Worksheets in Mathcad

Introduction to Scientific Computing

Measuring Errors

True Error  [MATHCAD] Approximate Error  [MATHCAD]

Binary Representation

Decimal to binary representation [MATHCAD] Binary to decimal representation [MATHCAD]

Measuring Errors

Decimal to floating point representation [MATHCAD] Binary to floating point representation [MATHCAD]

Propagation of Errors

Propagation of Errors [MATHCAD]

Differentiation

Continuous Functions

Forward Divided Difference [MATHCAD] Backward Divided Difference [MATHCAD] Central Divided Difference [MATHCAD] Continuous functions Second Order Derivative [MATHCAD]

Discrete Data

Discrete functions [MATHCAD]

Nonlinear Equations

Bisection Method

Method [MATHCAD] Convergence [MATHCAD] Pitfall: Slow convergence of bisection method simulation [MATHCAD]

Newton-Raphson Method

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]

Secant Method

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]

Simultaneous Linear Equations

Gaussian Elimination

Method [MATHCAD]

Gauss-Seidel Method

Method [MATHCAD] Convergence [MATHCAD]

LU Decomposition

Method [MATHCAD]

Interpolation

Direct Method

Method [MATHCAD]

Newton’s Divided Difference Method

Method [MATHCAD]

Lagrange Method

Method [MATHCAD]

Spline Method

Method [MATHCAD]

Regression

Linear Regression

Method [MATHCAD]

Nonlinear Regression

Without Data Linearization [MATHCAD] With Data Linearization [MATHCAD] Polynomial Regression [MATHCAD] Comparing with and without Data Linearization [MATHCAD]

Adequacy of a Regression Model

Adequacy [MATHCAD]

Integration

Trapezoidal Rule

Method [MATHCAD] Convergence [MATHCAD]

Simpson’s 1/3rd Rule

Method [MATHCAD] Convergence [MATHCAD]

Romberg Rule

Method [MATHCAD] Convergence [MATHCAD]

Gauss-Quadrature Rule

Method [MATHCAD] Convergence [MATHCAD]

Integrating Discrete Functions

Integrating discrete functions [MATHCAD]

Ordinary Differential Equations

Euler’s Method

Method [MATHCAD] Convergence [MATHCAD]

Runge-Kutta 2nd order Method

Method [MATHCAD] Convergence [MATHCAD]

Runge-Kutta 4th order Method

Method [MATHCAD] Convergence [MATHCAD]

Shooting Method

Method [MATHCAD]

Finite Difference Method

Method [MATHCAD]

Partial Differential Equations

Parabolic Partial Differential Equations

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

Elliptic Partial Differential Equations

Gauss-Seidel Method [MATHCAD] Lieberman Method [MATHCAD]

Fast Fourier Transforms

Continuous Fourier Series

Method [MATHCAD]

Discrete Fourier Transform

Method [MATHCAD]

Fast Fourier Transform

Method  [MATHCAD]