• Editor-in-Chief
• Associate Editors
• Preface
• Contributors

## Chapter   1      Analysis

• 1.1   Constants
• 1.1.1   Types of numbers
• 1.1.2   Roman numerals
• 1.1.3   Arrow notation
• 1.1.4   Representation of numbers
• 1.1.5   Binary prefixes
• 1.1.6   Decimal multiples and prefixes
• 1.1.7   Decimal equivalents of common fractions
• 1.1.10   Hexadecimal--decimal fraction conversion table
• 1.2   Special numbers
• 1.2.1   Powers of 2
• 1.2.2   Powers of 16 in decimal scale
• 1.2.3   Powers of 10 in hexadecimal scale
• 1.2.4   Special constants
• 1.2.5   Constants in different bases
• 1.2.6   Factorials
• 1.2.7   Bernoulli polynomials and numbers
• 1.2.8   Euler polynomials and numbers
• 1.2.9   Fibonacci numbers
• 1.2.10   Powers of integers
• 1.2.11   Sums of powers of integers
• 1.2.12   Negative integer powers
• 1.2.13   de-Bruijn sequences
• 1.2.14   Integer sequences
• 1.3   Series and products
• 1.3.1   Definitions
• 1.3.2   General properties
• 1.3.3   Convergence tests
• 1.3.4   Types of series
• 1.3.5   Summation formulae
• 1.3.6   Improving convergence: Shanks transformation
• 1.3.7   Summability methods
• 1.3.8   Operations with power series
• 1.3.9   Miscellaneous sums and series
• 1.3.10   Infinite series
• 1.3.11   Infinite products
• 1.3.12   Infinite products and infinite series
• 1.4   Fourier series
• 1.4.1   Special cases
• 1.4.2   Alternate forms
• 1.4.3   Useful series
• 1.4.4   Expansions of basic periodic functions
• 1.5   Complex analysis
• 1.5.1   Definitions
• 1.5.2   Operations on complex numbers
• 1.5.3   Functions of a complex variable
• 1.5.4   Cauchy--Riemann equations
• 1.5.5   Cauchy integral theorem
• 1.5.6   Cauchy integral formula
• 1.5.7   Taylor series expansions
• 1.5.8   Laurent series expansions
• 1.5.9   Zeros and singularities
• 1.5.10   Residues
• 1.5.11   The argument principle
• 1.5.12   Transformations and mappings
• 1.6   Interval analysis
• 1.6.1   Interval arithmetic rules
• 1.6.2   Interval arithmetic properties
• 1.7   Real analysis
• 1.7.1   Relations
• 1.7.2   Functions (mappings)
• 1.7.3   Sets of real numbers
• 1.7.4   Topological space
• 1.7.5   Metric space
• 1.7.6   Convergence in R with metric |x-y|
• 1.7.7   Continuity in R with metric |x-y|
• 1.7.8   Banach space
• 1.7.9   Hilbert space
• 1.7.10   Asymptotic relationships
• 1.8   Generalized Functions
• 1.8.1   Delta function
• 1.8.2   Other generalized functions

