## About the Modules

The interactive educational modules on this site assist in learning basic concepts and algorithms of scientific computing.

Each module is a Java applet that is accessible through a web browser.

For each applet, you can select problem data and algorithm choices interactively and then receive immediate feedback on the results, both numerically and graphically.

** << Choose from the categories on
the left.**

**Developers:** Michael Heath, Evan VanderZee, Jessica
Schoen, Jeffrey Naisbitt, Sukolsak Sakshuwong, Jing Zou, and Nicholas Exner

**Sponsor:** Computational Science and
Engineering, University of Illinois at Urbana-Champaign

## About the Book

Although the modules can be used alone or in conjunction with any
textbook, some of the specific examples are based on the book
*Scientific Computing, An Introductory Survey, 2nd edition,*
by Michael T. Heath, published by McGraw-Hill, New York, 2002.

## Floating-Point Arithmetic

## Floating-Point Arithmetic

The following modules illustrate the structure and behavior of finite-precision, floating-point number systems.

## Linear Equations

## Systems of Linear Equations

The following modules illustrate properties of systems of linear equations and demonstrate the behavior of algorithms for solving them.

## Linear Least Squares

## Linear Least Squares

The following modules illustrate properties of linear least squares problems and demonstrate the behavior of algorithms for solving them.

## Eigenvalue Problems

## Eigenvalue Problems

The following modules illustrate properties of eigenvalues and eigenvectors of matrices, and demonstrate the behavior of algorithms for computing them.

## Nonlinear Equations

## Nonlinear Equations

The following modules illustrate properties of nonlinear equations and demonstrate the behavior of algorithms for solving them.

### Nonlinear Equations in One Dimension

- Interval Bisection
- Fixed-Point Iteration
- Newton's Method
- Secant Method
- Inverse Interpolation
- Linear Fractional Interpolation

### Systems of Nonlinear Equations in Two Dimensions

## Optimization

## Optimization

The following modules demonstrate algorithms for solving optimization problems.

### One-Dimensional Optimization

### Unconstrained Optimization

### Constrained Optimization

### Nonlinear Least Squares

## Interpolation

## Interpolation

The following modules illustrate various types of basis functions for interpolation, as well as the resulting interpolants.

## Numerical Integration and Differentiation

## Numerical Integration and Differentiation

The following modules illustrate numerical integration and differentiation.

## Ordinary Differential Equations

## Ordinary Differential Equations

The following modules illustrate numerical methods for solving initial value problems and boundary value problems for ordinary differential equations.

### Initial Value Problems

- Euler's Method
- Backward Euler
- Trapezoid Method
- Picard Iteration
- Runge-Kutta
- Taylor Series
- Extrapolation
- Collocation
- Predictor-Corrector
- Adams-Bashforth
- BDF Methods
- Stiff ODEs
- Error Estimation
- Stability

### Boundary Value Problems

### Applications

## Partial Differential Equations

## Partial Differential Equations

The following modules illustrate numerical methods for solving partial differential equations.

## Fast Fourier Transform

## Fast Fourier Transform

The following modules illustrate the FFT algorithm for computing the discrete Fourier transform and demonstrate applications of the DFT.

## Random Numbers and Simulation

## Random Numbers and Simulation

The following modules illustrate random number generators and their applications to stochastic simulation.

- Linear Congruential Generators
- Buffon Needle Problem
- Quasi-Random Sequences
- Random Walk
- Monte Carlo Integration in 1-D
- Monte Carlo Integration in 2-D