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 Interpolationarycentric
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