## Chapter   2      Algebra

• 2.1   Proofs without words
• 2.2   Elementary algebra
• 2.2.1   Basic algebra
• 2.2.2   Progressions
• 2.2.3   DeMoivre's theorem
• 2.2.4   Partial fractions
• 2.3   Polynomials
• 2.3.2   Cubic polynomials
• 2.3.3   Quartic polynomials
• 2.3.4   Quartic curves
• 2.3.5   Quintic polynomials
• 2.3.6   Tschirnhaus' transformation
• 2.3.7   Polynomial norms
• 2.3.8   Cyclotomic polynomials
• 2.3.9   Other polynomial properties
• 2.4   Number theory
• 2.4.1   Divisibility
• 2.4.2   Congruences
• 2.4.3   Chinese remainder theorem
• 2.4.4   Continued fractions
• 2.4.5   Diophantine equations
• 2.4.6   Greatest common divisor
• 2.4.7   Least common multiple
• 2.4.8   Magic squares
• 2.4.9   Mobius function
• 2.4.10   Prime numbers
• 2.4.11   Prime numbers of special forms
• 2.4.12   Prime numbers less than 100,000
• 2.4.13   Factorization table
• 2.4.14   Factorization of 2m-1
• 2.4.15   Euler Totient function
• 2.5   Vector algebra
• 2.5.1   Notation for vectors and scalars
• 2.5.2   Physical vectors
• 2.5.3   Fundamental definitions
• 2.5.4   Laws of vector algebra
• 2.5.5   Vector norms
• 2.5.6   Dot, scalar, or inner product
• 2.5.7   Vector or cross product
• 2.5.8   Scalar and vector triple products
• 2.6   Linear and matrix algebra
• 2.6.1   Definitions
• 2.6.2   Types of matrices
• 2.6.3   Conformability for addition and multiplication
• 2.6.4   Determinants and permanents
• 2.6.5   Matrix norms
• 2.6.6   Singularity, rank, and inverses
• 2.6.7   Systems of linear equations
• 2.6.8   Linear spaces and linear mappings
• 2.6.9   Traces
• 2.6.10   Generalized inverses
• 2.6.11   Eigenstructure
• 2.6.12   Matrix diagonalization
• 2.6.13   Matrix exponentials
• 2.6.15   Matrix factorizations
• 2.6.16   Theorems
• 2.6.17   The vector operation
• 2.6.18   Kronecker products
• 2.6.19   Kronecker sums
• 2.7   Abstract algebra
• 2.7.1   Definitions
• 2.7.2   Groups
• 2.7.3   Rings
• 2.7.4   Fields
• 2.7.6   Finite fields
• 2.7.7   Homomorphisms and isomorphisms
• 2.7.8   Matrix classes that are groups
• 2.7.9   Permutation groups
• 2.7.10   Tables

## Chapter   3      Discrete Mathematics

• 3.1   Symbolic logic
• 3.1.1   Propositional calculus
• 3.1.2   Tautologies
• 3.1.3   Truth tables as functions
• 3.1.4   Rules of inference
• 3.1.5   Deductions
• 3.1.6   Predicate calculus
• 3.2   Set theory
• 3.2.1   Sets
• 3.2.2   Set operations and relations
• 3.2.3   Connection between sets and probability
• 3.2.4   Venn diagrams
• 3.2.5   Paradoxes and theorems of set theory
• 3.2.6   Inclusion/Exclusion
• 3.2.7   Partially ordered sets
• 3.3   Combinatorics
• 3.3.1   Sample selection
• 3.3.2   Balls into cells
• 3.3.3   Binomial coefficients
• 3.3.4   Multinomial coefficients
• 3.3.5   Arrangements and derangements
• 3.3.6   Partitions
• 3.3.7   Bell numbers
• 3.3.8   Catalan numbers
• 3.3.9   Stirling cycle numbers
• 3.3.10   Stirling subset numbers
• 3.3.11   Tables
• 3.4   Graphs
• 3.4.1   Notation
• 3.4.2   Basic definitions
• 3.4.3   Constructions
• 3.4.4   Fundamental results
• 3.4.5   Tree diagrams
• 3.5   Combinatorial design theory
• 3.5.1   t-Designs
• 3.5.2   Balanced incomplete block designs (BIBDs)
• 3.5.3   Difference sets
• 3.5.4   Finite geometry
• 3.5.5   Steiner triple systems
• 3.5.7   Latin squares
• 3.5.8   Room squares
• 3.5.9   Costas arrays
• 3.6   Communication theory
• 3.6.1   Information theory
• 3.6.2   Block coding
• 3.6.3   Source coding for English text
• 3.6.4   Morse code
• 3.6.5   Gray code
• 3.6.6   Finite fields
• 3.6.7   Binary sequences
• 3.7   Difference equations
• 3.7.1   The calculus of finite differences
• 3.7.2   Existence and uniqueness
• 3.7.3   Linear independence: general solution
• 3.7.4   Homogeneous equations with constant coefficients
• 3.7.5   Non-homogeneous equations
• 3.7.6   Generating functions and Z transforms
• 3.7.7   Closed-form solutions for special equations
• 3.8   Discrete Dynamical Systems and Chaos
• 3.8.1   Chaotic one-dimensional maps
• 3.8.2   Logistic map
• 3.8.3   Julia sets and the Mandelbrot set
• 3.9   Game theory
• 3.9.1   Two person non-cooperative matrix games
• 3.9.2   Voting power
• 3.10   Operations research
• 3.10.1   Linear programming
• 3.10.2   Duality and complementary slackness
• 3.10.3   Linear integer programming
• 3.10.4   Branch and bound
• 3.10.5   Network flow methods
• 3.10.6   Assignment problem
• 3.10.7   Dynamic programming
• 3.10.8   Shortest path problem
• 3.10.9   Heuristic search techniques

