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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Entries from August 2008
August 30, 2008
A better way to show decimal to binary conversion
August 23, 2008
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.
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August 19, 2008
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 [...]
August 11, 2008
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 [...]
August 7, 2008
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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August 4, 2008
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 [...]
