| 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 |
Table of Contents
Study Materials
Readings
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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.
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.