A MOOC on Introduction to Numerical Methods

After the rigorous and comprehensive development and assessment of the NSF funded innovative open courseware on Numerical Methods between 2002 and 2012, we are offering a FREE Massive Open Online Course (MOOC) in Numerical Methods at http://udemy.com/numericalmethodsguy

Start your journey today whether you are learning numerical methods for the first time or just need a refresher.  Unlike other MOOCs, you have a lifetime access to the course. Ask questions within the course and we can keep the conversation going!

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About: Numerical methods are techniques to approximate mathematical procedures (example of a mathematical procedure is an integral).  Approximations are needed because we either cannot solve the procedure analytically (example is the standard normal cumulative  distribution function) or because the analytical method is intractable (example is solving a set of a thousand simultaneous linear equations for a thousand unknowns).

Materials Included: Textbook Chapters, Video Lectures, Quizzes, Solutions to Quizzes

How Long to Complete: About 40 hours of lectures need to be watched and estimated  time to read textbook and do quizzes is 80 hours.  It is a typical 15-week semester length course.

Course Structure: For each section, you have video lectures, followed by a textbook chapter, a quiz and solutions to quizzes.

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This post is brought to you by Holistic Numerical Methods: Numerical Methods for the STEM undergraduate at http://nm.MathForCollege.com, the textbook on Numerical Methods with Applications available from the lulu storefront, the textbook on Introduction to Programming Concepts Using MATLAB, and the YouTube video lectures available at http://nm.MathForCollege.com/videos. Subscribe to the blog via a reader or email to stay updated with this blog. Let the information follow you.

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Using Taylor polynomial to approximately solve an ordinary differential equation

Taylor polynomial is an essential concept in understanding numerical methods. Examples abound and include finding accuracy of divided difference approximation of derivatives and forming the basis for Romberg method of numerical integration.

In this example, we are given an ordinary differential equation and we use the Taylor polynomial to approximately solve the ODE for the value of the dependent variable at a particular value of the independent variable. As a homework assignment, do the following.
1) compare the approximate solution with the exact one, and
2) get another approximate solution by using a third order Taylor polynomial.

Taylor polynomial approximation of solving ordinary differential equations

You can visit the above example by opening a pdf or video file.

This post is brought to you by Holistic Numerical Methods: Numerical Methods for the STEM undergraduate at http://nm.MathForCollege.com, the textbook on Numerical Methods with Applications available from the lulu storefront, the textbook on Introduction to Programming Concepts Using MATLAB, and the YouTube video lectures available at http://nm.MathForCollege.com/videos.  Subscribe to the blog via a reader or email to stay updated with this blog. Let the information follow you.

Proving the denominator of the linear regression formula for its constants is greater than zero.

In a previous blog, we wrote without proof that the denominator of the constants of the linear regression formulas are greater than zero.  In this blog, we show the proof.


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, the textbook on Introduction to Programming Concepts Using MATLAB, and the YouTube video lectures available athttp://numericalmethods.eng.usf.edu/videos.  Subscribe to the blog via areader or email to stay updated with this blog. Let the information follow you.

Saylor Foundation Harnesses Numerical Methods Resources

 Saylor Foundation (http:/saylor.org) is harnessing quality open courseware resources available around the world.   More than 90% of the resources for the Numerical Methods for Engineers course at the site http://www.saylor.org/courses/me205/ is composed of content from the http://numericalmethods.eng.usf.edu website.

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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, the textbook on Numerical Methods with Applications available from the lulu storefront, the textbook on Introduction to Programming Concepts Using MATLAB, and the YouTube video lectures available athttp://numericalmethods.eng.usf.edu/videos.  Subscribe to the blog via areader or email to stay updated with this blog. Let the information follow you.

YouTube Videos on Numerical Methods Cross 1-Million Views Mark

In a short 2.5 years since starting the numericalmethodsguy YouTube channel in January 2009, this month the channel crossed the benchmark of receiving 1 million video views.  Currently the channel gets between 2,500-3,500 video views per day.  Although we have playlists on the channel, the playlist for all the available topics are given on single webpage at http://numericalmethods.eng.usf.edu/videos/index.html

Complete resources on each topic of available numerical methods including textbook chapters, videos, multiple-choice tests, PPTs, and worksheets are  given at http://numericalmethods.eng.usf.edu/topics/textbook_index.html
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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, the textbook on Numerical Methods with Applications available from the lulu storefront, the textbook on Introduction to Programming Concepts Using MATLAB, and the YouTube video lectures available at http://numericalmethods.eng.usf.edu/videos.  Subscribe to the blog via a reader or email to stay updated with this blog. Let the information follow you.

Poems on Numerical Methods

In Summer 2009, I gave a HW assignment of writing a poem to my mostly right-brained students.  The results were great; I think they think they are poets and they know it.  The poems were all compiled and can be viewed at http://numericalmethods.eng.usf.edu/EML3041/homework/poems2009summer.html.

So happy reading and let me know what you think.  I selected 14 poems out of the 60 or so submitted and am polling the class to select the best three.  The top three poem writers will get prizes including a dollar to get the 89c Chicken Burritto at Taco Bell for “thinking outside the bun” or the biggie fries at Wendy’s for thinking “square rather than round”.

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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, the textbook on Numerical Methods with Applications available from the lulu storefront, and the YouTube video lectures available at http://numericalmethods.eng.usf.edu/videos and http://www.youtube.com/numericalmethodsguy

Subscribe to the blog via a reader or email to stay updated with this blog. Let the information follow you.

A problem using central divided difference error order

This is a problem I asked in the first examination of my Numerical Methods course in Spring 2009.   The question is that if one gives you an approximate value of the derivative of a function at a certain point using the central divided difference formula for two different step sizes, would you be able to find a better estimate of the derivative?

This post is brought to you by Holistic Numerical Methods: Numerical Methods for the STEM undergraduate at http://nm.mathforcollege.com, the textbook on Numerical Methods with Applications available from the lulu storefront, and the YouTube video lectures available at http://www.youtube.com/numericalmethodsguy.

Subscribe to the blog via a reader or email to stay updated with this blog. Let the information follow you.