## Chapter   4      Geometry

• 4.1   Coordinate systems in the plane
• 4.1.1   Convention
• 4.1.2   Substitutions and transformations
• 4.1.3   Cartesian coordinates in the plane
• 4.1.4   Polar coordinates in the plane
• 4.1.5   Homogeneous coordinates in the plane
• 4.1.6   Oblique coordinates in the plane
• 4.2   Plane symmetries or isometries
• 4.2.1   Formulae for symmetries: Cartesian coordinates
• 4.2.2   Formulae for symmetries: homogeneous coordinates
• 4.2.3   Formulae for symmetries: polar coordinates
• 4.2.4   Crystallographic groups
• 4.2.5   Classifying the crystallographic groups
• 4.3   Other transformations of the plane
• 4.3.1   Similarities
• 4.3.2   Affine transformations
• 4.3.3   Projective transformations
• 4.4   Lines
• 4.4.1   Lines with prescribed properties
• 4.4.2   Distances
• 4.4.3   Angles
• 4.4.4   Concurrence and collinearity
• 4.5   Polygons
• 4.5.1   Triangles
• 4.5.3   Regular polygons
• 4.6   Conics
• 4.6.1   Alternative characterization
• 4.6.2   The general quadratic equation
• 4.6.3   Additional properties of ellipses
• 4.6.4   Additional properties of hyperbolas
• 4.6.5   Additional properties of parabolas
• 4.6.6   Circles
• 4.7   Special plane curves
• 4.7.1   Algebraic curves
• 4.7.2   Roulettes (spirograph curves)
• 4.7.3   Curves in polar coordinates
• 4.7.4   Spirals
• 4.7.5   The Peano curve and fractal curves
• 4.7.6   Fractal objects
• 4.7.7   Classical constructions
• 4.8   Coordinate systems in space
• 4.8.1   Cartesian coordinates in space
• 4.8.2   Cylindrical coordinates in space
• 4.8.3   Spherical coordinates in space
• 4.8.4   Relations between Cartesian, cylindrical, and spherical coordinates
• 4.8.5   Homogeneous coordinates in space
• 4.9   Space symmetries or isometries
• 4.9.1   Formulae for symmetries: Cartesian coordinates
• 4.9.2   Formulae for symmetries: homogeneous coordinates
• 4.10   Other transformations of space
• 4.10.1   Similarities
• 4.10.2   Affine transformations
• 4.10.3   Projective transformations
• 4.11   Direction Angles and Direction Cosines
• 4.12   Planes
• 4.12.1   Planes with prescribed properties
• 4.12.2   Concurrence and coplanarity
• 4.13   Lines in space
• 4.13.1   Distances
• 4.13.2   Angles
• 4.13.3   Concurrence, coplanarity, parallelism
• 4.14   Polyhedra
• 4.14.1   Convex regular polyhedra
• 4.14.2   Polyhedra nets
• 4.15   Cylinders
• 4.16   Cones
• 4.17   Surfaces of revolution: the torus
• 4.18.1   Spheres
• 4.19   Spherical geometry & trigonometry
• 4.19.1   Right spherical triangles
• 4.19.2   Oblique spherical triangles
• 4.20   Differential geometry
• 4.20.1   Curves
• 4.20.2   Surfaces
• 4.21   Angle conversion
• 4.22   Knots up to eight crossings

