Numerical integration of gridded values
- The basics
- Newton-Cotes techniques
- Rectangular rule (also called the mid-point rule)
- 1) Trapezoid rule. 2) Summary of Trapezoid rule.
- 1) Simpson's rule - note its only valid for even number of intervals (odd number of points)! 2) Summary of 1/3 Simpson's rule. 3) Summary of 3/8 Simpson's rule.
- How to use Simpson's rule for odd number of intervals - combine 1/3 and 3/8 Simpson's rules!
- Introduction
- 1) Richards extrapolation. 2) Summary of Richard's extrapolation. 3) Definition of Richard's extrapolation.
- 1) Romberg integration. 2) Summary of Romberg integration. 3) Good explanation of Romberg integration. 4) This is an example of sequence (series) acceleration.
- Gaussian quadrature
- Improper integrals
- Advanced material - adaptive integration. Example with MPI FORTRAN code.
- Random numbers
- Typical pseudo-random number generator equation - Linear congruential generator. What is a modulus operator? How to compute the modulus.
- A popular pseudo-random number generator -- the Mersenne Twister. The recurrence equation is complicated, but has a VERY LONG period.
- Random number generation in Excel. Summary of Excel function RAND
- Tests for true randomness: 1) DIEHARD (like the movie). 2) NIST Test suite.
- Online random number generator
- Monte Carlo simulations
- The classic dice example
- Example: Collision-coalescnce process
- Example: Light scattering
- Example: Tornado risk assessment
- Random walk. Spreadsheet example.
- Adding "noise" to a dataset. Spreadsheet example of a line with "noise" added.
- Create a randomized list. Create a random normal distrbution. Spreadsheet examples.
- DIEHARDER: contains both DIEHARD and NIST Test Suite
- R routine version of DIEHARDER
- Mersenne twister, FORTRAN routine
- Linear Congruent Method, FORTRAN routine
- Random number generation, Matlab
- Random number generator, Mathematica
- Random walk, FORTRAN routine
- Matlab trapezoid rule function. Matlab routine.
- Matlab Simpson rule function. Matlab routine.
- Matlab Romberg function. Matlab routine.
- Matlab built-in functions for integration.
- Mathematica functions.
- R routine for integration.
- FORTRAN trapezoid rule subroutine. Driver program.
- FORTRAN Simpson rule subroutine .
- FORTRAN adaptive integration. Driver program.
- FORTRAN Monte Carlo integration. Driver program.