Mathematical handbook of formulas and tables

Contents......Page 4
Part A: Formulas......Page 8
1. Greek Alphabet and Special Constants......Page 9
2. Special Products and Factors......Page 11
3. The Binomial Formula and Binomial Coefficients......Page 13
4. Complex Numbers......Page 16
5. Solutions of Algebraic Equations......Page 19
6. Conversion Factors......Page 21
7. Geometric Formulas......Page 22
8. Formulas from Plane Analytic Geometry......Page 28
9. Special Plane Curves......Page 34
10. Formulas from Solid Analytic Geometry......Page 40
11. Special Moments of Inertia......Page 47
12. Trigonometric Functions......Page 49
13. Exponential and Logarithmic Functions......Page 59
14. Hyperbolic Functions......Page 62
15. Derivatives......Page 68
16. Indefinite Integrals......Page 73
17. Tables of Special Indefinite Integrals......Page 77
18. Definite Integrals......Page 114
19. Basic Differential Equations and Solutions......Page 122
20. Formulas from Vector Analysis......Page 125
21. Series of Constants......Page 140
22. Taylor Series......Page 144
23. Bernoulli and Euler Numbers......Page 148
24. Fourier Series......Page 150
25. The Gamma Function......Page 155
26. The Beta Function......Page 158
27. Bessel Functions......Page 159
28. Legendre and Associated Legendre Functions......Page 170
29. Hermite Polynomials......Page 175
30. Laguerre and Associated Laguerre Polynomials......Page 177
31. Chebyshev Polynomials......Page 181
32. Hypergeometric Functions......Page 184
33. Laplace Transforms......Page 186
34. Fourier Transforms......Page 199
35. Elliptic Functions......Page 204
36. Miscellaneous and Riemann Zeta Functions......Page 209
37. Inequalities......Page 211
38. Infinite Products......Page 213
39. Descriptive Statistics......Page 214
40. Probability......Page 223
41. Random Variables......Page 229
42. Interpolation......Page 233
43. Quadrature......Page 237
44. Solution of Nonlinear Equations......Page 239
45. Numerical Methods for Ordinary Differential Equations......Page 241
46. Numerical Methods for Partial Differential Equations......Page 243
47. Iteration Methods for Linear Systems......Page 246
Part B: Tables......Page 248
1. Four Place Common Logarithms log[sub(10)] N or log N......Page 249
2. Sin x (x in degrees and minutes)......Page 251
3. Cos x (x in degrees and minutes)......Page 252
4. Tan x (x in degrees and minutes)......Page 253
5. Conversion of Radians to Degrees, Minutes, and Seconds or Fractions of Degrees......Page 254
6. Conversion of Degrees, Minutes, and Seconds to Radians......Page 255
7. Natural or Napierian Logarithms log[sub(e)] x or ln x......Page 256
8. Exponential Functions e[sup(x)]......Page 258
9. Exponential Functions e[sup(-x)]......Page 259
10. Exponential, Sine, and Cosine Integrals......Page 260
11. Factorial n......Page 261
12. Gamma Function......Page 262
13. Binomial coefficients......Page 263
15. Bessel Functions J[sub(1)](x)......Page 265
17. Bessel Functions Y[sub(1)](x)......Page 266
19. Bessel Functions I[sub(1)](x)......Page 267
21. Bessel Functions K[sub(1)](x)......Page 268
23. Bessel Functions Bei(x)......Page 269
25. Bessel Functions Kei(x)......Page 270
26. Values for Approximate Zeros of Bessel Functions......Page 271
27. Legendre Polynomials P[sub(n)](x)......Page 272
28. Legendre Polynomials P[sub(n)](cos θ)......Page 273
29. Complete Elliptic Integrals of First and Second Kinds......Page 274
31. Incomplete Elliptic Integral of the Second Kind......Page 275
32. Compound amount: (1 + r)[sup(n)]......Page 276
33. Present Value of an Amount: (1 + r)[sup(-n)]......Page 277
34. Amount of an Annuity: (1+r)[sup(n)] - 1/r......Page 278
35. Present Value of an Annuity: 1-(1+r)[sup(-n)]/r......Page 279
36. Areas Under the Standard Normal Curve......Page 280
37. Ordinates of the Standard Normal curve......Page 281
38. Percentile Values (t[sub(p)]) for Student\'s t Distribution......Page 282
39. Percentile Values (χ[sup(2)][sub(p)]) for χ[sup(2)] (Chi-Square) Distribution......Page 283
40. 95th Percentile Values for the F distribution......Page 284
41. 99th Percentile Values for the F distribution......Page 285
42. Random Numbers......Page 286
Index of Special Symbols and Notations......Page 287
C......Page 289
I......Page 290
O......Page 291
S......Page 292
Z......Page 293