## Chapter   5      Continuous Mathematics

• 5.1   Differential calculus
• 5.1.1   Limits
• 5.1.2   Derivatives
• 5.1.3   Derivatives of common functions
• 5.1.4   Derivative formulae
• 5.1.5   Derivative theorems
• 5.1.6   The two-dimensional chain rule
• 5.1.7   l'Hospital's rule
• 5.1.8   Maxima and minima of functions
• 5.1.9   Vector calculus
• 5.1.10   Matrix and vector derivatives
• 5.2   Differential forms
• 5.2.1   Products of 1-forms
• 5.2.2   Differential 2-forms
• 5.2.3   The 2-forms in Rn
• 5.2.4   Higher dimensional forms
• 5.2.5   The exterior derivative
• 5.2.6   Properties of the exterior derivative
• 5.3   Integration
• 5.3.1   Definitions
• 5.3.2   Properties of integrals
• 5.3.3   Methods of evaluating integrals
• 5.3.4   Types of integrals
• 5.3.5   Integral inequalities
• 5.3.6   Convergence tests
• 5.3.7   Variational principles
• 5.3.8   Continuity of integral anti-derivatives
• 5.3.9   Asymptotic integral evaluation
• 5.3.10   Special functions defined by integrals
• 5.3.11   Applications of integration
• 5.3.12   Moments of inertia for various bodies
• 5.3.13   Tables of integrals
• 5.4   Table of Indefinite Integrals
• 5.4.1   Elementary forms
• 5.4.2   Forms containing a+bx
• 5.4.3   Forms containing c2 +- x2 and x2-c2
• 5.4.4   Forms containing a+bx and c+dx
• 5.4.5   Forms containing a+bxn
• 5.4.6   Forms containing c3 +- x3
• 5.4.7   Forms containing c4 +- x4
• 5.4.8   Forms containing a+b x+c x2
• 5.4.9   Forms containing SQRT(a+b x
• 5.4.10   Forms containing SQRT(a+b x) and SQRT(c+d x)
• 5.4.11   Forms containing SQRT(x2 +- a2)
• 5.4.12   Forms containing SQRT(a2-x2)
• 5.4.13   Forms containing SQRT(a+bx+cx2)
• 5.4.14   Forms containing SQRT(2ax-x2)
• 5.4.15   Miscellaneous algebraic forms
• 5.4.16   Forms involving trigonometric functions
• 5.4.17   Forms involving inverse trigonometric functions
• 5.4.18   Logarithmic forms
• 5.4.19   Exponential forms
• 5.4.20   Hyperbolic forms
• 5.4.21   Bessel functions
• 5.5   Table of definite integrals
• 5.5.1   Table of semi-integrals
• 5.6   Ordinary differential equations
• 5.6.1   Linear differential equations
• 5.6.2   Solution techniques
• 5.6.3   Integrating factors
• 5.6.4   Variation of parameters
• 5.6.5   Green's functions
• 5.6.6   Table of Green's functions
• 5.6.7   Transform techniques
• 5.6.8   Named ordinary differential equations
• 5.6.9   Liapunov's direct method
• 5.6.10   Lie groups
• 5.6.11   Stochastic differential equations
• 5.6.12   Types of critical points
• 5.7   Partial differential equations
• 5.7.1   Classifications of PDEs
• 5.7.2   Named partial differential equations
• 5.7.3   Transforming partial differential equations
• 5.7.4   Well-posedness of PDEs
• 5.7.5   Green's functions
• 5.7.6   Quasi-linear equations
• 5.7.7   Separation of variables
• 5.7.8   Solutions of Laplace's equation
• 5.7.9   Solutions to the wave equation
• 5.7.10   Particular solutions to some PDEs
• 5.8   Eigenvalues
• 5.9   Integral equations
• 5.9.1   Definitions
• 5.9.2   Connection to differential equations
• 5.9.3   Fredholm alternative
• 5.9.4   Special equations with solutions
• 5.10   Tensor analysis
• 5.10.1   Definitions
• 5.10.2   Algebraic tensor operations
• 5.10.3   Differentiation of tensors
• 5.10.4   Metric tensor
• 5.10.5   Results
• 5.10.6   Examples of tensors
• 5.11   Orthogonal coordinate systems
• 5.11.1   Table of orthogonal coordinate systems
• 5.12   Control theory

