|
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] |
