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Mathematical Handbook of Formulas and Tables

Engineering Physics
Engineering Mathematics

Mathematical Handbook of Formulas and Tables
Murray R. Spiegel, Ph.D
282 pages

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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.


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


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