Mathematics in F#

General

Complex Numbers

Illustrates how to work with complex numbers using the DoubleComplex structure.

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Elementary Functions

Illustrates how to use additional elementary functions.

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BigNumbers

Illustrates the basic use of the arbitrary precision classes: BigInteger, BigRational, BigFloat.

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Prime Numbers

Illustrates working with prime numbers and the IntegerMath class in the Numerics.NET namespace.

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FFT/Fourier Transforms

Illustrates how to compute the forward and inverse Fourier transform of a real or complex signal using classes in the Numerics.NET.SignalProcessing namespace.

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Generic Algorithms

Illustrates how to write algorithms that are generic over the numerical type of the arguments.

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Calculus

Basic Integration

Illustrates the basic numerical integration classes.

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Advanced Integration

Illustrates more advanced numerical integration using the AdaptiveIntegrator class.

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Higher Dimensional Numerical Integration

Illustrates numerical integration of functions in higher dimensions using classes in the Numerics.NET.Calculus namespace.

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Numerical Differentiation

Illustrates how to approximate the derivative of a function.

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Differential Equations

Illustrates integrating systems of ordinary differential equations (ODE's).

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Curves

Basic Polynomials

Illustrates the basic use of the Polynomial class .

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Advanced Polynomials

Illustrates more advanced uses of the Polynomial class, including real and complex root finding, calculating least squares polynomials and polynomial arithmetic.

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Chebyshev Series

Illustrates the basic use of the ChebyshevSeries class .

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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 Numerics.NET.Curves namespace.

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Nonlinear Curve Fitting

Illustrates nonlinear least squares curve fitting of predefined and user-defined curves using the NonlinearCurveFitter class.

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Piecewise Curves

Illustrates working with piecewise constant and piecewise linear curves using classes from the Numerics.NET.Curves namespace.

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Cubic Splines

Illustrates using natural and clamped cubic splines for interpolation using classes in the Numerics.NET.LinearAlgebra namespace.

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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.

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Root Bracketing Solvers

Illustrates the use of the root bracketing solvers for solving equations in one variable.

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Nonlinear Systems

Illustrates the use of the NewtonRaphsonSystemSolver and DoglegSystemSolver classes for solving systems of nonlinear equations.

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Optimization

Optimization In One Dimension

Illustrates the use of the Brent and Golden Section optimizer classes in the Numerics.NET.Optimization namespace for one-dimensional optimization.

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Optimization In Multiple Dimensions

Illustrates the use of the multi-dimensional optimizer classes in the Numerics.NET.Optimization namespace for optimization in multiple dimensions.

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Linear Programming

Illustrates solving linear programming (LP) problems using classes in the Numerics.NET.Optimization.LinearProgramming namespace.

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Mixed Integer Programming

Illustrates how to solve mixed integer programming by solving Sudoku puzzles using the linear programming solver.

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Quadratic Programming

Illustrates how to solve optimization problems a quadratic objective function and linear constraints using classes in the Numerics.NET.Optimization namespace.

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Nonlinear Programming

Illustrates solving nonlinear programs (optimization problems with linear or nonlinear constraints) using the NonlinearProgram and related classes.

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Random numbers and Quasi-Random Sequences

Random Number Generators

Illustrates how to use specialized random number generator classes in the Numerics.NET.Statistics.Random namespace.

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Non-Uniform Random Numbers

Illustrates how to generate random numbers from a non-uniform distribution.

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Quasi-Random Sequences

Illustrates how to generate quasi-random sequences like Fauré and Sobol sequences using classes in the Numerics.NET.Statistics.Random namespace.

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