## Chapter   6      Special Functions

• 6.1   Trigonometric or circular functions
• 6.1.1   Definition of angles
• 6.1.2   Characterization of angles
• 6.1.3   Circular functions
• 6.1.4   Circular functions of special angles
• 6.1.5   Evaluating sines and cosines at multiples of pi
• 6.1.6   Symmetry and periodicity relationships
• 6.1.7   Functions in terms of angles in the first quadrant
• 6.1.8   One circular function in terms of another
• 6.1.9   Circular functions in terms of exponentials
• 6.1.10   Fundamental identities
• 6.1.11   Angle sum and difference relationships
• 6.1.12   Double angle formulae
• 6.1.13   Multiple angle formulae
• 6.1.14   Half angle formulae
• 6.1.15   Powers of circular functions
• 6.1.16   Products of sine and cosine
• 6.1.17   Sums of circular functions
• 6.2   Circular functions and planar triangles
• 6.2.1   Right triangles
• 6.2.2   General plane triangles
• 6.2.3   Half angle formulae
• 6.2.4   Solution of triangles
• 6.2.5   Tables of trigonometric functions
• 6.3   Inverse circular functions
• 6.3.1   Definition in terms of an integral
• 6.3.2   Principal values of the inverse circular functions
• 6.3.3   Fundamental identities
• 6.3.4   Functions of negative arguments
• 6.3.5   Relationship to inverse hyperbolic functions
• 6.3.6   Sum and difference of two inverse trigonometric functions
• 6.4   Ceiling and floor functions
• 6.5   Exponential function
• 6.5.1   Exponentiation
• 6.5.2   Definition of ez
• 6.5.3   Derivative and integral of ex
• 6.6   Logarithmic functions
• 6.6.1   Definition of the natural logarithm
• 6.6.2   Logarithm of special values
• 6.6.3   Relating the logarithm to the exponential
• 6.6.4   Identities
• 6.6.5   Series expansions for the natural logarithm
• 6.6.6   Derivative and integration formulae
• 6.7   Hyperbolic functions
• 6.7.1   Definitions of the hyperbolic functions
• 6.7.2   Range of values
• 6.7.3   Hyperbolic functions in terms of one another
• 6.7.4   Relations among hyperbolic functions
• 6.7.5   Relationship to circular functions
• 6.7.6   Series expansions
• 6.7.7   Symmetry relationships
• 6.7.8   Sum and difference formulae
• 6.7.9   Multiple argument relations
• 6.7.10   Sums of functions
• 6.7.11   Products of functions
• 6.7.12   Half--argument formulae
• 6.7.13   Differentiation formulae
• 6.8   Inverse hyperbolic functions
• 6.8.1   Range of values
• 6.8.2   Relationships among inverse hyperbolic functions
• 6.8.3   Relationships with logarithmic functions
• 6.8.4   Relationships with circular functions
• 6.8.5   Sum and difference of functions
• 6.9   Gudermannian Function
• 6.9.1   Fundamental identities
• 6.9.2   Derivatives of Gudermannian
• 6.9.3   Relationship to hyperbolic and circular functions
• 6.9.4   Numerical values of hyperbolic functions
• 6.10   Orthogonal polynomials
• 6.10.1   Hermite polynomials
• 6.10.2   Jacobi polynomials
• 6.10.3   Laguerre polynomials
• 6.10.4   Generalized Laguerre polynomials
• 6.10.5   Legendre polynomials
• 6.10.6   Chebyshev polynomials, first kind
• 6.10.7   Chebyshev polynomials, second kind
• 6.10.8   Tables of orthogonal polynomials
• 6.10.9   Zernike polynomials
• 6.10.10   Spherical harmonics
• 6.11   Gamma function
