# 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

Gauss-Seidel Method

LU Decomposition

###### Interpolation

Direct Method

Newton’s Divided Difference Method

Lagrange Method

Spline Method

###### Regression

Linear Regression

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]

###### Integration

Trapezoidal Rule

Simpson’s 1/3rd Rule

Romberg Rule

Integrating Discrete Functions

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

###### Ordinary Differential Equations

Euler’s Method

Runge-Kutta 2nd order Method

Runge-Kutta 4th order Method

Shooting Method

Finite Difference Method

###### Optimization

Golden Section Search Method

Method [MAPLE] [MATHEMATICA] [MATLAB]

Newton’s Method

Method [MAPLE] [MATHEMATICA] [MATLAB]

Multidimensional Direct Search Method

Method [MAPLE] [MATHEMATICA] [MATLAB]

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