Holistic Numerical Methods

Transforming Numerical Methods Education for the STEM Undergraduate

  
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language

Mathematica

INTEGRATION

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Major

Mechanical

BACKGROUND

Pre-Requisites for Integral Calculus [PDF] [DOC]

Objectives of Integral Calculus [PDF] [DOC]

What is Integration? [PDF] [DOC]

A Primer on Integral Calculus [PDF] [DOC]

Test Your Knowledge of Background of Integral Calculus [HTML] [FLASH] [PDF] [DOC]

 

PHYSICAL PROBLEM

Find the vertical distance covered by a rocket when introduced to an equation for its velocity. [PDF] [DOC]

 

NUMERICAL METHOD

TRAPEZOIDAL RULE

Pre-Requisites for Trapezoidal Method [PDF] [DOC]

Objectives of Trapezoidal Method [PDF] [DOC]

A Textbook Chapter on Trapezoidal Rule? [PDF] [DOC]

Trapezoidal Rule Derivation [YOUTUBE 10:51]

Trapezoidal Rule: Example [YOUTUBE  7:18] 

Trapezoidal Rule Multiple Segment Rule: Motivation [YOUTUBE 4:53]

Trapezoidal Rule Multiple Segment Rule: Derivation [YOUTUBE 7:48]

Trapezoidal Rule Multiple Segment Rule: Example: Part 1 [YOUTUBE 8:17]

Trapezoidal Rule Multiple Segment Rule: Example: Part 2 [YOUTUBE 3:41]

Trapezoidal Rule Multiple Segment Rule: Error Derivation [YOUTUBE  8:46] 

Trapezoidal Rule Multiple Segment Rule: Error Example [YOUTUBE  8:52] 

Method of Undetermined Coefficients: Trapezoidal Rule Derivation [YOUTUBE 10:00]

A Power Point Presentation on Trapezoidal Method [PDF] [PPT]

Worksheet of Trapezoidal method [PDF] [NB]

Convergence Worksheet of Trapezoidal Method [PDF] [NB]

Test Your Knowledge of Trapezoidal Method [HTML] [FLASH] [PDF] [DOC]

 

SIMPSON'S 1/3rd RULE

Pre-Requisites for Simpson's 1/3 Rule [PDF] [DOC]

Objectives of Simpson's 1/3 Rule [PDF] [DOC]

How Does Simpson's 1/3rd Rule Method Work? [PDF] [DOC]

A Power Point Presentation on Simpson's 1/3rd Rule Method [PDF] [PPT]

Worksheet of Simpson's 1/3rd Rule Method [PDF] [NB]

Convergence Worksheet of Simpson's 1/3rd Rule Method [PDF] [NB]

Test Your Knowledge of Simpson's 1/3 Rule [HTML] [FLASH] [PDF] [DOC]

 

ROMBERG INTEGRATION

Pre-Requisites for Romberg Method [PDF] [DOC]

Objectives of Romberg Method [PDF] [DOC]

How Does Romberg Method Work? [PDF] [DOC]

A Power Point Presentation on Romberg Method [PDF] [PPT]

Worksheet of Romberg Method [PDF] [NB]

Convergence Worksheet of Romberg Method [PDF] [NB]

Test Your Knowledge of Romberg Method [HTML] [PDF] [DOC]

 

GAUSS QUADRATURE

Pre-Requisites for Gauss-Quadrature  [PDF] [DOC]

Objectives of Gauss-Quadrature  [PDF] [DOC]

How does Gauss-Quadrature Method Work? [PDF] [DOC]

Method of Undetermined Coefficients: Trapezoidal Rule Derivation [YOUTUBE 10:00]

2-pt Gaussian Quadrature Rule: Derivation  [YOUTUBE  8:43] 

n-pt Gaussian Quadrature Rule: Discussion [YOUTUBE 8:52]

Converting Limits of Integration [YOUTUBE 7:13]

Gaussian Quadrature Rule: Example [ YOUTUBE 8:55]

1-pt Gaussian Quadrature Rule: Derivation  [YOUTUBE  8:36] 

Complete Derivation of Two Point Gaussian Quadrature Rule: Part 1 [ YOUTUBE 9:46]

Complete Derivation of Two Point Gaussian Quadrature Rule: Part 2 [ YOUTUBE 3:31]

Complete Derivation of Two Point Gaussian Quadrature Rule: Part 3 [ YOUTUBE 9:58]

A Power Point Presentation on Gauss-Quadrature Method [PDF] [PPT]

Worksheet of Gauss-Quadrature Method [PDF] [NB]

Convergence Worksheet of Gauss-Quadrature Method [PDF] [NB]

Test Your Knowledge of Gauss-Quadrature Method [HTML] [FLASH] [PDF] [DOC]

 

ANECDOTES

Integrating Discrete Function  [PDF] [DOC] | [NB] [PDF]

Integrating Discrete Functions by Average Method [YOUTUBE 8:29]

Integrating Discrete Functions by Trapezoidal Rule [YOUTUBE  10:52] 

Integrating Discrete Functions via Polynomial Interpolation [YOUTUBE 9:32]

Integrating Improper Integrals  [PDF] [DOC] 

Newton [HTML] [PDF] [DOC]

Cotes [HTML] [PDF] [DOC]

Gauss [HTML] [PDF] [DOC]

Simpson [HTML] [PDF] [DOC]

Romberg [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 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