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Introduction | |

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C# and the.NET Framework | |

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Installing C# and the.NET Framework | |

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Overview of Object-Oriented Programming (OOP) | |

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Your First C# Program | |

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Overview of the IDE Debugger | |

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Overview of the C# Language | |

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Data Types | |

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Value Types | |

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Reference Types | |

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Type-Parameter Types | |

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Pointer Types | |

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Variable Declaration | |

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Constant Declaration | |

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Nullable Types | |

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Scope | |

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Characters | |

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Strings | |

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Formatting of Output Data | |

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Type Conversion | |

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Reading Keyboard Input Data | |

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Basic Expressions and Operators | |

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Program Flow Mechanisms | |

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Jump Statements | |

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Arrays | |

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Enumerations | |

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Structures | |

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Exceptions | |

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Classes | |

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Constructors and Destructors | |

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Methods | |

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Indexers | |

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Overloading Methods, Constructors and Operators | |

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Delegates | |

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Events | |

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Collections | |

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File Input/Output | |

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Output Reliability, Accuracy and Precision | |

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The.NET Framework Math Class Library | |

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Introduction | |

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The.NET Framework Math Class - Fields | |

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The Math. pi and Math. e Fields | |

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The.NET Framework Math Class - Methods | |

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The Minimum and Maximum Methods | |

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The Power, Exponential and Logarithmic Methods | |

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Special Multiplication, Division and Remainder Methods | |

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The Absolute Value Method | |

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The Sign Method | |

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Angular Units of Measurement | |

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The Trigonometric Functions | |

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The Inverse Trigonometric Functions | |

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The Hyperbolic Functions | |

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The Inverse Hyperbolic Functions | |

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Rounding Off Numeric Data | |

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The Ceiling Method | |

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The Floor Method | |

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The Truncation Method | |

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The Round Method | |

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Vectors and Matrices | |

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Introduction | |

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A Real Number Vector Library in C# | |

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A Real Number Matrix Library in C# | |

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Complex Numbers | |

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Introduction | |

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Fundamental Concepts | |

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Complex Number Arithmetic | |

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Elementary Functions of a Complex Number | |

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Exponentials | |

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Logarithms | |

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Powers and Roots | |

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Trigonometric and Hyperbolic Functions | |

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Inverse Trigonometric and Hyperbolic Functions | |

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A Complex Number Library in C# | |

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A Complex Number Vector Library in C# | |

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A Complex Number Matrix Library in C# | |

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Generic vs. Non-Generic Coding | |

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Sorting and Searching Algorithms | |

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Introduction | |

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Sorting Algorithms | |

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Comparison Sorts | |

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Bubble Sort | |

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Cocktail Sort | |

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Odd-Even Sort | |

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Comb Sort | |

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Gnome Sort | |

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Quicksort | |

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Insertion Sort | |

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Shell Sort | |

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Selection Sort | |

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Merge Sort | |

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Bucket Sort | |

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Heap Sort | |

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Count Sort | |

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Radix Sort | |

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Search Algorithms | |

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Linear Search | |

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Binary Search | |

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Interpolation Search | |

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Searching for the Maximum and Minimum Values | |

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Searching for the N-th Largest or M-th Smallest Value | |

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Some Useful Utilities | |

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Bits and Bytes | |

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Introduction | |

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Numeric Systems | |

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Bit Manipulation and Bitwise Operators | |

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Assorted Bits and Bytes | |

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Interpolation | |

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Introduction | |

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Linear Interpolation | |

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Bilinear Interpolation | |

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Polynomial Interpolation | |

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Lagrange Interpolation | |

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Barycentric Interpolation | |

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Newton's Divided Differences Interpolation | |

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Cubic Spline Interpolation | |

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Natural Cubic Splines | |

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Clamped Cubic Splines | |

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Linear Equations | |

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Introduction | |

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Gaussian Elimination | |

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Gauss-Jordan Elimination | |

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LU Decomposition | |

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Iteration Methods | |

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Gauss-Jacobi Iteration | |

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Gauss-Seidel Iteration | |

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Eigenvalues and Jacobi's Algorithm | |

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Nonlinear Equations | |

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Introduction | |

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Linear Incremental Method | |

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Bisection Method | |

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The Secant Method | |

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False Positioning Method | |

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Fixed Point Iteration | |

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Newton-Raphson Method | |

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Random Numbers | |

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Introduction | |

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The C# Built-In Random Number Generator | |

