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WORKSHEETS |
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INTRODUCTION TO SCIENTIFIC COMPUTING |
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Measuring Errors |
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True Error
[MAPLE] [MATHCAD]
[MATHEMATICA]
[MATLAB]
Approximate Error
[MAPLE] [MATHCAD]
[MATHEMATICA]
[MATLAB
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Binary
Representation |
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Decimal to binary representation
[MAPLE] [MATHCAD]
[MATHEMATICA]
[MATLAB]
Binary to decimal representation
[MAPLE] [MATHCAD]
[MATHEMATICA]
[MATLAB]
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Measuring Errors |
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Decimal to floating point
representation
[MAPLE] [MATHCAD]
[MATHEMATICA]
[MATLAB]
Binary to floating point
representation
[MAPLE] [MATHCAD]
[MATHEMATICA]
[MATLAB]
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Propagation of Errors |
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Propagation of Errors
[MAPLE] [MATHCAD]
[MATHEMATICA]
[MATLAB]
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Differentiation |
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Continuous Functions |
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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]
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Discrete
Data |
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Discrete
functions
[MAPLE]
[MATHCAD]
[MATHEMATICA]
[MATLAB] |
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Nonlinear Equations |
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Bisection Method |
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Method [MAPLE]
[MATHCAD]
[MATHEMATICA]
[MATLAB]
Convergence
[MAPLE]
[MATHCAD]
[MATHEMATICA]
[MATLAB]
Pitfall: Slow convergence of
bisection method simulation [MAPLE]
[MATHCAD]
[MATHEMATICA]
[MATLAB]
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Newton-Raphson Method |
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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]
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Secant Method |
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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]
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SIMULTANEOUS LINEAR EQUATIONS |
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Gaussian Elimination |
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Method
[MAPLE]
[MATHCAD]
[MATHEMATICA]
[MATLAB]
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Gauss-Seidel Method |
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Method [MAPLE]
[MATHCAD]
[MATHEMATICA]
[MATLAB]
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Convergence
[MAPLE]
[MATHCAD]
[MATHEMATICA]
[MATLAB] |
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LU
Decomposition |
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Method [MAPLE]
[MATHCAD]
[MATHEMATICA]
[MATLAB] |
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Interpolation |
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Direct Method |
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Method [MAPLE]
[MATHCAD]
[MATHEMATICA]
[MATLAB]
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Newton's Divided Difference Method |
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Method [MAPLE]
[MATHCAD]
[MATHEMATICA]
[MATLAB]
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Lagrange
Method |
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Method [MAPLE]
[MATHCAD]
[MATHEMATICA]
[MATLAB] |
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Spline
Method |
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Method
[MAPLE]
[MATHCAD]
[MATHEMATICA]
[MATLAB] |
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REGRESSION |
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Linear Regression |
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Method [MAPLE]
[MATHCAD]
[MATHEMATICA]
[MATLAB]
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Nonlinear Regression |
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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]
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Adequacy of a Regression Model |
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Adequacy [MAPLE]
[MATHCAD]
[MATHEMATICA]
[MATLAB]
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Integration |
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Trapezoidal Rule |
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Method [MAPLE]
[MATHCAD]
[MATHEMATICA]
[MATLAB]
Convergence
[MAPLE]
[MATHCAD]
[MATHEMATICA]
[MATLAB]
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Simpson's 1/3rd Rule |
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Method [MAPLE]
[MATHCAD]
[MATHEMATICA]
[MATLAB]
Convergence [MAPLE]
[MATHCAD]
[MATHEMATICA]
[MATLAB]
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Romberg Rule |
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Method [MAPLE]
[MATHCAD]
[MATHEMATICA]
[MATLAB]
Convergence [MAPLE]
[MATHCAD]
[MATHEMATICA]
[MATLAB]
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Gauss-Quadrature Rule
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Method
[MAPLE]
[MATHCAD]
[MATHEMATICA]
[MATLAB]
Convergence
[MAPLE]
[MATHCAD]
[MATHEMATICA]
[MATLAB] |
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Integrating Discrete Functions |
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Integrating discrete functions [MAPLE] [MATHCAD] [MATHEMATICA] [MATLAB] |
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ORDINARY DIFFERENTIAL EQUATIONS |
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Euler's Method |
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Method
[MAPLE]
[MATHCAD]
[MATHEMATICA]
[MATLAB]
Convergence
[MAPLE]
[MATHCAD]
[MATHEMATICA]
[MATLAB] |
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Runge-Kutta 2nd order Method |
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Method [MAPLE]
[MATHCAD]
[MATHEMATICA]
[MATLAB]
Convergence [MAPLE]
[MATHCAD]
[MATHEMATICA]
[MATLAB]
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Runge-Kutta 4th order Method |
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Method [MAPLE]
[MATHCAD]
[MATHEMATICA]
[MATLAB]
Convergence [MAPLE]
[MATHCAD]
[MATHEMATICA]
[MATLAB]
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Shooting Method
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Method
[MAPLE]
[MATHCAD]
[MATHEMATICA]
[MATLAB] |
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Finite Difference Method |
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Method [MAPLE] [MATHCAD] [MATHEMATICA] [MATLAB] |
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OPTIMIZATION |
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Golden Section Search Method |
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Method
[MAPLE]
[MATHEMATICA]
[MATLAB] |
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Newton's Method
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Method [MAPLE]
[MATHEMATICA]
[MATLAB]
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Multidimensional Direct Search Method
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Method
[MAPLE]
[MATHEMATICA]
[MATLAB]
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Multidimensional Gradient Method
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Method
[MAPLE]
[MATHEMATICA]
[MATLAB] |
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PARTIAL DIFFERENTIAL EQUATIONS |
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Parabolic Partial Differential
Equations |
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Explicit Method
[MATLAB]
[MAPLE]
[MATHEMATICA]
[MATHCAD]
Implicit Method Parabolic PDEs
[MATLAB]
[MAPLE]
[MATHEMATICA]
[MATHCAD]
Crank Nicolson Method Parabolic PDEs
[MATLAB]
[MAPLE]
[MATHEMATICA]
[MATHCAD] |
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Elliptic Partial Differential
Equations |
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Direct Method
[MATLAB]
[MAPLE]
[MATHEMATICA]
[MATHCAD]
Gauss-Seidel Method
[MATLAB]
[MAPLE]
[MATHEMATICA]
[MATHCAD]
Lieberman Method
[MATLAB]
[MAPLE]
[MATHEMATICA]
[MATHCAD]
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fast
fourier transforms |
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Continuous Fourier Series
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Method
[MATLAB]
[MATHCAD]
[MATHEMATICA] |
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Discrete Fourier Transform
|
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Method
[ [MATLAB]
[MATHCAD]
[MATHEMATICA]
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Fast Fourier Transform |
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Method
[MATLAB]
[MATHCAD]
[MATHEMATICA]
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