(This guide could serve to both your individual and group projects)
Project Summary
You are tasked to find daily problems (real-world problems) which are solvable by numerical methods. Just select one problem and present a case presentation for this.
1. Problem
- the problem may range from simple to complex ones. But of course, good credit would be given for those who solves the complex problem
2. Case Presentation
- In the presentation, the solution for the given problem would be presented alongside the analysis undertaken that leads to it. It would be best to have a thorough approach such that the reason for using a numerical method would be provided. You can do this by differentiating your chosen method with the other available methods, if there are any that can also solve the selected problem. A discussion on your analysis would be necessary and an additional algorithm is required. You can provide a working program for the algorithm.
Deliverables
Submit a hardcopy of your output (group and individual works)
Have a 5-10 minutes presentation (prepare for questions afterwards)
for questions: stephen_562001 @ yahoo.com
Final Project Guide - Case Presentation
Finals Lecture Notes
For your finals lecture notes, you can download lectures from this site: http://numericalmethods.eng.usf.edu
That is where the resources in our class lectures were taken from.
Those items colored in red are the ones discussed/used in class, the rest can be utilized as supplemental notes.
Here is a listing of the topics:
- Regression -
BACKGROUND
A primer on statistical terminology for regression analysis [PDF] [DOC]
Introduction to regression [PDF] [DOC]
Test your knowledge on background of regression analysis [HTML] [PDF] [DOC]
PHYSICAL PROBLEM
Infrared spectroscopy [PDF] [DOC]
NUMERICAL METHOD
How does Linear Regression work? [PDF] [DOC]
A Power point presentation on Linear Regression [PDF] [PPT]
Simulation of Linear Regression [PDF] [MFILE]
Test your knowledge of Linear Regression [HTML] [PDF] [DOC]
How does Nonlinear Regression work? [PDF] [DOC]
A Power point presentation on Nonlinear regression [PDF] [PPT]
Simulation of Nonlinear Regression without Data Linearization [PDF] [MFILE]
Simulation of Nonlinear Regression with Data Linearization [PDF] [MFILE]
Simulation of Polynomial Regression [PDF] [MFILE]
Test your knowledge of Nonlinear Regression [HTML] [PDF] [DOC]
ANECDOTES
Comparing nonlinear regression models - with and without data linearization [PDF] [MFILE]
On adequacy of regression models [PDF] [DOC] [PDF] [MFILE]
Multivariate least squares fitting [PDF] [DOC] - Interpolation -
BACKGROUND
What is Interpolation? [PDF] [DOC]
History of Interpolation [PDF] [DOC]
Test your knowledge on background of interpolation [HTML] [PDF] [DOC]
PHYSICAL PROBLEM
A physical problem of finding how much time it would take water to boil in a kettle. It requires interpolating specific heat of saturated water vs. temperature data. [PDF] [DOC]
NUMERICAL METHOD
How does the direct method work? [PDF] [DOC]
A Power point presentation [PDF] [PPT]
Simulations of the method [PDF] [MFILE]
Test your knowledge of the method [HTML] [PDF] [DOC]
How does the Newton's divided difference polynomial method work? [PDF] [DOC]
A Power point presentation [PDF] [PPT]
Simulations of the method [PDF] [MFILE]
Test your knowledge of the method [HTML] [PDF] [DOC]
How does the Lagrange method work? [PDF] [DOC]
A Power point presentation [PDF] [PPT]
Simulations of the method [PDF] [MFILE]
Test your knowledge of the method [HTML] [PDF] [DOC]
SPLINE METHOD (not part of the coverage)
How does the spline method work? [PDF] [DOC]
A Power point presentation [PDF] [PPT]
Simulations of the method [PDF] [MFILE]
Test your knowledge of the method [HTML] [PDF] [DOC]
ANECDOTES
The lurking dangers of extrapolation! [PDF] [DOC] [MFILE] [PDF]
Why is higher order interpolation is a bad idea? [PDF] [DOC] [MFILE] [PDF]
Comparison of spline and polynomial interpolation. [PDF] [DOC] [MFILE] [PDF]
How choice of points of interpolation affects approximations! [PDF] [DOC] [MFILE] [PDF]
How splines can help in developing a shorter path for a robot! [PDF] [DOC] [MFILE] [PDF]
- Differentiation -
- Integration -
If you would like to select specific examples related to your field of study (chemical, mechanical, electronics, electrical, computer, etc...) you may opt to use this link: http://numericalmethods.eng.usf.edu/resource.html and from here, using the drop down select, choose the Mathematical Procedure (could be regression, interpolation...), the Math package (you may use matlab) and lastly, your engineering major then press the Go button.
Midterm Exam is on February 22, 2009
If you are reading this post on a Saturday (Feb 21), that means, the exam will be tomorrow at the COE Amphitheater, 2-5PM.
Midterms Lecture Slides presentation
Here are the powerpoint slides used during our lectures (in the zip file):
[download]
Take note of the Exam Coverage:
1. Bracketing Methods
2. Open Methods
3. Multiroot
4. Bairstow Methods (Root of Polynomials)
5. Optimization