Table of Contents

Introduction
   Overview
   What This Book Includes
   Is This Book for You
   What Do You Need to Use This Book
   How The Book Is Organized
   Using Code Examples
   Customer Support


Chapter 1: Overview of C# Programming
   Your First C# program

   Data Types

      Value-Type Variables
      Reference-Type Variables
   Math Operators and Functions

      Math Operators
      Logical Operators
      Built-In Math Functions
      Math Operation Example
   Selection Statements

      If Statement
      Switch Statement
   Loop Statements

      For Loop
      Foreach Loop
      While Loop
      Do Loop
   Methods

      Creating a Method
      Calling a Method
   Properties

      Field Members
      Exposing a Property
      Using Properties
      Read-Only and Write-Only Properties
      Auto-Implemented properties

Chapter 2: Complex Numbers and Functions
   Complex Numbers and Operators

      Complex Numbers in C#
         Common Public Properties
         Test Public Properties
         Common Public Methods
         Equality and Hashing
      Complex Operators
         Unary Operator
         Addition Operator
         Subtraction Operator
         Multiplication Operator
         Division Operator
         Testing Math Operator
   Complex Functions

      Basic Math Functions
         Square Root Function
         Exponential Function
         Pow Function
         Logarithm Function
         Testing Math Functions
      Trigonometric Functions
         Sine Function
         Cosine Function
         Tangent Function
         Testing Trigonometrix Functions
      Inverse Trigonometric Functions
         Inverse Sine Function
         Inverse Cosine Function
         Inverse Tangent Function
         Testing Inverse Trigonometrix Functions
      Hyperbolic Trigonometric Functions
         Hyperbolic Sine Function
         Hyperbolic Cosine Function
         Hyperbolic Tangent Function
         Testing Hyperbolic Trigonometrix Functions
      Inverse Hyperbolic Trigonometric Functions
         Inverse Hyperbolic Sine Function
         Inverse Hyperbolic Cosine Function
         Inverse Hyperbolic Tangent Function
         Testing Hyperbolic Inverse Trigonometrix Functions

Chapter 3: Vectors and Matrices
   Real Vector Structure

      basic Definitions
      Mathematical Operators
      Vector Multiplications
         Scalar or Dot product
         Cross Product
         Triple Scalar Product
         Triple Vector Product
   Complex Vector Class

      Implementation
      Testing the VectorC Class
   Real Matrix Class

      basic Definitions
      Matrix and Vector Multiplications
         Vector from Matrix
         Swap, Transpose, and Trace
         Transformations
         Matrix Multiplication
      Mathematical Operators
      Determinant
      Inverse
      Testing the Real Matrix
   Complex matrix Class

      Implementation
      Testing the Complex Matrix

Chapter 4: Linear Algebraic Equations
   Gauss-Jordan Elimination

      Algorithms
      Implementation
      Testing Gauss-Jordan Elimination
   LU Decomposition

      Algorithms
      Implementation
      Matrix Inverse
      Testing LU Decomposition
   Iteration Methods

      Gauss-Jacobi Iteration
      Gauss-Seidel Iteration
      Testing Iteration Methods

Chapter 5: Nonlinear Equations
   Incremental Method

      Implementation
      Testing the Incremental Method
   Fixed Point Method

      Implementation
      Testing the Fixed Method
   Bisection Method

      Implementation
      Testing the Bisection Method
   False Position Method

      Implementation
      Testing the False Position Method
   Newton-Raphson Method

      Implementation
      Testing the Newton-Raphson Method
   Secant Method

      Implementation
      Testing the Secant Method
   Newton Multiroot Method

      Implementation
      Testing the Newton Multiroot Method
   Birge-Vieta Method

      Implementation
      Testing the Birge-Vieta Method
   System of Equations

      Algorithm
      Implementation
      Testing the NewtonMultiEquations Method

Chapter 6: Special Functions
   Gamma and Beta Functions

      Gamma Function
         Implementation
         testing the Gamma Method
      Beta Function
         Implementation
         testing the Beta Method
   Error Function

      Implementation
      Testing the Erf and Erfc Methods
   Sine and Cosine Integral Function

      Implementation
      Testing the Si and Ci Methods
   Laguerre Function

      Implementation
      Testing the Laguerre Method
   Hermite Polynomials

      Implementation
      Testing the Hermite Method
   Chebyshev Polynomials

      Implementation
      Testing the Chebyshev Method
   Legendre Polynomials

      Implementation
      Testing the Legendre Method
   Bessel Functions

      Implementation
      Testing the Bessel Method

Chapter 7: Random Numbers and Distribution Functions
   Built-in Random Number Generators

   Normal Distribution

      Probability Density Function
      Normal Random Number Generator
      Testing the Normal Distribution
   Exponential Distribution

      Probability Density Function
      Exponential Random Number Generator
      Testing the Exponential Distribution
   Chi and Chi-Square Distributions

      Probability Density Function
      Chi and Chi-Square Random Number Generators
      Testing the Chi and Chi-Square Distributions
   Cauchy Distribution

      Probability Density Function
      Cauchy Random Number Generator
      Testing the Cauchy Distribution
   Student T Distribution

      Probability Density Function
      Student T Random Number Generator
      Testing the Student T Distribution
   Gamma Distribution

      Probability Density Function
      Gamma Random Number Generator
      Testing the Gamma Distribution
   Beta Distribution

