WORKSHEETS IN MATHEMATICA

INTRODUCTION TO SCIENTIFIC COMPUTING

Measuring Errors

True Error    [MATHEMATICA] 

Approximate Error    [MATHEMATICA]

Binary Representation

Decimal to binary representation   [MATHEMATICA] 

Binary to decimal representation   [MATHEMATICA] 

Measuring Errors

Decimal to floating point representation   [MATHEMATICA] 

Binary to floating point representation   [MATHEMATICA] 

Propagation of Errors

Propagation of Errors    [MATHEMATICA] 

Differentiation

Continuous Functions

Forward Divided Difference        [MATHEMATICA] 

Backward Divided Difference       [MATHEMATICA] 

Central Divided Difference      [MATHEMATICA]  

Continuous functions Second Order Derivative      [MATHEMATICA] 

Discrete Data

Discrete functions       [MATHEMATICA]

Nonlinear Equations

Bisection Method

Method   [MATHEMATICA]

Convergence   [MATHEMATICA]

Pitfall: Slow convergence of bisection method simulation   [MATHEMATICA]

Newton-Raphson Method

Method   [MATHEMATICA]

Convergence   [MATHEMATICA]

Pitfall: Division by zero   [MATHEMATICA]

Pitfall: Slow Convergence at Inflection Points   [MATHEMATICA]

Pitfall: Root jumps over several roots   [MATHEMATICA]

Pitfall: Roots oscillates around local maxima and minima   [MATHEMATICA]

Secant Method

Simulation of secant method    [MATHEMATICA]

Convergence Simulation of secant method    [MATHEMATICA]

Pitfall: Division by zero in secant method simulation    [MATHEMATICA]

Pitfall: Root jumps over several roots in secant method    [MATHEMATICA]

SIMULTANEOUS LINEAR EQUATIONS

Gaussian Elimination

Method   [MATHEMATICA]

Gauss-Seidel Method

Method     [MATHEMATICA] 

Convergence     [MATHEMATICA] 

LU Decomposition

Method   [MATHEMATICA]

Interpolation

Direct Method

Method   [MATHEMATICA]

Newton's Divided Difference Method

Method     [MATHEMATICA] 

Lagrange Method

Method   [MATHEMATICA]

Spline Method

Method     [MATHEMATICA] 

REGRESSION

Linear Regression

Method   [MATHEMATICA]

Nonlinear Regression

Without Data Linearization     [MATHEMATICA] 

With Data Linearization     [MATHEMATICA] 

Polynomial Regression     [MATHEMATICA] 

Comparing with and without Data Linearization     [MATHEMATICA] 

Adequacy of a Regression Model

Adequacy   [MATHEMATICA]

Integration

Trapezoidal Rule

Method   [MATHEMATICA]

Convergence   [MATHEMATICA]

Simpson's 1/3rd Rule

Method   [MATHEMATICA]

Convergence   [MATHEMATICA]

Romberg Rule

Method   [MATHEMATICA]

Convergence   [MATHEMATICA]

Gauss-Quadrature Rule

Method   [MATHEMATICA]

Convergence   [MATHEMATICA]

Integrating Discrete Functions

Integrating discrete functions   [MATHEMATICA]

ORDINARY DIFFERENTIAL EQUATIONS

Euler's Method

Method   [MATHEMATICA]

Convergence   [MATHEMATICA]

Runge-Kutta 2nd order Method

Method   [MATHEMATICA]

Convergence   [MATHEMATICA]

Runge-Kutta 4th order Method

Method   [MATHEMATICA]

Convergence   [MATHEMATICA]

Shooting Method

Method   [MATHEMATICA]

Finite Difference Method

Method   [MATHEMATICA]