Numerical Methods Simulations Maple Mathcad Mathematica Matlab

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]