      Probability Density Function
      Beta Random Number Generator
      Testing the Beta Distribution
   Poisson Distribution

      Probability Density Function
      Poisson Random Number Generator
      Testing the Poisson Distribution
   Binomial Distribution

      Probability Density Function
      Binomial Random Number Generator
      Testing the Binomial Distribution

Chapter 8: Interpolation
   Linear Interpolation

      Algorithm
      Implementation
      Testing the Linear Interpolation
   Lagrange Interpolation

      Algorithm
      Implementation
      Testing the Lagrange Interpolation
   B Interpolation
arycentric
      Algorithm
      Implementation
      Testing the Barycentric Interpolation
   Newton Divided Difference Interpolation

      Algorithm
      Implementation
      Testing the Newton Divided Difference Interpolation
   Cubic Spline Interpolation

      Algorithm
      Implementation
      Testing the Spline Interpolation
   Bilinear Interpolation

      Algorithm
      Implementation
      Testing the Bilinear Interpolation

Chapter 9: Curve Fitting
   Least Squares Fit

   Straight Line Fit

      Implementation
      Testing the Straight Line Fit
   Linear Regression

      Implementation
      Testing the Linear Regression
   Polynomial Fit

      Implementation
      Testing the Polynomial Fit
   Weighted Linear Regression

      Implementation
      Exponential Function Fit
   Simple Moving Average

      Implementation
      Testing the Simple Moving Average
   Weighted Moving Average

      Implementation
      Testing the Weighted Moving Average
   Exponential Moving Average

      Implementation
      Testing the Exponential Moving Average

Chapter 10: Optimization
   Bisection Method

      Implementation
      Testing the Bisection Method
   Golden Search Method

      Implementation
      Testing the Golden Search Method
   Newton Method

      Implementation
      Testing the Newton Method
   Brent Method

      Implementation
      Testing the Brent Method
   Newton Method for Multi-variable Functions

      Implementation
      Testing the MultiNewton Method
   Simplex Method

      Implementation
      Testing the Simplex Method
   Simulated Annealing Method

      Implementation
      Testing the Simulated Annealing Method
   Differential Evolution

      Algorithm
      Implementation
      Testing Differential Evolution

Chapter 11: Numerical Differentiation
   Finite Difference Formulas

   Forward Difference Method

      Implementation
      Testing the Forworward Difference Method
   Backward Difference Method

      Implementation
      Testing the Backworward Difference Method
   Central Difference Method

      Implementation
      Testing the Central Difference Method
   Extended Central Difference Method

      Implementation
      Testing the Extended central Difference Method
   Richardson Extrapolation

      Implementation
      Testing the Richardson Extrapolation
   Derivatives by Interpolation

      Implementation
      Testing the Derivatives by Interpolation

Chapter 12: Numerical Integration
   Newtown-Cotes Formulas

      Trapezoidal Rule
         Implementation
         Testing the Trapezoidal Method
      Simpson's Rule
         Implementation
         Testing the Simpson Method
      Higher Order Rules
   Romberg Integration

      Implementation
      Testing the Romberg Method
   Gaussian Integration

      Gauss-Legendre Integration
         Implementation
         Testing Gauss-Legendre Integration
      Gauss-Laguerre Integration
         Implementation
         Testing Gauss-Laguerre Integration
      Gauss-Hermite Integration
         Implementation
         Testing Gauss-hermite Integration
      Gauss-Chebyshev Integration
         Implementation
         Testing Gauss-Chebyshev Integration

Chapter 13: Ordinary Differential Equations
   Euler Method

      Implementation
      testing Euler's Method
   Second-Order Runge-Kutta Method

      Implementation
      Testing the Second-Order Runge-Kutta Method
   Fourth-Order Runge-Kutta Method

      Implementation
      Testing the Fourth-Order Runge-Kutta Method
   Adaptive Runge-Kutta Method

      Implementation
      Testing the Adaptive Runge-Kutta Method
   Runge-Kutta Method for Systems

      Implementation
      Testing the MultiRungeKutta4 Method
   Adaptive Runge-Kutta Method for Systems

      Implementation
      Testing the MultiRungeKuttaFehlberg Method

Chapter 14: Boundary Value Problems
   Shooting Method

      Implementation
      Testing the Shooting2 Method
   Finite Difference for Linear Equation

      Algorithm
      Implementation
      Testing FiniteDifferenceLinear2 Method
   Finite Difference for Nonlinear Equation

      Algorithm
      Implementation
      Testing FiniteDifferenceNonlinear2 Method
   Finite Difference for Higher-Order Equation

      Algorithm
      Implementation
      Testing FiniteDifferenceLinear4 Method

Chapter 15: Eigenvalue Problems
   Jacobi Method

      Algorithm
      Implementation
      Testing the Jacobi Method
   Power Interation

      Algorithm
      Implementation
      Testing the Power Method
   Inverse Interation

      Algorithm
      Implementation
      Testing the Inverse Method
   Rayleigh Method

      Algorithm
      Implementation
      Testing the Rayleigh Method
   Rayleigh-Quotient Method

      Algorithm
      Implementation
      Testing the Rayleigh-Quotient Method
   Matrix Tridiagonalization

      Algorithm
      Implementation
      Testing the Tridiagonalize Method
   Eigenvalues of Symmetric Tridiagonal Matrices

      LU Decomposition of Tridiagonal Matrices
      Implementation
      Examples

Index