Holistic Numerical Methods

Transforming Numerical Methods Education for the STEM Undergraduate

  
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WOLFRAM DEMONSTRATIONS

(External link | What are Wolfram Demonstrations? | Do need free Mathematica Player to run)

INTRODUCTION TO SCIENTIFIC COMPUTING

MEASURING ERRORS (CHAPTER 01.02)
  Precision Error [NBP]

 

SOURCES OF ERROR (CHAPTER 01.03)
 

Accuracy of  Series of Approximation [NBP]

 

BINARY REPRESENTATION (CHAPTER 01.04)
 

Numbers in Various Bases [NBP]

Counting in Binary [NBP]

 

TAYLOR'S THEOREM REVISITED (CHAPTER 01.07)
 

Taylor Series [NBP]

Taylor Polynomial [NBP]

Taylor-Maclaurin Series [NBP]

Accuracy of  Series of Approximation [NBP]

DIFFERENTIATION

BACKGROUND (CHAPTER 02.01)
 

The Definition of a Derivative [NBP]

 

Differentiation of Continuous Functions (CHAPTER 02.02)
 

The Definition of a Derivative [NBP]

Differential of a Function [NBP]

NONLINEAR EQUATIONS

QUADRATIC EQUATIONS (CHAPTER 03.01)
 

Solve Quadratic Equations with Integer Coefficients [NBP]

The Number of Distinct Real Roots of a Real Polynomial [NBP]

Quadratic Equation [NBP]

Geometric Solution of a Quadratic Equation  [NBP]

Solution of Quadratic Equations [NBP]

 

CUBIC EQUATIONS METHOD (CHAPTER 03.02)
 

The Number of Distinct Real Roots of a Real Polynomial [NBP]

Cubic Equation [NBP]

 

BISECTION METHOD (CHAPTER 03.03)
  A Simulation of Bisection Method [NBP]

 

Newton-Raphson Method (CHAPTER 03.04)
 

Learning Newton's Method [NBP]

Square Roots with Newton's Method [NBP]

Newton's Method [NBP]

 

SECANT METHOD (CHAPTER 03.05)
 

Secant Method of Finding Roots [NBP]

Approximating the Tangent to a Curve with Secants [NBP]

SIMULTANEOUS LINEAR EQUATIONS

BACKGROUND (CHAPTER 04.01)
 

Matrix Multiplication [NBP]

INTERPOLATION

 

Direct Method ((CHAPTER 05.02)
 

Interpolating a Set of Data [NBP]

Polynomial Interpolation [NBP]

 

LAGRANGE METHOD (CHAPTER 05.04)
 

Interval Interpolating Polynomial [NBP]

 

SPLINE Interpolation (CHAPTER 05.05)
 

Interpolating Polynomial [NBP]

Runge's Phenomenon [NBP]

REGRESSION

Linear Regression (CHAPTER 06.03)
 

Least Squares Criteria for the Least Squares Regression Line [NBP]

Linear and Quadratic Curve Fitting Practice [NBP]

Interactive Curve Fitting [NBP]

Fitting a Curve to Five Points [NBP]

 

Nonlinear Regression (CHAPTER 06.04)
 

Curve Fitting [NBP]

Interactive Curve Fitting [NBP]

Linear and Quadratic Curve Fitting Practice [NBP]

Fitting a Curve to Five Points [NBP]

INTEGRATION

 

primer ON INTEGRAL CALCULUS (CHAPTER 07.01)
 

Numerical Integration Using Rectangles, the Trapezoidal Rule, or Simpson's Rule [NBP]

 

Trapezoidal Rule (CHAPTER 07.02)
 

Numerical Integration Using Rectangles, the Trapezoidal Rule, or Simpson's Rule [NBP]

 

SIMPSON'S 1/3 RULE (CHAPTER 07.03)
 

Numerical Integration Using Rectangles, the Trapezoidal Rule, or Simpson's Rule [NBP]

 

Gauss Quadrature Rule (CHAPTER 07.05)
 

Gaussian Quadrature [NBP]

 

Discrete Data Integration (CHAPTER 07.06)
 

The Definition of a Derivative [NBP]

Using Sampled Data to Estimate Derivatives, Integrals, and Interpolated Values [NBP]

ORDINARY DIFFERENTIAL EQUATIONS

Primer on ODE (CHAPTER 08.01)
 

Numerical Methods of Differential Equations [NBP]

 

EuLER's METHOD (CHAPTER 08.02)
 

Global and Local Errors in Runge-Kutta Methods [NBP]

 

RuNGE-KUTTA 2ND ORDER METHOD (CHAPTER 08.03)
 

Global and Local Errors in Runge-Kutta Methods [NBP]

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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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