Polygonal Approximation 4

Approximation of Differential Equations I. Polygonal Method Worksheet 4 of 4: 1. Step-by-step construction: [url]http://www.geogebratube.org/material/show/id/27865[/url] 2. Transfer the procedure to the Spreadsheet view: [url]http://www.geogebratube.org/material/show/id/27754[/url] 3. Improvement: add a term in the Taylor expansion: [url]http://www.geogebratube.org/material/show/id/29108[/url] [b]*4. Comparison of formulas:[/b] -vary h -choose two or three terms from the Taylor expansion. -correction formula (following Tenenbaum and Pollard, [i]Ordinary Differential Equations[/i], Lesson 44) Additional free parameters: -constant coefficients in the differential equation -initial values I have also included a direction field ____ These materials are self-instructional. If they can be of use to you, let me know how to make them better. I have not explained the error calculation or the formulas I made for the lists of points. I am happy to fill in this missing information if it will be of use. Also, if my methods are slow and klunky, tell me!

 

Ryan Hirst

 
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approximation  differential  equations  methods  series  starting  taylor 
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