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]