Numerical Methods YouTube Video Progress

Since January 2009, I have been videotaping numerical methods course lectures in the Educational Outreach studio of University of South Florida, Tampa. Videos are made in 10-minute segments, not just because that is the limit of the length of YouTube videos, but because we firmly believe in making our resources pedagogically neutral. Ten [...]

Is a square matrix strictly diagonally dominant?

A square matrix A is strictly diagonally dominant if for all rows the absolute value of the diagonal element in a row is strictly greater than than the sum of absolute value of the rest of the elements in that row.
In this posting, I show a MATLAB program that finds whether a square matrix is [...]

A better way to show conversion of decimal fractional number to binary

This post is brought to you by Holistic Numerical Methods: Numerical Methods for the STEM undergraduate at http://numericalmethods.eng.usf.edu, the textbook on Numerical Methods with Applications available from the lulu storefront, and the YouTube video lectures available at http://www.youtube.com/numericalmethodsguy.  
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Finding height of atmosphere using nonlinear regression

Here is an example of finding the height of the atmosphere using nonlinear regression of the mass density of air vs altitude above sea level.

This post is brought to you by Holistic Numerical Methods: Numerical Methods for the STEM undergraduate at http://numericalmethods.eng.usf.edu.
An abridged (for low cost) book on Numerical Methods with Applications will be in [...]

A better way to show decimal to binary conversion

This post is brought to you by Holistic Numerical Methods: Numerical Methods for the STEM undergraduate at http://numericalmethods.eng.usf.edu.
An abridged (for low cost) book on Numerical Methods with Applications will be in print (includes problem sets, TOC, index) on December 10, 2008 and available at lulu storefront.
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Accuracy of Taylor series

So how many terms should I use in getting a certain pre-determined accuracy in a Taylor series. One way is to use the formula for the Taylor’s theorem remainder and its bounds to calculate the number of terms. This is shown in the example below.

This post is brought to you by Holistic Numerical [...]

Taylor series example

If Archimedes were to quote Taylor’s theorem, he would have said, “Give me the value of the function at a single point, and the value of all (first, second, and so on) its derivatives, and I can give you the value of the function at any other point”.
It is very important to note that [...]

Taylor Series Revisited

Taylor series is a very important concept that is used in numerical methods. From the concept of truncation error to finding the true error in Trapezoidal rule, having a clear understanding of Taylor series is extremely important. Other places in numerical methods where Taylor series concept is used include: the derivation [...]

Runge-Kutta 2nd order equations derived

In my class, I present the 2nd order Runge-Kutta method equations without proof. Although I do discuss where the equations come from, there are still students who want to see the proof. So here it is.

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This post is brought to you by Holistic Numerical Methods: Numerical Methods for the STEM undergraduate at http://numericalmethods.eng.usf.edu
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A Matlab program for comparing Runge-Kutta methods

In a previous post, we compared the results from various 2nd order Runge-Kutta methods to solve a first order ordinary differential equation. In this post, I am posting the matlab program. It is better to download the program as single quotes in the pasted version do not translate properly when pasted into a [...]