Holistic Numerical Methods

Transforming Numerical Methods Education for the STEM Undergraduate

  
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language

Mathematica

DIFFERENTIATION

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Major

Mechanical

BACKGROUND

 

Pre-Requisites for Learning Differential Calculus [PDF] [DOC]

Objectives of Differential Calculus [PDF] [DOC]

A Primer on Differential Calculus  [PDF] [DOC]

Test Your Knowledge on Background of Differentiation [HTML] [FLASH] [PDF] [DOC]

 

PHYSICAL PROBLEM

 

Finding the acceleration of a rocket from its velocity. [PDF] [DOC]

 

NUMERICAL METHODS

 

CONTINUOUS FUNCTIONS

 

 

Pre-Requisites for Learning Numerical Differentiation of Continuous Functions [PDF] [DOC]

Objectives of Numerical Differentiation of Continuous Functions [PDF] [DOC]

How does Numerical Differentiation of Continuous Functions Work? [PDF] [DOC]

Forward Divided Difference: Part 1 of 2 [YOUTUBE 9:28]

Forward Divided Difference: Part 2 of 2 [YOUTUBE 4:41]

Backward Divided Difference: Part 1 of 2 [YOUTUBE 9:08]

Backward Divided Difference: Part 2 of 2[YOUTUBE 5:32]

Central Divided Difference [YOUTUBE 9:53]

Higher Order Derivative Divided Difference: Theory [YOUTUBE 8:37] |

Higher Order Derivative Divided Difference: Example [YOUTUBE 6:04]

Accuracy of Divided Difference Formulas: Part 1 of 2 [YOUTUBE 8:16]

Accuracy of Divided Difference Formulas  Part 2 of 2 [YOUTUBE 3:51]

A Power Point Presentation on Numerical Differentiation of Continuous Functions [PDF] [PPT]

Worksheet for Numerical Differentiation of Continuous Functions Forward Divided Difference [PDF] [NB]

Worksheet for Numerical Differentiation of Continuous Functions Backward Divided Difference [PDF] [NB]

Worksheet for Numerical Differentiation of Continuous Functions Central Divided Difference [PDF] [NB]

Worksheet for Numerical Differentiation of Continuous Functions Second Order Derivative [PDF] [NB]

Test Your Knowledge of Numerical Differentiation of Continuous Functions [HTML] [FLASH] [PDF] [DOC]

 

DISCRETE FUNCTIONS

 

 

Pre-Requisites for Learning Numerical Differentiation of Discrete Functions [PDF] [DOC]

Objectives of Numerical Differentiation of Discrete Functions [PDF] [DOC]

How does Numerical Differentiation of Discrete Functions Work? [PDF] [DOC]

Divided Difference Approach [YOUTUBE 10:07]

Polynomial Interpolation Method [YOUTUBE 8:09]

Newton's Divided Difference Polynomial Method: Theory [YOUTUBE 7:45]

Newton's Divided Difference Polynomial Method: Example [YOUTUBE  8:28]

A Power Point Presentation on Numerical Differentiation of Discrete Functions [PDF] [PPT]

Worksheet for Numerical Differentiation of Discrete Functions [PDF] [NB]

Test Your Knowledge of Numerical Differentiation of Discrete Functions [HTML] [FLASH] [PDF] [DOC]

 

ANECDOTES

 

Effect of Step Size on Accuracy of Numerical First Derivative

        Forward Divided Difference  [PDF] [PPT]

        Backward Divided Difference  [PDF] [PPT]

        Central Divided Difference [PDF] [PPT]

Comparing the Forward Divided Difference, Backward Divided Difference & Central Divided Difference [PDF] [NB]

Effect of Significant Digits on the Value of the Numerical Derivative [PDF] [NB]
 

 

 

 

 

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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 mathforcollege@yahoo.com.   This material is based upon work supported by the National Science Foundation under Grant# Creative Commons License0126793, 0341468, 0717624,  0836981, 0836916, 0836805.  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 Mathematica, MathCAD, USF, FAMU and MSOE.  Based on a work at http://nm.mathforcollege.com.  Holistic Numerical Methods licensed under a Creative Commons Attribution-NonCommercial-NoDerivs 3.0 Unported License.

ANALYTICS