Holistic Numerical Methods

Transforming Numerical Methods Education for the STEM Undergraduate

 

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WORKSHEETS

INTRODUCTION TO SCIENTIFIC COMPUTING

 

Measuring Errors

   

True Error  [MAPLE] [MATHCAD] [MATHEMATICA] [MATLAB]

Approximate Error  [MAPLE] [MATHCAD] [MATHEMATICA] [MATLAB

 

Binary Representation

   

Decimal to binary representation [MAPLE] [MATHCAD] [MATHEMATICA] [MATLAB]

Binary to decimal representation [MAPLE] [MATHCAD] [MATHEMATICA] [MATLAB]

 

Measuring Errors

   

Decimal to floating point representation [MAPLE] [MATHCAD] [MATHEMATICA] [MATLAB]

Binary to floating point representation [MAPLE] [MATHCAD] [MATHEMATICA] [MATLAB]

 

Propagation of Errors

   

Propagation of Errors  [MAPLE] [MATHCAD] [MATHEMATICA] [MATLAB]

 

Differentiation

 

Continuous Functions

   

Forward Divided Difference  [MAPLE]   [MATHCAD]   [MATHEMATICA]  [MATLAB]

Backward Divided Difference [MAPLE]   [MATHCAD]   [MATHEMATICA]  [MATLAB]

Central Divided Difference [MAPLE]   [MATHCAD]  [MATHEMATICA]   [MATLAB]

Continuous functions Second Order Derivative  [MAPLE]  [MATHCAD]  [MATHEMATICA]  [MATLAB]

 

Discrete Data

   

Discrete functions  [MAPLE]  [MATHCAD]   [MATHEMATICA] [MATLAB]

 

Nonlinear Equations

 

Bisection Method

   

Method [MAPLE] [MATHCAD] [MATHEMATICA] [MATLAB]

Convergence [MAPLE] [MATHCAD] [MATHEMATICA] [MATLAB]

Pitfall: Slow convergence of bisection method simulation [MAPLE] [MATHCAD] [MATHEMATICA] [MATLAB]

 

Newton-Raphson Method

   

Method [MAPLE] [MATHCAD] [MATHEMATICA] [MATLAB]

Convergence [MAPLE] [MATHCAD] [MATHEMATICA] [MATLAB]

Pitfall: Division by zero [MAPLE] [MATHCAD] [MATHEMATICA] [MATLAB]

Pitfall: Slow Convergence at Inflection Points [MAPLE] [MATHCAD] [MATHEMATICA] [MATLAB]

Pitfall: Root jumps over several roots [MAPLE] [MATHCAD] [MATHEMATICA] [MATLAB]

Pitfall: Roots oscillates around local maxima and minima [MAPLE] [MATHCAD] [MATHEMATICA] [MATLAB]

 

Secant Method

   

Simulation of secant method  [MAPLE] [MATHCAD] [MATHEMATICA] [MATLAB]

Convergence Simulation of secant method  [MAPLE] [MATHCAD] [MATHEMATICA] [MATLAB]

Pitfall: Division by zero in secant method simulation  [MAPLE] [MATHCAD] [MATHEMATICA] [MATLAB]

Pitfall: Root jumps over several roots in secant method  [MAPLE] [MATHCAD] [MATHEMATICA] [MATLAB]

     

SIMULTANEOUS LINEAR EQUATIONS

 

Gaussian Elimination

   

Method [MAPLE] [MATHCAD] [MATHEMATICA] [MATLAB]

 

Gauss-Seidel Method

   

Method [MAPLE]  [MATHCAD]  [MATHEMATICA]  [MATLAB]

   

Convergence [MAPLE]  [MATHCAD]  [MATHEMATICA]  [MATLAB]

 

LU Decomposition

   

Method [MAPLE] [MATHCAD] [MATHEMATICA] [MATLAB]

     

Interpolation

 

Direct Method

   

Method [MAPLE] [MATHCAD] [MATHEMATICA] [MATLAB]

 

Newton's Divided Difference Method

   

Method [MAPLE]  [MATHCAD]  [MATHEMATICA]  [MATLAB]

 

Lagrange Method

   

Method [MAPLE] [MATHCAD] [MATHEMATICA] [MATLAB]

 

Spline Method

   

Method [MAPLE]  [MATHCAD]  [MATHEMATICA]  [MATLAB]

     

REGRESSION

 

