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Primary Text
Notes on pertinent material will be provided.
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
Recktenwald, Gerald. Numerical Methods with MATLAB®: Implementation and Application. Upper Saddle River, NJ: Prentice-Hall Inc., 2000. ISBN: 9780201308600.
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.
Course readings.
| 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 |
|