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]

Optimization

Golden Section Search Method

Method [MATHEMATICA]

Newton’s Method

Method [MATHEMATICA]

Multidimensional Direct Search Method

Method [MATHEMATICA]

Multidimensional Gradient Method

Method [MATHEMATICA]

Partial Differential Equations

Parabolic Partial Differential Equations

Explicit Method [MATHEMATICA] Implicit Method Parabolic PDEs [MATHEMATICA] Crank Nicolson Method Parabolic PDEs [MATHEMATICA]

Elliptic Partial Differential Equations

Direct Method [MATHEMATICA] Gauss-Seidel Method [MATHEMATICA] Lieberman Method [MATHEMATICA]

Fast Fourier Transforms

Continuous Fourier Series

Method [MATHEMATICA]

Discrete Fourier Transform

Method [MATHEMATICA]

Fast Fourier Transform

Method [MATHEMATICA]