Numerical Methods, Algorithms and Tools in C - Waldemar Dos Passos

Résumé :
Along with providing the C# source code online, this book presents practical, ready-to-use mathematical routines employing the C# programming language from Microsoft. It shows how to write mathematically intense object-oriented computer programs. It covers a spectrum of computational tools, including sorting algorithms and optimization methods.

Sommaire:
Introduction C# and the .NET Framework Installing C# and the .NET Framework Overview of Object-Oriented Programming (OOP) Your First C# Program Overview of the IDE Debugger Overview of the C# Language The .NET Framework Math Class Library Introduction A .NET Framework Math Class-Fields A .NET Framework Math Class-Methods Vectors and Matrices Introduction The C# Vector Library The C# Matrix Library Complex Numbers Introduction Fundamental Concepts Complex Number Arithmetic Elementary Functions of a Complex Number A Complex Number Library in C# Complex Number Vectors Complex Number Matrices Generic vs. Non-Generic Coding Sorting and Searching Algorithms Introduction Sorting Algorithms Comparison Sorts Count Sort Radix Sort Search Algorithms Bits and Bytes Introduction Numeric Systems Bit Manipulation and Bitwise Operators Assorted Bits and Bytes Interpolation Introduction Linear Interpolation Bilinear Interpolation Polynomial Interpolation Cubic Spline Interpolation Linear Equations Introduction Gaussian Elimination Gauss-Jordan Elimination LU Decomposition Iteration Methods Eigenvalues and Jacobi's Algorithm Non-Linear Equations Introduction Linear Incremental Method Bisection Method The Secant Method False Positioning Method Fixed Point Iteration Newton-Raphson Method Random Numbers Introduction The C# Built-In Random Number Generator Other Random Number Generators True Random Number Generators Probability Distribution Functions Histograms Discrete Distributions Continuous Distributions Shuffling Algorithms Numerical Differentiation Introduction Finite Difference Formulas Richardson Extrapolation Derivatives by Polynomial Interpolation Numerical Integration Introduction Newton-Cotes Formulas Romberg Integration Gaussian Quadrature Methods Monte Carlo Methods Convolution Integrals Statistical Functions Introduction Some Useful Tools Basic Statistical Functions Special Functions Introduction Factorials Combinations and Permutations Gamma Function Beta Function Error Function Sine and Cosine Integral Functions Laguerre Polynomials Hermite Polynomials Chebyshev Polynomials Legendre Polynomials Bessel Functions Curve Fitting Methods Introduction Least Squares Fit Weighted Least Squares Fit Linear Regression The x2 Test for Goodness of Fit Ordinary Differential Equations Introduction Euler Method Runge-Kutta Methods Coupled Differential Equations Partial Differential Equations Introduction The Finite Difference Method Parabolic Partial Differential Equations Hyperbolic Partial Differential Equations Elliptic Partial Differential Equations Optimization Methods Introduction Gradient Descent Method Linear Programming Simulated Annealing Method Genetic Algorithms References Index