Table of Contents for MATH77/mathc90

• Table of Contents   pdf   ps   dvi
• Introduction   pdf   ps   dvi
• Mathematical Functions
  • Inverse Hyperbolic Functions
  • 2.2 Error Function
  • 2.3 Gamma and Log-Gamma Functions
  • 2.4 Bessel Functions J₀, J₁, Y₀ and Y₁
  • 2.5 Bessel Functions of General Orders J_n and Y_n
  • 2.6 Bessel Functions I₀, I₁, K₀ and K₁
  • (Empty)
  • 2.8 Complete Elliptic Integrals K and E
  • 2.9 Incomplete Elliptic Integrals
  • 2.10 Exponential Integrals Ei and E₁
  • 2.11 Finite Legendre Series
  • 2.12 Finite Laguerre Series
  • 2.13 Inverse Error Function and Inverse Complementary Error Function
  • 2.14 Sine and Cosine Integrals
  • 2.15 Procedures to Avoid Loss of Precision: ln (1+x), etc
  • 2.16 Complex Error Function w(z)
  • 2.17 Fresnel Integrals
  • 2.18 Digamma or psi Function
  • 2.19 Incomplete Gamma Function Ratio
  • 2.20 Binomial Coefficients
• Pseudorandom Number Generation
  • 3.1 Uniform Random Numbers
  • 3.2 Gaussian (Normal) Random Numbers and Vectors
  • 3.3 Random Numbers: Exponential, Rayleigh, and Poisson
• Linear Systems of Equations and Linear Least-Squares
  • 4.1 Square Nonsingular Systems of Linear Equations
  • 4.2 Linear Least-Squares and Covariance Matrix
  • 4.3 Singular Value Decomposition and Analysis
  • 4.4 Sequential Preprocessing of Linear Least-Squares Data
  • 4.5 Sequential Solution of a Banded Least-Squares Problem
  • 4.6 Solution of a Positive-Definite System with Cholesky Factorization
  • 4.7 Sparse Square Nonsingular Systems of Equations
• Matrix Eigenvalues and Eigenvectors
  • 5.1 Eigenvalues and Eigenvectors of a Symmetric Matrix
  • 5.2 Eigenvalues and Eigenvectors of a Hermitian Complex Matrix
  • 5.3 Eigenvalues of an Unsymmetric Matrix
  • 5.4 Eigenvalues and Eigenvectors of an Unsymmetric Matrix
• Matrix-Vector Utility Subprograms
  • 6.1 Vector and Matrix Output
  • 6.2 Extended Vector and Matrix Output
  • 6.3 Basic Linear Algebra Subprograms (BLAS1)
  • 6.4 One Householder Transformation
• Polynomial Root Finding
  • 7.1 Roots of a Polynomial
  • 7.2 Roots of a Quadratic Polynomial
  • 7.3 Compute Polynomial Coefficients from Roots
• Nonlinear Equation Solving
  • 8.1 Zero of a Univariate Function
  • 8.2 Solve System of Nonlinear Equations
  • 8.3 Check Code for Computing Derivatives
  • 8.4 Computing Numerical Derivatives, Gradients and Jacobians
• Minimization
  • 9.1 Local Minimum of a Univariate Function
  • 9.2 Local Minimum of a Multivariate Function, with Linear Constraints
  • 9.3 Nonlinear Least-Squares
• Finite Fourier Transforms
  • 10.0 Overview of Fourier Transforms and Spectral Analysis   pdf   ps   dvi
  • 10.1 One-Dimensional Real Fourier Transforms
  • 10.2 Trigonometric, Cosine, and Sine Fourier Transforms
  • 10.3 Complex Fourier Transform
  • 10.4 Multi-dimensional Real Fourier Transform
  • 10.5 Primitive Fast Fourier Transform
• Curve Fitting
  • 11.1 Polynomial Least-Squares Curve Fit
  • 11.2 Evaluation, Integration, and Differentiation of Polynomials
  • 11.3 Conversion between Chebyshev and Monomial Representations of a Polynomial
  • 11.4 Least-Squares Cubic Spline Fit
  • 11.5 Least-Squares Data Fitting Using K^th Order Splines with Constraints
  • 11.6 Low-level Subprograms for Operations on Splines
• Table Look-Up and Interpolation
  • 12.1 One-Dimensional Table Look Up, Interpolation, and Differentiation
  • 12.2 Multi-Dimensional Table Look Up, Interpolation, and Differentiation
  • 12.3 Table Look-up With Hermite Cubic Interpolation
  • 12.4 C⁰ and C¹ Surface Interpolation to Scattered Data
• Definite Integrals (Quadrature)
  • 13.0 Effective Use of the Quadrature Software   pdf   ps   dvi
  • 13.1 Numerical Evaluation of Integrals Over One Dimension
  • 13.2 Numerical Evaluation of Integrals Over More Than One Dimension
• Ordinary Differential Equations
  • 14.1 Variable Order Adams Method for Ordinary Differential Equations
  • 14.2 Explicit Runge-Kutta Method for Ordinary Differential Equations
  • 14.3 Solve a Differential/Algebraic System
• Statistics
  • 15.1 Basic Statistics and Histogram
  • 15.2 Cumulative Distribution Function and Percentage Points for Normal Probability Distribution
  • 15.3 Cumulative Distribution Function for Chi-Square Probability Distribution
  • 15.4 Cumulative Distribution Function for Poisson Probability Distribution
• Graphics
  • 16.1 Character-based Graphics --- One or More XY Graphs
  • 16.2 Character-based Graphics --- Single Print Line
  • 16.3 Plotting Using TeX
• Special Arithmetic
  • 17.1 Computation Using Derivative Arrays or Univariate Taylor Series
  • 17.2 Computation Using Partial Derivative Arrays or Multivariate Taylor Series
  • 17.3 Double Precision Complex Computation
• Sorting
  • 18.1 Sorting One-dimensional Arrays in Memory
  • 18.2 Sorting Data of Arbitrary Structure in Memory
  • 18.3 Sorting Partially Ordered Data of Arbitrary Structure in Memory
  • 18.4 Sorting Data Sets Too Large to Fit in Memory
• Library Utilities
  • 19.1 System Parameters
  • 19.2 Error Message Processor
  • 19.3 Extended Error Message Processor
  • 19.4 Converting Codes to Different Versions
  • 19.5 Checking the Installed Library
  • 19.6 Running Problems in Matrix Market Format With Codes in Chapter 4.7
  • 19.7 Checking and Output of Program Unit Interfaces
• Appendix A -- Files Required by Each Entry   pdf   ps   dvi
• Appendix B -- Entry Names and Common Block Names   pdf   ps   dvi
• Appendix C -- Usage of the mathc90 Library   pdf   ps   dvi
• Appendix D -- Function Prototypes for the mathc90 Library   pdf   ps   dvi
• Index   pdf   ps   dvi

Revised March 14, 2006