Holistic Numerical Methods

Transforming Numerical Methods Education for the STEM Undergraduate

 

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POWER POINT PRESENTATIONS

INTRODUCTION TO SCIENTIFIC COMPUTING

      Introduction to numerical methods [PDF] [PPT]

      Measuring errors [PDF] [PPT]

      Sources of error [PDF] [PPT]

      Binary representation of numbers [PDF] [PPT]

      Floating point representation of numbers [PDF] [PPT]

      Propagation of errors [PDF] [PPT]

      Taylor series [PDF] [PPT]

 

differentiation

     Continuous functions [PDF] [PPT]

     Discrete functions [PDF] [PPT]

     Effect of step size on accuracy of numerical first derivative: Forward Divided Difference [PDF] [PPT]

     Effect of step size on accuracy of numerical first derivative Backward Divided Difference [PDF] [PPT]

     Effect of step size on accuracy of numerical first derivative: Central Divided Difference [PDF] [PPT]

 

NONLINEAR EQUATIONS

    Bisection Method [PDF] [PPT]

     Newton-Raphson Method [PDF] [PPT]

     Secant Method [PDF] [PPT]

 

SIMULTANEOUS LINEAR Equations

    Gaussian Elimination [PDF] [PPT]

     LU Decomposition method [PDF] [PPT]

     Gauss-Seidel method [PDF] [PPT]

 

Interpolation

    Direct Method [PDF] [PPT]

     Newton's Divided Difference Method [PDF] [PPT]

     Lagrange Method [PDF] [PPT]

     Spline Method [PDF] [PPT]

 

REGRESSION

     Linear Regression [PDF] [PPT]

     Nonlinear regression [PDF] [PPT]

 

Integration

   Trapezoidal Rule [PDF] [PPT]
    Simpson's 1/3rd Rule
[PDF] [PPT]

     Romberg Rule [PDF] [PPT]
    Gauss-Quadrature Rule
[PDF] [PPT]

 

ordinary differential equations

    Euler's Method [PDF] [PPT]

    Runge-Kutta 2nd order Method [PDF] [PPT]

     Runge-Kutta 4th order Method [PDF] [PPT]
    Shooting Method
[PDF] [PPT]

    Finite Difference Method [PDF] [PPT]

 

OPTIMIZATION

   Golden Section Search Method [PDF] [PPT]

    Newton's Method [PDF] [PPT]

    Multidimensional Direct Search Method [PDF] [PPT]

    Multidimensional Gradient Method [PDF] [PPT]

 

PARTIAL DIFFERENTIAL equations

   Introduction to Partial Differential Equations [PDF] [PPT]

    Parabolic Partial Differential Equations [PDF] [PPT]

    Elliptic Partial Differential Equations [PDF] [PPT]

 

FAST FOURIER TRANSFORMS

   Introduction to Fourier Series [PDF] [PPT]  

   Continuous Fourier Series [PDF] [PPT]

    Fourier Transform Pair [PDF] [PPT]

    Discrete Fourier Transform [PDF] [PPT]

   Informal Development of Fast Fourier Transform [PDF] [PPT]


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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.  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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