Holistic Numerical Methods

Transforming Numerical Methods Education for the STEM Undergraduate

  
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language

Mathematica

INTRODUCTION TO SCIENTIFIC COMPUTING

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Major

Industrial

BACKGROUND

 

INTRODUCTION TO NUMERICAL METHODS

 

Pre-Requisites for Learning Numerical Methods [PDF] [DOC]

Objectives of Introduction to Numerical Methods [PDF] [DOC]

Textbook Chapter on Introduction to Numerical Methods [PDF] [DOC]

A PowerPoint Presentation on Introduction to Numerical Methods [PDF] [PPT]

Test Your Knowledge on Introduction to Numerical Methods [HTML] [FLASH] [PDF] [DOC]

On Steps of Solving an Engineering Problem: Part 1 of 2 [YOUTUBE 8:54]

On Steps of Solving an Engineering Problem: Part 2 of 2 [YOUTUBE 7:35]

Enumerating Use of Numerical Methods for Mathematical Procedures: Part 1 of 2 [YOUTUBE 10:42]

Enumerating Use of Numerical Methods for Mathematical Procedures: Part 2 of 2 [YOUTUBE 7:13]

 

TOPICS

 

MEASURING ERRORS

 

 

Pre-Requisites for Learning Measuring Errors [PDF] [DOC]

Objectives of Measuring Errors [PDF] [DOC]

Textbook Chapter on Measuring Errors [PDF] [DOC]

A PowerPoint Presentation on Measuring Errors [PDF] [PPT]

Worksheet for True Error [PDF] [NB]

Worksheet for Approximate Error [PDF] [NB]

Test Your Knowledge on Measuring Errors [HTML] [FLASH] [PDF] [DOC]

True Error: Definition & Example [YOUTUBE 8:10]

Relative True Error: Definition & Example [YOUTUBE 7:39]

Approximate Error Definition & Example  [YOUTUBE 6:39]

Relative Approximate Error: Definition & Example  [YOUTUBE 8:45]

 

 

SOURCES OF ERROR

 

 

Pre-Requisites for Learning Sources of Error [PDF] [DOC]

Objectives of Sources of Error [PDF] [DOC]

Textbook Notes on Sources of Error [PDF] [DOC]

A PowerPoint Presentation on Sources of Error [PDF] [PPT]

Test Your Knowledge on Sources of Error [HTML] [FLASH] [PDF] [DOC]

Round-off Error: Definition and Examples [YOUTUBE 3:47]

Effect of Carrying Significant Digits [YOUTUBE 7:48]

Truncation Error: Definition [YOUTUBE 8:34]

Truncation Error: Example: Series [YOUTUBE 6:44]

Truncation Error: Example: Integration [YOUTUBE 6:12]

Truncation Error: Example: Differentiation [YOUTUBE 10:14]

 

 

BINARY REPRESENTATION OF NUMBERS

 

 

Pre-Requisites for Learning Binary Representation [PDF] [DOC]

Objectives of Binary Representation [PDF] [DOC]

Textbook Notes on Binary Representation of Numbers [PDF] [DOC]

A PowerPoint Presentation on Binary Representation of Numbers [PDF] [PPT]

Worksheet for Decimal to Binary Representation [PDF] [NB]

Worksheet for Binary to Decimal Representation [PDF] [NB]

Test Your Knowledge on Binary Representation of Numbers [HTML] [FLASH] [PDF] [DOC]

Introduction to Binary Representation [YOUTUBE 6:41]

Base-10 to Base-2 Conversion Method [YOUTUBE 9:14]

Base-10 to Base-2 Conversion Another Method [YOUTUBE 9:14]

 

 

FLOATING POINT REPRESENTATION OF NUMBERS

 

 

Pre-Requisites for Learning Floating Point Representation [PDF] [DOC]

Objectives of Floating Point Representation [PDF] [DOC]

Textbook Notes on Floating Point Representation of Numbers [PDF] [DOC]

A PowerPoint Presentation on Floating Point Representation of Numbers [PDF] [PPT]

Worksheet for Decimal to Floating Point Representation [PDF] [NB]

Worksheet for Floating Point to Decimal Representation [PDF] [NB]

Test Your Knowledge on Floating Point Representation of Numbers [HTML] [FLASH] [PDF] [DOC]

Floating Point Representation Background: Part 1 of 3 [ YOUTUBE 7:37]

Floating Point Representation Background: Part 2 of 3 [ YOUTUBE 10:43]

Floating Point Representation Background: Part 3  of 3[ YOUTUBE 1:58]

Floating Point Representation: Example  [YOUTUBE 10:10]

Floating Point Representation - Biased Exponent: Example [YOUTUBE 8:51]

IEEE-754 Single Precision Representation: Part 1 of 2 [YOUTUBE 4:57]

IEEE-754 Single Precision Representation: Part 2 of 2 [YOUTUBE 8:38]

 

 

PROPAGATION OF ERRORS

 

 

Pre-Requisites for Learning Propagation of Errors  [PDF] [DOC]

Objectives of Propagation of Errors [PDF] [DOC]

Textbook Notes on Propagation of Errors [PDF] [DOC]

A PowerPoint Presentation on Propagation of Errors [PDF] [PPT]

Worksheet for Propagation of Errors [PDF] [NB]

Test your knowledge on Propagation of Errors [HTML] [FLASH] [PDF] [DOC]

 

 

TAYLOR THEOREM REVISITED

 

 

Pre-Requisites for Learning Taylor Series Revisited [PDF] [DOC]

Objectives of Taylor Series Revisited [PDF] [DOC]

Textbook Notes on Taylor Series [PDF] [DOC]

A PowerPoint Presentation on Taylor series [PDF] [PPT]

Test Your Knowledge on Taylor Series [HTML] [FLASH] [PDF] [DOC]

Introduction to Taylor Series [YOUTUBE 7:28]

Taylor Series: Example [YOUTUBE 6:31]

Taylor Series: Deriving the Series for exp(x)  [YOUTUBE 5:30]

Taylor Series: Example: Finding sin(2.0) [YOUTUBE 10:32]

 

ANECDOTES

 

 

Worksheet on quadratic equation solution to illustrate subtraction of close numbers [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