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
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.
The following modules illustrate the structure and behavior of finite-precision, floating-point number systems.
The following modules illustrate properties of systems of linear equations and demonstrate the behavior of algorithms for solving them.
Linear Least Squares
The following modules illustrate properties of linear least squares problems and demonstrate the behavior of algorithms for solving them.
The following modules illustrate properties of eigenvalues and eigenvectors of matrices, and demonstrate the behavior of algorithms for computing them.
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
The following modules demonstrate algorithms for solving optimization problems.
Nonlinear Least Squares
The following modules illustrate various types of basis functions for interpolation, as well as the resulting interpolants.
Numerical Integration and Differentiation
The following modules illustrate numerical integration and differentiation.
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
- Taylor Series
- BDF Methods
- Stiff ODEs
- Error Estimation
Boundary Value Problems
Partial Differential Equations
The following modules illustrate numerical methods for solving partial differential equations.
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
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