Holistic Numerical Methods

Transforming Numerical Methods Education for the STEM Undergraduate

 

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language

Mathematica

ORDINARY DIFFERENTIAL EQUATION

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Major

Electrical


BACKGROUND

Pre-Requisites for Ordinary Differential Equations [PDF] [DOC]

Objectives of Ordinary Differential Equations [PDF] [DOC]

What are Ordinary Differential Equations? [PDF] [DOC]

A Primer on Ordinary Differential Equations [PDF] [DOC]

Exact Solution of 1st order ODE [YOUTUBE 6:48]

Exact Solution of 1st order ODE: Another Example [YOUTUBE 7:37]

Exact Solution of 2nd order ODE: Distinct Roots of Characteristic Equation [YOUTUBE  8:50] 

Exact Solution of 2nd order ODE: Repeated Roots of Characteristic Equation [YOUTUBE  8:41] 

Exact Solution of 2nd order ODE: Complex Roots of Characteristic Equation [YOUTUBE  9:34]

Test Your Knowledge of Background of Ordinary Differential Equation [HTML] [FLASH] [PDF] [DOC]

 

PHYSICAL PROBLEM

How much time will it take the ball to cool down? [PDF] [DOC]

 

NUMERICAL METHOD

EULER'S METHOD

Pre-Requisites for Euler's Method [PDF] [DOC]

Objectives of Euler's Method [PDF] [DOC]

How does Euler's method Work? [PDF] [DOC]

Euler's Method of Solving ODEs: Derivation  [YOUTUBE 9:53]

Euler's Method of Solving ODEs: Example [YOUTUBE 10:57] 

Euler's Method of Estimating Integrals: Theory [YOUTUBE  7:11] 

Euler's Method of Estimating Integrals: Example [YOUTUBE  8:58]

A Power Point Presentation on Euler's Method [PDF] [PPT]

Worksheet of Euler's Method [NB]

Convergence Worksheet of Euler's Method [NB]

Test Your Knowledge of Euler's method [HTML] [FLASH] [PDF] [DOC]

 

RUNGE-KUTTA 2nd ORDER METHOD

Pre-Requisites for Runge-Kutta 2nd Order Method [PDF] [DOC]

Objectives of Runge-Kutta 2nd Order Method [PDF] [DOC]

How does Runge-Kutta 2nd Order Method Work? [PDF] [DOC]

Runge-Kutta 2nd Order Method: Background [YOUTUBE 9:46]

Runge-Kutta 2nd Order Method: Formulas [YOUTUBE  10:57] 

Runge-Kutta 2nd Order Method: Heun's Method  [YOUTUBE  9:27]

Runge-Kutta 2nd Order Method: Midpoint Method  [YOUTUBE  10:45]

Runge-Kutta 2nd Order Method: Ralston's Method Part 1 of 2 [ YOUTUBE 7:09]

Runge-Kutta 2nd Order Method: Ralston's Method Part 2 of 2 [ YOUTUBE 5:00]

Runge-Kutta 2nd Order Method: Derivation Part 1 of 2 [ YOUTUBE 7:08]|

Runge-Kutta 2nd Order Method: Derivation Part 2 of 2 [ YOUTUBE 5:31]

A Power Point Presentation on Runge-Kutta 2nd Order Method [PDF] [PPT]

Worksheet of Runge-Kutta 2nd Order Method [NB]

Convergence Worksheet of Runge-Kutta 2nd Order Method [NB]

Test Your Knowledge of Runge-Kutta 2nd Order Method [HTML] [FLASH] [PDF] [DOC]

 

RUNGE-KUTTA 4th ORDER METHOD

Pre-Requisites for Runge-Kutta 4th Order Method [PDF] [DOC]

Objectives of Runge-Kutta 4th Order Method [PDF] [DOC]

How does Runge-Kutta 4th Order Method Work? [PDF] [DOC]

Runge Kutta 4th Order Method: Formulas [YOUTUBE 9:54]

Runge Kutta 4th Order Method: Example: Part 1 of 2 [YOUTUBE 9:29]

Runge Kutta 4th Order Method: Example: Part 2 of 2 [YOUTUBE 8:48]

A Power Point Presentation on Runge-Kutta 4th Order Method [PDF] [PPT]

Worksheet of Runge-Kutta 4th Order Method [NB]

Convergence Worksheet of Runge-Kutta 4th Order Method [NB]

Test Your Knowledge of Runge-Kutta 4th Order Method [HTML] [FLASH] [PDF] [DOC]

 

SHOOTING METHOD

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

Objectives of Shooting Method [PDF] [DOC]

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

Power Point Presentation on Shooting Method [PDF] [PPT]

Worksheet of Shooting Method [NB]

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

 

FINITE DIFFERENCE METHOD

Pre-Requisites for Finite Difference Method [PDF] [DOC]

Objectives of Finite Difference Method [PDF] [DOC]

How does Finite Difference Method Work? [PDF] [DOC]

Finite Difference Method of Solving Ordinary Differential Equations: Background Part 1 of 2 [YOUTUBE 3:46]

Finite Difference Method of Solving Ordinary Differential Equations: Background Part 2 of 2 [YOUTUBE 8:40]

Finite Difference Method: Example Beam: Part 1 of 2  [YOUTUBE 6:13]

Finite Difference Method: Example Beam: Part 2 of 2  [YOUTUBE 6:21]

Finite Difference Method: Example Pressure Vessel: Part 1 of 2  [YOUTUBE 9:55]

Finite Difference Method: Example Pressure Vessel: Part 2 of 2  [YOUTUBE 9:50]

A Power Point Presentation on Finite Difference Method [PDF] [PPT]

Worksheet of Finite Difference Method [NB]

Test Your Knowledge of Finite Difference Method [HTML] [FLASH] [PDF] [DOC]

 

ANECDOTES

On Solving Higher Order and Coupled Ordinary Differential Equations [PDF] [DOC] [NB]

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 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