .m files and 2 .ds file.)

Problem set 2 (PDF)

(PDF - 3.4 MB)

(ZIP) (The ZIP file contains: 16 .m files, 2 .xls files, and 2 .ds files.)

Problem set 3 (PDF)

(PDF - 3.0 MB)

(ZIP) (The ZIP file contains: 12 .m files, 2 .ds files, and 1 .mw file.)

Problem set 4 (PDF)

(PDF - 2.5 MB)

(ZIP) (The ZIP file contains: .c2p29_pset4_1a.m, .c2p29_pset4_1b.m, .c2p29_pset4_1d.m, c2p29_pset4_1a.m, c2p29_pset4_1b.m, c2p29_pset4_1c.m, and c2p29_pset4_1d.m.)

Quiz 1 (PDF)

(PDF)

Quiz 2 (PDF) (ZIP) (The ZIP file contains: 15 .m files, 1 .mat file, and 4 .ds files.)

(PDF - 1.2 MB)