Book:Murray R. Spiegel/Mathematical Handbook of Formulas and Tables/Third Edition

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Murray R. Spiegel, Seymour Lipschutz and John Liu: Mathematical Handbook of Formulas and Tables (3rd Edition)

Published $\text {2009}$, Schaum

ISBN 0-07-154855-6


Contents

Preface

Part $\text A$: FORMULAS

Section $\text I$: 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 $\text {II}$: 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 $\text {III}$: Elementary Transcendental Functions
12. Trigonometric Functions
13. Exponential and Logarithmic Functions
14. Hyperbolic Functions
Section $\text {IV}$: Calculus
15. Derivatives
16. Indefinite Integrals
17. Tables of Special Indefinite Integrals
18. Definite Integrals
Section $\text V$: Differential Equations and Vector Analysis
19. Basic Differential Equations and Solutions
20. Formulas from Vector Analysis
Section $\text {VI}$: Series
21. Series of Constants
22. Taylor Series
23. Bernoulli and Euler Numbers
24. Fourier Series
Section $\text {VII}$: Special Functions and Polynomials
25. The Gamma Function
26. The Beta Function
27. Bessel Functions
28. Legendre Functions and Associated Legendre Functions
29. Hermite Polynomials
30. Laguerre Polynomials and Associated Laguerre Polynomials
31. Chebyshev Polynomials
32. Hypergeometric Functions
Section $\text {VIII}$: Laplace and Fourier Transforms
33. Laplace Transforms
34. Fourier Transforms
Section $\text {IX}$: Elliptic and Miscellaneous Special Functions
35. Elliptic Functions
36. Miscellaneous and Riemann Zeta Functions
Section $\text X$: Inequalities and Infinite Products
37. Inequalities
38. Infinite Products
Section $\text {XI}$: Probability and Statistics
39. Descriptive Statistics
40. Probability
41. Random Variables
Section $\text {XII}$: 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


Part $\text B$: TABLES

Section $\text I$: Logarithmic, Trigonometric, Exponential Functions
1. Four Place Common Logarithms $\log_{10} N$ or $\log N$
2. $\operatorname{Sin} x$ ($x$ in degrees and minutes)
3. $\operatorname{Cos} x$ ($x$ in degrees and minutes)
4. $\operatorname{Tan} x$ ($x$ 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 $\log_e x$ or $\ln x$
8. Exponential Functions $e^x$
9. Exponential Functions $e^{-x}$
10. Exponential, Sine and Cosine Integrals
Section $\text {II}$: Factorial and Gamma Function, Binomial Coefficients
11. Factorial $n$
12. Gamma Function
13. Binomial coefficients
Section $\text {III}$: Bessel Functions
14. Bessel Functions $\map {J_0} x$
15. Bessel Functions $\map {J_1} x$
16. Bessel Functions $\map {Y_0} x$
17. Bessel Functions $\map {Y_1} x$
18. Bessel Functions $\map {I_0} x$
19. Bessel Functions $\map {I_1} x$
20. Bessel Functions $\map {K_0} x$
21. Bessel Functions $\map {K_1} x$
22. Bessel Functions $\map {\operatorname{Ber} } x$
23. Bessel Functions $\map {\operatorname{Bei} } x$
24. Bessel Functions $\map {\operatorname{Ker} } x$
25. Bessel Functions $\map {\operatorname{Kei} } x$
26. Values for Approximate Zeros of Bessel Functions
Section $\text {IV}$: Legendre Polynomials
27. Legendre Polynomials $\map {P_n} x$
28. Legendre Polynomials $\map {P_n} {\cos \theta}$
Section $\text V$: Elliptic Integrals
29. Complete Elliptic Integrals of First and Second Kinds
30. Incomplete Elliptic Integrals of the First Kind
31. Incomplete Elliptic Integrals of the Second Kind
Section $\text {VI}$: Financial Tables
32. Compound Amount: $\paren {1 + r}^n$
33. Present Value of an Amount: $\paren {1 + r}^{-n}$
34. Amount of an Annuity: $\dfrac {\paren {1 + r}^n - 1} r$
35. Present Value of an Annuity: $\dfrac {1 - \paren {1 + r}^{-n}} r$
Section $\text {VII}$: Probability and Statistics
36. Areas under the Standard Normal Curve
37. Ordinates of the Standard Normal Curve
38. Percentile Values ($t_p$) for Student's $t$ Distribution
39. Percentile Values ($\chi_p^2$ for $\chi^2$ (Chi-Square) Distribution
40. $95$th Percentile Values for the $F$ Distribution
41. $99$th Percentile Values for the $F$ Distribution
42. Random Numbers
Index of Special Symbols and Notations
Index


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