• 6.11.1   Recursion formula
• 6.11.2   Gamma function of special values
• 6.11.3   Properties
• 6.11.4   Asymptotic expansion
• 6.11.5   Logarithmic derivative of the gamma function
• 6.11.6   Numerical values
• 6.12   Beta function
• 6.12.1   Numerical values of the beta function
• 6.13   Error functions
• 6.13.1   Properties
• 6.13.2   Error function of special values
• 6.13.3   Expansions
• 6.13.4   Special cases
• 6.14   Fresnel integrals
• 6.14.1   Properties
• 6.14.2   Asymptotic expansion
• 6.14.3   Numerical values of error functions and Fresnel integrals
• 6.15   Sine, cosine, and exponential integrals
• 6.15.1   Sine and cosine integrals
• 6.15.2   Exponential integrals
• 6.15.3   Logarithmic integral
• 6.15.4   Numerical values
• 6.16   Polylogarithms
• 6.16.1   Polylogarithms of special values
• 6.16.2   Polylogarithms properties
• 6.17   Hypergeometric functions
• 6.17.1   Special cases
• 6.17.2   Properties
• 6.17.3   Recursion formulae
• 6.18   Legendre functions
• 6.18.1   Differential equation: Legendre function
• 6.18.2   Definition
• 6.18.3   Singular points
• 6.18.4   Relationships
• 6.18.5   Recursion relationships
• 6.18.6   Integrals
• 6.18.7   Polynomial case
• 6.18.8   Differential equation: associated Legendre function
• 6.18.9   Relationships between the associated and ordinary Legendre functions
• 6.18.10   Orthogonality relationship
• 6.18.11   Recursion relationships
• 6.19   Bessel functions
• 6.19.1   Differential equation
• 6.19.2   Singular points
• 6.19.3   Relationships
• 6.19.4   Series expansions
• 6.19.5   Recurrence relationships
• 6.19.6   Behavior as z->0
• 6.19.7   Integrals
• 6.19.8   Fourier expansion
• 6.19.9   Auxiliary functions
• 6.19.10   Inverse relationships
• 6.19.11   Asymptotic expansions
• 6.19.12   Zeros of Bessel functions
• 6.19.13   Half order Bessel functions
• 6.19.14   Modified Bessel functions
• 6.19.15   Airy functions
• 6.19.16   Numerical values for the Bessel functions
• 6.20   Elliptic integrals
• 6.20.1   Definitions
• 6.20.2   Properties
• 6.20.3   Numerical values of the elliptic integrals
• 6.21   Jacobian elliptic functions
• 6.21.1   Properties
• 6.21.2   Derivatives and integrals
• 6.21.3   Series expansions
• 6.22   Clebsch--Gordan coefficients
• 6.23   Integral transforms: Preliminaries
• 6.24   Fourier integral transform
• 6.24.1   Existence
• 6.24.2   Properties
• 6.24.3   Inversion formula
• 6.24.4   Poisson summation formula
• 6.24.5   Shannon's sampling theorem
• 6.24.6   Uncertainty principle
• 6.24.7   Fourier sine and cosine transforms
• 6.25   Discrete Fourier transform (DFT)
• 6.25.1   Properties
• 6.26   Fast Fourier transform (FFT)
• 6.27   Multidimensional Fourier transforms
• 6.28   Laplace transform
• 6.28.1   Existence and domain of convergence
• 6.28.2   Properties
• 6.28.3   Inversion formulae
• 6.28.4   Convolution
• 6.29   Hankel transform
• 6.29.1   Properties
• 6.30   Hartley transform
• 6.31   Hilbert transform
• 6.31.1   Existence
• 6.31.2   Properties
• 6.31.3   Relationship with the Fourier transform
• 6.32   Z-Transform
• 6.32.1   Examples
• 6.32.2   Properties
• 6.32.3   Inversion formula
• 6.32.4   Convolution and product
• 6.33   Tables of transforms

