If you can't see the slideshow(above), just download the file.
Lecture04 - Gaussian Elimination, LU Decomposition and Gauss-Seidel Method - [Download]

If you can't see the slideshow(above), just download the file.
Lecture03 - Linear Algebraic Equations - [Download]

Aside from the class lecture slides provided here, lectures notes (in PDF format) are also made available here.

1. Approximation and Errors [download]

2. Systems of Linear Equations [download]

3. Root Finding [download]

*These are accompanying notes for the Numerical Methods for Engineers, 4/e, Chapra, et. al. by Ronald D. Ziemian, et. al.

(the 4th and 5th editions of the NME book have only slight differences)

Here are some book resources that you can download. Due to our school's internet firewall, you may not be able to download using the school's network.

Numerical Methods Books

[1]. Numerical Methods For Engineers and Scientists Second Edition by Joe D.Hoffman

[2]. Numerical Methods in Engineering with MATLAB by J. Kiusalaas

[3]. Fundamental Numerical Methods and Data Analysis by G. W. Collins

[4]. Numerical Recipes in C by W. Press, et. al.

Scilab Books/Notes

[1] Modeling and Simulation in Scilab/Scicos by S. Campbell, et. al.

[2] Scilab Primer

[3] Tutorials on Scilab

Disclaimer: These ebooks are not hosted on this blog. Only links to file sharing site/s is/are provided. This blog author is not responsible for the files.

If you can't see the slideshow(above), just download the file.
Lecture02 - Approximation and Errors - [Download]

If you can't see the slideshow(above), just download the file.
Lecture01 - Representation of Numbers - [Download]

If you can't see the slideshow(above), just download the file.
Lecture00 - Course Introduction & Mathematical Modelling - [Download]

*This post has been edited (11/26/08)

Here's a video on Numerical Error from a Numerical Methods And Programming class by Prof.P.B.Sunil Kumar, Dept. of Physics, IIT Madras (India)

Notes:

• The first part of the lecture talks on the Representation of Numbers(a continuation from past lecture) in our digital computer such as the integers and floating-point numbers.
• Difference of Chopping and rounding:
  Chopping is to merely chop off or cut off higher digits while rounding means that any quantity falling within an interval of length delta x will be represented as the nearest allowable number.
  Rounding yields lower error than chopping.
• The concept of zero
  The precise meaning of the number zero is lost while computing numerically
• Relationship between the exact(true) result and the approximation can be formulated as
  True value = approximation + error
  This relationship gives the value of the error but it does not take into account the order of the magnitude of the value under examination
• To account the magnitude of the quantities being evaluated, we normalize the error to the true value as in
  Fractional relative error = Error/true Value
  (Significance of this thought: An error of a centimeter is much more significant if we are measuring a rivet than a bridge. See the magnitude of the quantity of the item being evaluated)
• Fractional relative error multiplied by 100 would give us the Percent relative error
• In real applications, we don't know the true value. So an alternate solution is to normalize the error using the approximation itself as in,
     Ea = (approximate error/approximation)100%
  the subscript 'a' signifies that the error is normalized to an approximate value. "Ea" is read as "Epsilon sub a" 
• For iterative procedures, the error is estimated as the difference between the present and previous approximations. Thus the percent relative error is determined according to:
   Ea = [(present approximation - previous approximation)/present approximation] 100%
  Generally, one is not concerned with the sign of the error but is interested whether the absolute value is lower than a pre-specified tolerance Es.
  Computation in the iterative method is repeated until
    |Ea| < Es
  

In summary

• Two errors encountered are round-off errors(due to finite representation of numbers) and truncation errors(due to the use of an approximation instead of a finite mathematical operation).  Rounding errors appears due to arithmetic operations using finite floating point numbers and is a major source of error.
• The only way to minimize round-off errors is to increase the number of significant figures of the computer
• A decrease in step-size (for iterative) can lead to subtractive cancellation or an increase in computations, thus the truncation errors are decreased as the round-off errors are increased.
  

This would be your online companion to our ES 84-Numerical Methods class. Soft copies of our lecture notes will be posted here, as well as other resources to be used in our class.

Have fun learning!