Holistic Numerical Methods

Transforming Numerical Methods Education for the STEM Undergraduate

 

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ANECDOTES

DIFFERENTIATION

 

Effect of step size on accuracy of numerical first derivative:

      Forward Divided Difference  [PDF] [PPT]

      Backward Divided Difference [PDF][PPT]

Effect of step size on accuracy of numerical first derivative: Central Divided Difference [PDF] [PPT]

Comparing the Forward Divided Difference, Backward Divided Difference

     Central Divided Difference [PDF] [MWS] | [PDF] [MCD] | [PDF] [NB] | |PDF] [MFILE]

Effect of Significant Digits on the Value of the

      Numerical Derivative [PDF] [MWS] | [PDF] [MCD]|[PDF] [NB]|[PDF] [MFILE]


NONLINEAR EQUATIONS

 

Quest for cubic equation solution [PDF] [DOC]

Newton [HTML] [PDF] [DOC]

Raphson [HTML] [PDF] [DOC]

Galois [HTML] [PDF] [DOC]


SIMULTANEOUS LINEAR EQUATIONS

 

Effect of significant digits on solution of equations

        Simulation [MWS]  [MCD] [NB] [MFILE] | Textbook notes (pages 5-16 of) [PDF] [DOC]

Saving of computational time for finding inverse of a matrix using LU decomposition

           Simulation [MWS] [MCD] [NB] [MFILE]  | Textbook notes (pages 2-4 of) [PDF] [DOC]

Adequacy of Solutions [PDF] [MWS] | [PDF] [DOC]

Eigenvalues and Eigenvectors [DOC] [PDF]

Gauss [HTML] [PDF] [DOC]


INTERPOLATION

 

History of Interpolation [PDF] [DOC

Dangers of extrapolation through NASDAQ, [PDF] [DOC]|[MWS] [MCD] [MFILE] [NBM]

Higher order interpolation is a bad idea [PDF] [DOC]| [MWS] [MCD] [MFILE] [NBM]

Comparison of spline & polynomial interpolation [PDF] [DOC]|[MWS] [MCD] [MFILE] [NBM]

Choice of points of interpolation affects approximations [PDF] [DOC]|[MWS] [MCD] [MFILE] [NBM]

Splines help in developing a shorter path for a robot [PDF] [DOC]|[MWS] [MCD] [MFILE] [NBM]

Runge [HTML] [PDF] [DOC]

Newton [HTML] [PDF] [DOC]

Lagrange [HTML] [PDF] [DOC]


INTEGRATION

 

What is integration? [PDF] [DOC]

A Primer on Integral Calculus [PDF] [DOC]

Newton [HTML] [PDF] [DOC]

Cotes [HTML] [PDF] [DOC]

Gauss [HTML] [PDF] [DOC]

Simpson [HTML] [PDF] [DOC]

Romberg [HTML] [PDF] [DOC]


ORDINARY DIFFERENTIAL EQUATIONS

 

What are ordinary differential equations? [PDF] [DOC]

A primer on ordinary differential equations [PDF] [DOC]

On solving higher order and coupled ordinary differential equations [PDF] [DOC]

Euler [HTML] [PDF] [DOC]

Runge [HTML] [PDF] [DOC]

Kutta [HTML] [PDF] [DOC]


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Copyrights: University of South Florida, 4202 E Fowler Ave, Tampa, FL 33620-5350. All Rights Reserved. Questions, suggestions or comments, contact kaw@eng.usf.edu  This material is based upon work supported by the National Science Foundation under Grant# Creative Commons License0126793, 0341468, 0717624,  0836981, 0836916, 0836805, 1322586.  Any opinions, findings, and conclusions or recommendations expressed in this material are those of the author(s) and do not necessarily reflect the views of the National Science Foundation.  Other sponsors include Maple, MathCAD, USF, FAMU and MSOE.  Based on a work at http://mathforcollege.com/nm.  Holistic Numerical Methods licensed under a Creative Commons Attribution-NonCommercial-NoDerivs 3.0 Unported License.

 

ANALYTICS