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Other Random Number Generators | |

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True Random Number Generators | |

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Random Variate Generation Methods | |

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Histograms | |

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Random Variate Generation | |

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Discrete Distributions | |

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Bernoulli Distribution | |

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Binoulli Distribution | |

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Geometric Distribution | |

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Negative Binomial Distribution | |

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Poisson Distribution | |

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Uniform Distribution (discrete) | |

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Continuous Distributions | |

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Beta Distribution | |

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Beta Prime Distribution | |

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Cauchy Distribution | |

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Chi Distribution | |

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Chi-Square Distribution | |

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Erlang Distribution | |

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Exponential Distribution | |

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Extreme Value Distribution | |

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Gamma Distribution | |

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Laplace Distribution | |

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Logistic Distribution | |

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Lognormal Distribution | |

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Normal Distribution | |

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Pareto Distribution | |

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Rayleigh Distribution | |

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Student-t Distribution | |

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Triangular Distribution | |

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Uniform Distribution (continuous) | |

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Weibull Distribution | |

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Shuffling Algorithms | |

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Adding Random Noise to Data | |

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Removing Random Noise from Data | |

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Numerical Differentiation | |

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Introduction | |

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Finite Difference Formulas | |

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Forward Difference Method | |

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Backward Difference Method | |

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Central Difference Method | |

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Improved Central Difference Method | |

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Richardson Extrapolation | |

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Derivatives by Polynomial Interpolation | |

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Numerical Integration | |

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Introduction | |

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Newton-Cotes Formulas | |

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Rectangle Method | |

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Midpoint Method | |

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Trapezoidal Method | |

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Simpson's Method | |

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Simpson's 1/3 Method | |

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Simpson's 3/8 Method | |

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Romberg Integration | |

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Gaussian Quadrature Methods | |

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Gauss-Legendre Integration | |

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Gauss-Hermite Integration | |

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Gauss-Leguerre Integration | |

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Gauss-Chebyshev Integration | |

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Multiple Integration | |

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Monte Carlo Methods | |

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Monte Carlo Integration | |

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The Metropolis Algorithm | |

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Convolution Integrals | |

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Statistical Functions | |

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Introduction | |

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Some Useful Tools | |

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Basic Statistical Functions | |

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Mean and Weighted Mean | |

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Geometric and Weighted Geometric Mean | |

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Harmonic and Weighted Harmonic Mean | |

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Truncated Mean | |

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Root Mean Square | |

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Median, Range and Mode | |

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Mean Deviation | |

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Mean Deviation of the Mean | |

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Mean Deviation of the Median | |

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Variance and Standard Deviation | |

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Moments About the Mean | |

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Skewness | |

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Kurtosis | |

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Covariance and Correlation | |

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Miscellaneous Utilities | |

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Percentiles and Rank | |

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Special Functions | |

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Introduction | |

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Factorials | |

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Combinations and Permutations | |

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Combinations | |

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Permutations | |

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Gamma Function | |

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Beta Function | |

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Error Function | |

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Sine and Cosine Integral Functions | |

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Laguerre Polynomials | |

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Hermite Polynomials | |

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Chebyshev Polynomials | |

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Legendre Polynomials | |

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Bessel Functions | |

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Curve Fitting Methods | |

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Introduction | |

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Least Squares Fit | |

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Straight-Line Fit | |

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Weighted Least Squares Fit | |

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Weighted Straight-Line Fit | |

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Linear Regression | |

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Polynomial Fit | |

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Exponential Fit | |

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The X(2) Test for Goodness of Fit | |

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Ordinary Differential Equations | |

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Introduction | |

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Euler Method | |

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Runge-Kutta Methods | |

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Second-Order Runge-Kutta Method | |

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Fourth-Order Runge-Kutta Method | |

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Runge-Kutta-Fehlberg Method | |

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Coupled Differential Equations | |

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Partial Differential Equations | |

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Introduction | |

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The Finite Difference Method | |

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Parabolic Partial Differential Equations | |

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The Crank-Nicolson Method | |

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Hyperbolic Partial Differential Equations | |

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Elliptic Partial Differential Equations | |

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Optimization Methods | |

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Introduction | |

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Gradient Descent Method | |

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Linear Programming | |

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The Revised Simplex Method | |

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Simulated Annealing Method | |

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Genetic Algorithms | |

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References | |

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Index | |