Author(s): Murray R Spiegel, Seymour Lipshutz
Series: Schaum’s Outline Series
Edition: 5
Publisher: McGraw-Hill
Year: 2018
Language: English
Pages: 337
Cover......Page 1
Title Page......Page 4
Copyright Page......Page 5
Preface......Page 6
Contents......Page 8
Part A FORMULAS......Page 14
1. Greek Alphabet and Special Constants......Page 16
2. Special Products and Factors......Page 18
3. The Binomial Formula and Binomial Coefficients......Page 20
4. Complex Numbers......Page 23
5. Solutions of Algebraic Equations......Page 26
6. Conversion Factors......Page 28
7. Geometric Formulas......Page 29
8. Formulas from Plane Analytic Geometry......Page 35
9. Special Plane Curves......Page 41
10. Formulas from Solid Analytic Geometry......Page 47
11. Special Moments of Inertia......Page 54
12. Trigonometric Functions......Page 56
13. Exponential and Logarithmic Functions......Page 66
14. Hyperbolic Functions......Page 69
15. Derivatives......Page 75
16. Indefinite Integrals......Page 80
17. Tables of Special Indefinite Integrals......Page 84
18. Definite Integrals......Page 121
19. Basic Differential Equations and Solutions......Page 129
20. Formulas from Vector Analysis......Page 132
21. Series of Constants......Page 147
22. Taylor Series......Page 151
23. Bernoulli and Euler Numbers......Page 155
24. Fourier Series......Page 157
25. The Gamma Function......Page 162
26. The Beta Function......Page 165
27. Bessel Functions......Page 166
28. Legendre and Associated Legendre Functions......Page 177
29. Hermite Polynomials......Page 182
30. Laguerre and Associated Laguerre Polynomials......Page 184
31. Chebyshev Polynomials......Page 188
32. Hypergeometric Functions......Page 191
33. Laplace Transforms......Page 193
34. Fourier Transforms......Page 206
35. Elliptic Functions......Page 211
36. Miscellaneous and Riemann Zeta Functions......Page 216
37. Inequalities......Page 218
38. Infinite Products......Page 220
39. Descriptive Statistics......Page 221
40. Probability......Page 230
41. Random Variables......Page 236
42. Interpolation......Page 244
43. Quadrature......Page 248
44. Solution of Nonlinear Equations......Page 250
45. Numerical Methods for Ordinary Differential Equations......Page 252
46. Numerical Methods for Partial Differential Equations......Page 254
47. Iteration Methods for Linear Systems......Page 257
48. Basic Definitions, Expressions......Page 259
49. Pictures......Page 260
50. Quintuple, Turing Machine......Page 261
51. Computing with a Turing Machine......Page 263
52. Examples......Page 265
53. Basic Probability......Page 267
54. Interest Rates......Page 269
55. Arbitrage Theorem and Options......Page 270
56. Arbitrage Theorem......Page 271
57. Black-Scholes Formula......Page 272
58. The Delta Hedging Arbitrage Strategy......Page 273
Part B TABLES......Page 276
1. Four Place Common Logarithms log10 N or log N......Page 278
2. Sin x(x in Degrees and Minutes)......Page 280
3. Cos x(x in Degrees and Minutes)......Page 281
4. Tan x(x in Degrees and Minutes)......Page 282
5. Conversion of Radians to Degrees, Minutes, and Seconds or Fractions of Degrees......Page 283
6. Conversion of Degrees, Minutes, and Seconds to Radians......Page 284
7. Natural or Napierian Logarithms log x or ln x......Page 285
8. Exponential Functions ex......Page 287
9. Exponential Functions e-x......Page 288
10. Exponential, Sine, and Cosine Integrals......Page 289
11. Factorial n......Page 290
12. Gamma Function......Page 291
13. Binomial Coefficients......Page 292
15. Bessel Functions J1 (x)......Page 294
17. Bessel Functions Y1 (x)......Page 295
19. Bessel Functions I1 (x)......Page 296
21. Bessel Functions K1 (x)......Page 297
23. Bessel Functions Bei(x)......Page 298
25. Bessel Functions Kei(x)......Page 299
26. Values for Approximate Zeros of Bessel Functions......Page 300
27. Legendre Polynomials Pn (x)......Page 301
28. Legendre Polynomials Pn (cos ?)......Page 302
29. Complete Elliptic Integrals of First and Second Kinds......Page 303
31. Incomplete Elliptic Integral of the Second Kind......Page 304
32. Compound Amount: (1 + r)n......Page 305
33. Present Value of an Amount: (1 + r)-n......Page 306
34. Amount of an Annuity:......Page 307
35. Present Value of an Annuity:......Page 308
36. Areas Under the Standard Normal Curve from -8 to x......Page 309
37. Ordinates of the Standard Normal Curve......Page 310
38. Percentile Values (tp) for Student’s Distribution......Page 311
39. Percentile Values (X2p) for X2(Chi-Square) Distribution......Page 312
40. 95th Percentile Values for the F Distribution......Page 313
41. 99th Percentile Values for the F Distribution......Page 314
42. Random Numbers......Page 315
Index of Special Symbols and Notations......Page 316
C......Page 318
I......Page 319
O......Page 320
S......Page 321
Z......Page 322
