[Schaum's Outline 01] • Mathematical Handbook of Formulas and Tables · 5th Edition by Spiegel, Murray R. -- Read -- Imperial Library of Trantor

Index

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 loge 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 θ)

Section V Elliptic Integrals

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

Index of Special Symbols and Notations Index