WORKSHEETS IN MATHCAD |
INTRODUCTION TO SCIENTIFIC COMPUTING |
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Measuring Errors |
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True Error
[MATHCAD]
Approximate Error
[MATHCAD]
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Binary
Representation |
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Decimal to binary representation
[MATHCAD]
Binary to decimal representation
[MATHCAD]
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Measuring Errors |
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Decimal to floating point
representation
[MATHCAD]
Binary to floating point
representation
[MATHCAD]
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Propagation of Errors |
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Propagation of Errors
[MATHCAD]
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Differentiation |
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Continuous Functions |
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Forward Divided
Difference
[MATHCAD]
Backward
Divided Difference
[MATHCAD]
Central Divided
Difference
[MATHCAD]
Continuous
functions Second Order Derivative
[MATHCAD]
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Discrete
Data |
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Discrete
functions
[MATHCAD] |
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Nonlinear Equations |
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Bisection Method |
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Method
[MATHCAD]
Convergence
[MATHCAD]
Pitfall: Slow convergence of
bisection method simulation
[MATHCAD]
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Newton-Raphson Method |
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Method
[MATHCAD]
Convergence
[MATHCAD]
Pitfall: Division by zero
[MATHCAD]
Pitfall: Slow Convergence at
Inflection Points
[MATHCAD]
Pitfall: Root jumps over
several roots
[MATHCAD]
Pitfall: Roots oscillates
around local maxima and minima
[MATHCAD]
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Secant Method |
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Simulation of secant method
[MATHCAD]
Convergence Simulation of
secant method [MATHCAD]
Pitfall: Division by zero in
secant method simulation
[MATHCAD]
Pitfall: Root jumps over
several roots in secant method
[MATHCAD]
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SIMULTANEOUS LINEAR EQUATIONS |
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Gaussian Elimination |
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Method
[MATHCAD]
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Gauss-Seidel Method |
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Method
[MATHCAD]
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Convergence
[MATHCAD] |
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LU
Decomposition |
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Method
[MATHCAD] |
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Interpolation |
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Direct Method |
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Method [MATHCAD]
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Newton's Divided Difference Method |
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Method
[MATHCAD]
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Lagrange
Method |
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Method
[MATHCAD] |
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Spline
Method |
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Method
[MATHCAD] |
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REGRESSION |
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Linear Regression |
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Method [MATHCAD]
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Nonlinear Regression |
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Without Data Linearization
[MATHCAD]
With Data Linearization
[MATHCAD]
Polynomial Regression
[MATHCAD]
Comparing with and without Data
Linearization
[MATHCAD]
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Adequacy of a Regression Model |
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Adequacy [MATHCAD]
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Integration |
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Trapezoidal Rule |
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Method [MATHCAD]
Convergence
[MATHCAD]
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Simpson's 1/3rd Rule |
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Method
[MATHCAD]
Convergence
[MATHCAD]
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Romberg Rule |
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Method
[MATHCAD]
Convergence
[MATHCAD]
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Gauss-Quadrature Rule
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Method
[MATHCAD]
Convergence
[MATHCAD] |
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Integrating Discrete Functions |
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Integrating discrete functions [MATHCAD] |
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ORDINARY DIFFERENTIAL EQUATIONS |
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Euler's Method |
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Method
[MATHCAD]
Convergence
[MATHCAD] |
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Runge-Kutta 2nd order Method |
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Method
[MATHCAD]
Convergence
[MATHCAD]
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Runge-Kutta 4th order Method |
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Method
[MATHCAD]
Convergence
[MATHCAD]
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Shooting Method
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Method
[MATHCAD] |
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Finite Difference Method |
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Method [MATHCAD] |