Mathematics in C#
General
Complex Numbers
Illustrates how to work with complex numbers using the DoubleComplex structure.
Elementary Functions
Illustrates how to use additional elementary functions.
BigNumbers
Illustrates the basic use of the arbitrary precision classes: BigInteger, BigRational, BigFloat.
Prime Numbers
Illustrates working with prime numbers and the IntegerMath class in the Extreme.Mathematics namespace.
FFT/Fourier Transforms
Illustrates how to compute the forward and inverse Fourier transform of a real or complex signal using classes in the Extreme.Mathematics.SignalProcessing namespace.
Generic Algorithms
Illustrates how to write algorithms that are generic over the numerical type of the arguments.
Calculus
Basic Integration
Illustrates the basic numerical integration classes.
Advanced Integration
Illustrates more advanced numerical integration using the AdaptiveIntegrator class.
Higher Dimensional Numerical Integration
Illustrates numerical integration of functions in higher dimensions using classes in the Extreme.Mathematics.Calculus namespace.
Numerical Differentiation
Illustrates how to approximate the derivative of a function.
Differential Equations
Illustrates integrating systems of ordinary differential equations (ODE's).
Curves
Basic Polynomials
Illustrates the basic use of the Polynomial class .
Advanced Polynomials
Illustrates more advanced uses of the Polynomial class, including real and complex root finding, calculating least squares polynomials and polynomial arithmetic.
Chebyshev Series
Illustrates the basic use of the ChebyshevSeries class .
Curve Fitting and Interpolation
Linear Curve Fitting
Illustrates how to fit linear combinations of curves to data using the LinearCurveFitter class and other classes in the Extreme.Mathematics.Curves namespace.
Nonlinear Curve Fitting
Illustrates nonlinear least squares curve fitting of predefined and user-defined curves using the NonlinearCurveFitter class.
Piecewise Curves
Illustrates working with piecewise constant and piecewise linear curves using classes from the Extreme.Mathematics.Curves namespace.
Cubic Splines
Illustrates using natural and clamped cubic splines for interpolation using classes in the Extreme.Mathematics.LinearAlgebra namespace.
Solving Equations
Newton-Raphson Equation Solver
Illustrates the use of the NewtonRaphsonSolver class for solving equations in one variable and related functions for numerical differentiation.
Root Bracketing Solvers
Illustrates the use of the root bracketing solvers for solving equations in one variable.
Nonlinear Systems
Illustrates the use of the NewtonRaphsonSystemSolver and DoglegSystemSolver classes for solving systems of nonlinear equations.
Optimization
Optimization In One Dimension
Illustrates the use of the Brent and Golden Section optimizer classes in the Extreme.Mathematics.Optimization namespace for one-dimensional optimization.
Optimization In Multiple Dimensions
Illustrates the use of the multi-dimensional optimizer classes in the Extreme.Mathematics.Optimization namespace for optimization in multiple dimensions.
Linear Programming
Illustrates solving linear programming (LP) problems using classes in the Extreme.Mathematics.Optimization.LinearProgramming namespace.
Mixed Integer Programming
Illustrates how to solve mixed integer programming by solving Sudoku puzzles using the linear programming solver.
Quadratic Programming
Illustrates how to solve optimization problems a quadratic objective function and linear constraints using classes in the Extreme.Mathematics.Optimization namespace.
Nonlinear Programming
Illustrates solving nonlinear programs (optimization problems with linear or nonlinear constraints) using the NonlinearProgram and related classes.
Random numbers and Quasi-Random Sequences
Random Number Generators
Illustrates how to use specialized random number generator classes in the Extreme.Statistics.Random namespace.
Non-Uniform Random Numbers
Illustrates how to generate random numbers from a non-uniform distribution.
Quasi-Random Sequences
Illustrates how to generate quasi-random sequences like Fauré and Sobol sequences using classes in the Extreme.Statistics.Random namespace.