Mathematical Handbook of Formulas and Tables

Cover
Title Page
Copyright Page
Preface
Contents
Part A FORMULAS
	Section I Elementary Constants, Products, Formulas
		1. Greek Alphabet and Special Constants
		2. Special Products and Factors
		3. The Binomial Formula and Binomial Coefficients
		4. Complex Numbers
		5. Solutions of Algebraic Equations
		6. Conversion Factors
	Section II Geometry
		7. Geometric Formulas
		8. Formulas from Plane Analytic Geometry
		9. Special Plane Curves
		10. Formulas from Solid Analytic Geometry
		11. Special Moments of Inertia
	Section III Elementary Transcendental Functions
		12. Trigonometric Functions
		13. Exponential and Logarithmic Functions
		14. Hyperbolic Functions
	Section IV Calculus
		15. Derivatives
		16. Indefinite Integrals
		17. Tables of Special Indefinite Integrals
		18. Definite Integrals
	Section V Differential Equations and Vector Analysis
		19. Basic Differential Equations and Solutions
		20. Formulas from Vector Analysis
	Section VI Series
		21. Series of Constants
		22. Taylor Series
		23. Bernoulli and Euler Numbers
		24. Fourier Series
	Section VII Special Functions and Polynomials
		25. The Gamma Function
		26. The Beta Function
		27. Bessel Functions
		28. Legendre and Associated Legendre Functions
		29. Hermite Polynomials
		30. Laguerre and Associated Laguerre Polynomials
		31. Chebyshev Polynomials
		32. Hypergeometric Functions
	Section VIII Laplace and Fourier Transforms
		33. Laplace Transforms
		34. Fourier Transforms
	Section IX Elliptic and Miscellaneous Special Functions
		35. Elliptic Functions
		36. Miscellaneous and Riemann Zeta Functions
	Section X Inequalities and Infinite Products
		37. Inequalities
		38. Infinite Products
	Section XI Probability and Statistics
		39. Descriptive Statistics
		40. Probability
		41. Random Variables
	Section XII Numerical Methods
		42. Interpolation
		43. Quadrature
		44. Solution of Nonlinear Equations
		45. Numerical Methods for Ordinary Differential Equations
		46. Numerical Methods for Partial Differential Equations
		47. Iteration Methods for Linear Systems
	Section XIII Turing Machines
		48. Basic Definitions, Expressions
		49. Pictures
		50. Quintuple, Turing Machine
		51. Computing with a Turing Machine
		52. Examples
	Section XIV Mathematical Finance
		53. Basic Probability
		54. Interest Rates
		55. Arbitrage Theorem and Options
		56. Arbitrage Theorem
		57. Black-Scholes Formula
		58. The Delta Hedging Arbitrage Strategy
Part B TABLES
	Section I Logarithmic, Trigonometric, Exponential Functions
		1. Four Place Common Logarithms log10 N or log N
		2. Sin x(x in Degrees and Minutes)
		3. Cos x(x in Degrees and Minutes)
		4. Tan x(x in Degrees and Minutes)
		5. Conversion of Radians to Degrees, Minutes, and Seconds or Fractions of Degrees
		6. Conversion of Degrees, Minutes, and Seconds to Radians
		7. Natural or Napierian Logarithms log x or ln x
		8. Exponential Functions ex
		9. Exponential Functions e-x
		10. Exponential, Sine, and Cosine Integrals
	Section II Factorial and Gamma Function, Binomial Coefficients
		11. Factorial n
		12. Gamma Function
		13. Binomial Coefficients
	Section III Bessel Functions
		14. Bessel Functions J0 (x)
		15. Bessel Functions J1 (x)
		16. Bessel Functions Y0 (x)
		17. Bessel Functions Y1 (x)
		18. Bessel Functions I0 (x)
		19. Bessel Functions I1 (x)
		20. Bessel Functions K0 (x)
		21. Bessel Functions K1 (x)
		22. Bessel Functions Ber(x)
		23. Bessel Functions Bei(x)
		24. Bessel Functions Ker(x)
		25. Bessel Functions Kei(x)
		26. Values for Approximate Zeros of Bessel Functions
	Section IV Legendre Polynomials
		27. Legendre Polynomials Pn (x)
		28. Legendre Polynomials Pn (cos ?)
	Section V Elliptic Integrals
		29. Complete Elliptic Integrals of First and Second Kinds
		30. Incomplete Elliptic Integral of the First Kind
		31. Incomplete Elliptic Integral of the Second Kind
	Section VI Financial Tables
		32. Compound Amount: (1 + r)n
		33. Present Value of an Amount: (1 + r)-n
		34. Amount of an Annuity:
		35. Present Value of an Annuity:
	Section VII Probability and Statistics
		36. Areas Under the Standard Normal Curve from -8 to x
		37. Ordinates of the Standard Normal Curve
		38. Percentile Values (tp) for Student’s Distribution
		39. Percentile Values (X2p) for X2(Chi-Square) Distribution
		40. 95th Percentile Values for the F Distribution
		41. 99th Percentile Values for the F Distribution
		42. Random Numbers
Index of Special Symbols and Notations
Index
	A
	B
	C
	D
	E
	F
	G
	H
	I
	J
	K
	L
	M
	N
	O
	P
	Q
	R
	S
	T
	U
	V
	W
	X
	Y
	Z