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