Linear Regression

   

Method [MAPLE] [MATHCAD] [MATHEMATICA] [MATLAB]

 

Nonlinear Regression

   

Without Data Linearization [MAPLE]  [MATHCAD]  [MATHEMATICA]  [MATLAB]

With Data Linearization [MAPLE]  [MATHCAD]  [MATHEMATICA]  [MATLAB]

Polynomial Regression [MAPLE]  [MATHCAD]  [MATHEMATICA]  [MATLAB]

Comparing with and without Data Linearization [MAPLE]  [MATHCAD]  [MATHEMATICA]  [MATLAB]

 

Adequacy of a Regression Model

   

Adequacy [MAPLE] [MATHCAD] [MATHEMATICA] [MATLAB]

     

Integration

 

Trapezoidal Rule

   

Method [MAPLE] [MATHCAD] [MATHEMATICA] [MATLAB]

Convergence [MAPLE] [MATHCAD] [MATHEMATICA] [MATLAB]

 

Simpson's 1/3rd Rule

   

Method [MAPLE] [MATHCAD] [MATHEMATICA] [MATLAB]

Convergence [MAPLE] [MATHCAD] [MATHEMATICA] [MATLAB]

 

Romberg Rule

   

Method [MAPLE] [MATHCAD] [MATHEMATICA] [MATLAB]

Convergence [MAPLE] [MATHCAD] [MATHEMATICA] [MATLAB]

 

Gauss-Quadrature Rule

   

Method [MAPLE] [MATHCAD] [MATHEMATICA] [MATLAB]

Convergence [MAPLE] [MATHCAD] [MATHEMATICA] [MATLAB]

 

Integrating Discrete Functions

   

Integrating discrete functions [MAPLE] [MATHCAD] [MATHEMATICA] [MATLAB]

 

ORDINARY DIFFERENTIAL EQUATIONS

 

Euler's Method

   

Method [MAPLE] [MATHCAD] [MATHEMATICA] [MATLAB]

Convergence [MAPLE] [MATHCAD] [MATHEMATICA] [MATLAB]

 

Runge-Kutta 2nd order Method

   

Method [MAPLE] [MATHCAD] [MATHEMATICA] [MATLAB]

Convergence [MAPLE] [MATHCAD] [MATHEMATICA] [MATLAB]

 

Runge-Kutta 4th order Method

   

Method [MAPLE] [MATHCAD] [MATHEMATICA] [MATLAB]

Convergence [MAPLE] [MATHCAD] [MATHEMATICA] [MATLAB]

 

Shooting Method

   

Method [MAPLE] [MATHCAD] [MATHEMATICA] [MATLAB]

 

Finite Difference Method

   

Method [MAPLE] [MATHCAD] [MATHEMATICA] [MATLAB]

OPTIMIZATION

 

Golden Section Search Method

   

Method [MAPLE] [MATHEMATICA] [MATLAB]

 

Newton's Method

   

Method [MAPLE] [MATHEMATICA] [MATLAB]

 

Multidimensional Direct Search Method

   

Method [MAPLE] [MATHEMATICA] [MATLAB]

 

Multidimensional Gradient Method

   

Method [MAPLE] [MATHEMATICA] [MATLAB]

PARTIAL DIFFERENTIAL EQUATIONS

 

Parabolic Partial Differential Equations

   

Explicit Method [MATLAB] [MAPLE] [MATHEMATICA] [MATHCAD]

Implicit Method Parabolic PDEs [MATLAB] [MAPLE] [MATHEMATICA] [MATHCAD]

Crank Nicolson Method Parabolic PDEs [MATLAB] [MAPLE] [MATHEMATICA] [MATHCAD]

 

Elliptic Partial Differential Equations

   

Direct Method [MATLAB] [MAPLE] [MATHEMATICA] [MATHCAD]

Gauss-Seidel Method [MATLAB] [MAPLE] [MATHEMATICA] [MATHCAD]

Lieberman Method [MATLAB] [MAPLE] [MATHEMATICA] [MATHCAD]

fast fourier transforms

 

Continuous Fourier Series

   

Method [MATLAB] [MATHCAD] [MATHEMATICA]

 

Discrete Fourier Transform

   

Method [ [MATLAB] [MATHCAD] [MATHEMATICA]

 

Fast Fourier Transform

   

Method  [MATLAB] [MATHCAD] [MATHEMATICA]


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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.

 

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