## Chapter   7      Probability and Statistics

• 7.1   Probability theory
• 7.1.1   Introduction
• 7.1.2   Multivariate distributions
• 7.1.3   Random sums of random variables
• 7.1.4   Transforming variables
• 7.1.5   Central limit theorem
• 7.1.6   Inequalities
• 7.1.7   Averages over vectors
• 7.1.8   Geometric probability
• 7.2   Classical probability problems
• 7.2.2   Gambler's ruin problem
• 7.2.3   Card games
• 7.2.4   Distribution of dice sums
• 7.2.5   Birthday problem
• 7.3   Probability distributions
• 7.3.1   Discrete distributions
• 7.3.2   Continuous distributions
• 7.4   Queuing theory
• 7.4.1   Variables
• 7.4.2   Theorems
• 7.5   Markov chains
• 7.5.1   Transition function and matrix
• 7.5.2   Recurrence
• 7.5.3   Stationary distributions
• 7.5.4   Random walks
• 7.5.5   Ehrenfest chain
• 7.6   Random number generation
• 7.6.1   Methods of pseudorandom number generation
• 7.6.2   Generating non-uniform random variables
• 7.7   Control charts and reliability
• 7.7.1   Control charts
• 7.7.2   Acceptance sampling
• 7.7.3   Reliability
• 7.7.4   Failure time distributions
• 7.8   Risk analysis and decision rules
• 7.9   Statistics
• 7.9.1   Descriptive statistics
• 7.9.2   Statistical estimators
• 7.9.3   Cramer--Rao bound
• 7.9.4   Order statistics
• 7.9.5   Classic statistics problems
• 7.10   Confidence intervals
• 7.10.1   Confidence interval: sample from one population
• 7.10.2   Confidence interval: samples from two populations
• 7.11   Tests of hypotheses
• 7.11.1   Hypothesis tests: parameter from one population
• 7.11.2   Hypothesis tests: parameters from two populations
• 7.11.3   Hypothesis tests: distribution of a population
• 7.11.4   Hypothesis tests: distributions of two populations
• 7.11.5   Sequential probability ratio tests
• 7.12   Linear regression
• 7.12.1   Linear model yi=b0+b1xi+e
• 7.12.2   General model y=b0+b1x1+b2x2+...+bnxn+e
• 7.13   Analysis of variance (ANOVA)
• 7.13.1   One-factor ANOVA
• 7.13.2   Unreplicated two-factor ANOVA
• 7.13.3   Replicated two-factor ANOVA
• 7.14   Probability tables
• 7.14.1   Critical values
• 7.14.2   Table of the normal distribution
• 7.14.3   Percentage points, Student's t-distribution
• 7.14.4   Percentage points, chi-square distribution
• 7.14.5   Percentage points, F-distribution
• 7.14.6   Cumulative terms, binomial distribution
• 7.14.7   Cumulative terms, Poisson distribution
• 7.14.8   Critical values, Kolmogorov--Smirnov test
• 7.14.9   Critical values, two sample Kolmogorov--Smirnov test
• 7.14.10   Critical values, Spearman's rank correlation
• 7.15   Signal processing
• 7.15.1   Estimation
• 7.15.2   Kalman filters
• 7.15.3   Matched filtering (Wiener filter)
• 7.15.4   Walsh functions
• 7.15.5   Wavelets

## Chapter   8      Scientific Computing

• 8.1   Basic numerical analysis
• 8.1.1   Approximations and errors
• 8.1.2   Solution to algebraic equations
• 8.1.3   Interpolation
• 8.1.4   Fitting equations to data
• 8.2   Numerical linear algebra
• 8.2.1   Solving linear systems
• 8.2.2   Gaussian elimination
• 8.2.3   Gaussian elimination algorithm
• 8.2.4   Pivoting
• 8.2.5   Eigenvalue computation
• 8.2.6   Householder's method
• 8.2.7   QR algorithm
• 8.2.8   Non-linear systems and numerical optimization
• 8.3   Numerical integration and differentiation
• 8.3.1   Numerical integration
• 8.3.2   Numerical differentiation
• 8.3.3   Numerical summation
• 8.4   Programming techniques

## Chapter   9      Financial Analysis

• 9.1   Financial formulae
• 9.1.1   Definition of financial terms
• 9.1.2   Formulae connecting financial terms
• 9.1.3   Examples
• 9.2   Financial tables
• 9.2.1   Compound interest: find final value
• 9.2.2   Compound interest: find interest rate
• 9.2.3   Compound interest: find annuity

## Chapter   10      Miscellaneous

• 10.1   Units
• 10.1.1   SI system of measurement
• 10.1.2   United States customary system of weights and measures
• 10.1.3   Physical constants
• 10.1.4   Dimensional analysis/Buckingham pi
• 10.1.5   Units of physical quantities
• 10.1.6   Conversion: metric to English
• 10.1.7   Conversion: English to metric
• 10.1.8   Miscellaneous conversions
• 10.1.9   Temperature conversion
• 10.2   Interpretations of powers of 10
• 10.3   Calendar computations
• 10.3.1   Leap years
• 10.3.2   Day of week for any given day
• 10.3.3   Number of each day of the year
• 10.4   AMS classification scheme
• 10.5   Fields medals
• 10.6   Greek alphabet
• 10.7   Computer languages
• 10.7.1   Software contact information
• 10.8   Professional Mathematical Organizations
• 10.9   Electronic mathematical resources
• 10.10   Biographies of mathematicians