Readings

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Primary Text

Notes on pertinent material will be provided.

Amazon logo Chapra, Steven C., and Raymond P. Canale. Numerical Methods for Engineers. 5th ed. Boston, MA: McGraw Hill, 2006. ISBN: 9780073101569. (Required textbook)

If you are not familiar with MATLAB® you have to go through MATLAB® help tutorial. However, a two sessions workshop will be presented in the first two weeks to help you accelerate your MATLAB® learning.

Other Useful Texts

Amazon logo Recktenwald, Gerald. Numerical Methods with MATLAB®: Implementation and Application. Upper Saddle River, NJ: Prentice-Hall Inc., 2000. ISBN: 9780201308600.

Amazon logo Chapra, Steven C. Applied Numerical Methods with MATLAB® for Engineers and Scientists. 2nd ed. New York, NY: McGraw-Hill Companies Inc., 2007. ISBN: 9780071259217.

All the readings below come from the required textbook.


SES # TOPICS READINGS
1

Introduction to numerical methods in engineering

MATLAB® proficiency evaluation

First day of classes

Sections P.T. 1.1-1.3 and 1.1-1.2
2

Number representations

Errors of numerical operations

Recursion

Sections 3.1-3.4
3

Error analysis

Error propagation

Condition numbers

Sections 4.1-4.5
4

Roots of non-linear equations

General/Bisection/Secant/Newton-Raphson methods

Sections 5.1-5.4 and 6.1-6.5
5

Linear systems

Gaussian elimination

Sections 9.1-9.8
6

Linear systems

Multiple right-hand-sides

LU factorization

Sections 10.1-10.3
7

Special matrices

Examples

Section 11.1
8

Linear systems

Iterative techniques

Gauss-Seidel

Section 11.2
9

Root finding and linear systems

Examples and applications

Sections 8.1-8.4 and 12.1-12.4
10

Optimization

Curve fitting

Chapters 13, 14, and 17
11

Interpolation

Polynomial interpolation

Lagrange polynomials

Splines

Sections 18.1-18.6
12

Fourier interpolation

Fourier transforms

Sections 19.1-19.8
13 Quiz 1
14

Numerical integration

Newton-Cotes

Gaussian quadratutre

Sections 21.1-21.2 and 22.1-22.3
15

Numerical differentiation

Finite differences

Ordinary differential equations

Initial value problems

Euler's method

Sections 23.1-23.5 and 25.1-25.2
16

ODE-IVP

Runge-Kutta methods

Sections 25.3-23.5
17

Higher order ODEs

Boundary value problems

Sections 27.1-27.3

18

Partial differential equations

Introduction

Examples

Sections P.T. 8.1-8.2
19 PDE review
20

PDEs

Parabolic equations

Sections 30.1-30.5
21

PDEs

Elliptic equations

Sections 29.1-29.5
22 Finite element methods Sections 31.1-31.4
23

Boundary element methods

Panel methods (1)

24

Boundary element methods

Panel methods (2)

25 Review
26 Quiz 2