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