**Related Resources: math**

### Mathematical Handbook of Formulas and Tables

Engineering Physics

Engineering Mathematics

Mathematical Handbook of Formulas and Tables

Murray R. Spiegel, Ph.D

282 pages

Open: Mathematical Handbook of Formulas and Tables

Free Membership Minimum Required

Preface

The purpose of this handbook is to supply a collection of mathematical formulas and tables which will prove to be valuable to students and research workers in the fields of mathematics, physics, engineering and other sciences. To accomplish this, care has been taken to mclude those formulas and tables which are most likely to be needed in practice rather than highly specialized results which are rarely used. Every effort has been made to present results concisely as well as precisely so that they may be referred to with a maximum of ease as well as confidence.

Topics covered range from elementary to advanced. Elementary topics include those from algebra, geometry, trigonometry, analytic geometry and calculus. Advanced topics mclude those from differential equations, vector analysis, Fourier series, gamma and beta functions, Bessel and Legendre functions, Fourier and Laplace transforms, elliptic functions and various other special functions of importance. This wide coverage of topics has been adopted so as to provide within a single volume most of the important mathematical results needed by the student or research worker regardless of his particular field of interest or level of attainment.

The book is divided into two main parts. Part I presents mathematical formulas together with other material, such as definitions, theorems, graphs, diagrams, etc., essential for proper understanding and application of the formulas. Included in this first part are extensive tables of integrals and Laplace transforms which should be extremely useful to the student and research worker. Part II presents numerical tables such as the values of elementary functions (trigonometric, logarithmic, exponential, hyperbolic, etc.) as well as advanced functions (Bessel, Legendre, elliptic, etc.). In order to eliminate confusion especially to the beginner in mathematics, the numerical tables for each function are separated. Thus, for example, the sine and cosine functions for angles in degrees and minutes are given in separate tables rather than in one table so that there is no need to be concerned about the possibility of error due to looking in the wrong column or row.

TOC

1. Special Constants

2. Special Products and Factors

3. The Binomial Formula and Binomial Coefficients

4. Geometric Formulas

5. Trigonometric Functions

6. Complex Numbers

7. Exponential and Logarithmic Functions

8. Hyperbolic Functions

9. Solutions of Algebraic Equations

10. Formulas from Plane Analytic Geometry

11. Special Plane Curves

12. Formulas from Solid Analytic Geometry

13. Derivatives

14. Indefinite Integrals

15. Definite Integrals

16. The Gamma Function

17. The Beta Function

1 8. Basic Differential Equations and Solutions

19. Series of Constants

20. Taylor Series

21. Bernoulli and Euler Numbers

22. Formulas from Vector Analysis

23. Fourier Series

24. Bessel Functions

25. Legendre Functions

26. Associated Legendre Functions

27. Hermite Polynomials

28. Laguerre Polynomials

29. Associated Laguerre Polynomials

30. Chebyshev Polynomials

31. Hypergeometric Functions

32. Laplace Transforms

33. Fourier Transforms

34. Elliptic Functions

35. Miscellaneous Special Functions

36. Inequalities

37. Partial Fraction Expansions

38. Infinite Products

39. Probability Distributions

40. Special Moments of Inertia

41. Conversion Factors

Tables

1. Four Place Common Logarithms

2. Four Place Common Antilogarithms

3. Sin X (x in degrees and minutes)

4. Cos X {x in degrees and minutes)

5. Tan x (x in degrees and minutes)

6. Cotx {x in degrees and minutes)

7. Sec X {x in degrees and minutes)

8. Csc X {x in degrees and minutes)

9. Natural Trigonometric Functions (in radians)

10. log sin X {x in degrees and minutes)

11. log cos X {x in degrees and minutes)

12. log tan X {x in degrees and minutes)

13. Conversion of radians to degrees, minutes and seconds or fractions of a degree

14. Conversion of degrees, minutes and seconds to radians

15. Natural or Napierian Logarithms log x; or In x

16. Exponential functions e^{-x}

17. Exponential functions e^{-x}

18a. Hyperbolic functions sinh

18b. Hyperbolic functions cosh

18e. Hyperbolic functions tanhx

19. Factorial n

21. Binomial Coefficients

22. Squares, Cubes, Roots and Reciprocals

25. Amount of an Annuity:

27. Bessel functions Jo{x)

28. Bessel functions Ji{x)

29. Bessel functions Yq{x)

30. Bessel functions Yi{x)

31. Bessel functions Iq{x)

32. Bessel functions Ii{x)

33. Bessel functions Ko{x)

34. Bessel functions Ki{x)

35. Bessel functions Ber (x)

36. Bessel functions Bei (x)

37. Bessel functions Ker (x)

38. Bessel functions Kei (x)

39. Values for Approximate Zeros of Bessel Functions

40. Exponential, Sine and Cosine Integrals

41. Legendre Polynomials

42. Legendre Polynomials

43. Complete Elliptic Integrals of First and Second Kinds

44. Incomplete Elliptic Integral of the First Kind

45. Incomplete Elliptic Integral of the Second Kind

46. Ordinates of the Standard Normal Curve

47. Areas under the Standard Normal Curve

48. Percentile Values for Student's t Distribution

49. Percentile Values for the Chi Square Distribution

50. 95th Percentile Values for the F Distribution

51. 99th Percentile Values for the F Distribution

52. Random Numbers