CRC Standard Mathematical Tables and Formulas

✍ Scribed by Zwillinger, Daniel

• Publisher: CRC Press
• Year: 2018
• Tongue: English
• Leaves: 873
• Series: Advances in Applied Mathematics
• Edition: Thirty-third edition
• Category: Library

✦ Synopsis

Chapter 1 Numbers and Elementary Mathematics -- chapter 2 Algebra -- chapter 3 Discrete Mathematics -- chapter 4 Geometry -- chapter 5 Analysis -- chapter 6 Special Functions -- chapter 7 Probability and Statistics -- chapter 8 Scientific Computing -- chapter 9 Mathematical Formulas from the Sciences -- chapter 10 Miscellaneous.;"Containing more than 6,000 entries, CRC Standard Mathematical Tables and Formulas, 33rd Edition continues to provide essential formulas, tables, figures and detailed descriptions. The newest edition of this popular series also features many diagrams, group tables, and integrals that are not available online. This edition also incorporates important topics such as max plus algebra, financial options, pseudospectra, and proof methods. Newly updated topics reflecting new results include coupled analogues, general relativity, radar, and significant equations of mathematics."--Provided by publisher.

✦ Table of Contents

Cover......Page 1
Half Title......Page 2
Title......Page 4
Copyrights......Page 5
Table of Contents......Page 6
Preface......Page 12
Chapter 1. Numbers and Elementary Mathematics......Page 16
1.1 Proofs without words......Page 18
1.2 Constants......Page 20
1.3 Special numbers......Page 28
1.4 Interval analysis......Page 39
1.5 Fractal Arithmetic......Page 40
1.6 Max-Plus Algebra......Page 41
1.7 Coupled-analogues of Functions......Page 42
1.8 Number theory......Page 43
1.9 Series and products......Page 62
Chapter 2. Algebra......Page 82
2.1 Elementary algebra......Page 84
2.2 Polynomials......Page 88
2.3 Vector algebra......Page 93
2.4 Linear and matrix algebra......Page 98
2.5 Abstract algebra......Page 121
Chapter 3. Discrete Mathematics......Page 148
3.1 Sets......Page 150
3.2 Combinatorics......Page 155
3.3 Graphs......Page 166
3.4 Combinatorial design theory......Page 187
3.5 Difference equations......Page 199
Chapter 4. Geometry......Page 206
4.2 Grades and Degrees......Page 208
4.3 Coordinate systems in the plane......Page 209
4.4 Plane symmetries or isometries......Page 215
4.5 Other transformations of the plane......Page 222
4.6 Lines......Page 224
4.7 Polygons......Page 226
4.9 Quadrics......Page 234
4.10 Spherical geometry and trigonometry......Page 239
4.11 Conics......Page 244
4.12 Special plane curves......Page 255
4.13 Coordinate systems in space......Page 264
4.14 Space symmetries or isometries......Page 267
4.15 Other transformations of space......Page 270
4.17 Planes......Page 272
4.18 Lines in space......Page 274
4.19 Polyhedra......Page 276
4.21 Cones......Page 280
4.22 Differential geometry......Page 282
Chapter 5. Analysis......Page 290
5.1 Differential calculus......Page 292
5.2 Differential forms......Page 303
5.3 Integration......Page 306
5.4 Table of indefinite integrals......Page 320
5.5 Table of definite integrals......Page 358
5.6 Ordinary differential equations......Page 365
5.7 Partial differential equations......Page 377
5.8 Integral equations......Page 390
5.9 Tensor analysis......Page 393
5.10 Orthogonal coordinate systems......Page 403
5.11 Real analysis......Page 408
5.12 Generalized functions......Page 418
5.13 Complex analysis......Page 420
5.14 Significant Mathematical Equations......Page 432
Chapter 6. Special Functions......Page 434
6.2 Exponentiation......Page 436
6.4 Logarithmic functions......Page 437
6.5 Trigonometric functions......Page 439
6.6 Circular functions and planar triangles......Page 448
6.7 Tables of trigonometric functions......Page 452
6.8 Angle conversion......Page 455
6.9 Inverse circular functions......Page 456
6.10 Hyperbolic functions......Page 458
6.11 Inverse hyperbolic functions......Page 462
6.12 Gudermannian function......Page 464
6.13 Orthogonal polynomials......Page 466
6.14 Clebsch–Gordan coefficients......Page 473
6.15 Bessel functions......Page 475
6.16 Beta function......Page 484
6.17 Elliptic integrals......Page 485
6.18 Jacobian elliptic functions......Page 488
6.19 Error functions......Page 490
6.20 Fresnel integrals......Page 491
6.21 Gamma function......Page 493
6.22 Hypergeometric functions......Page 496
6.23 Lambert Function......Page 498
6.24 Legendre functions......Page 499
6.25 Polylogarithms......Page 503
6.26 Prolate SpheroidalWave Functions......Page 504
6.27 Sine, cosine, and exponential integrals......Page 505
6.28 Weierstrass Elliptic Function......Page 507
6.29 Integral transforms: List......Page 508
6.31 Fourier integral transform......Page 509
6.32 Discrete Fourier transform (DFT......Page 515
6.34 Multidimensional Fourier transforms......Page 517
6.35 Hankel transform......Page 518
6.36 Hartley transform......Page 519
6.37 Hilbert transform......Page 520
6.38 Laplace transform......Page 523
6.40 Z-Transform......Page 527
6.41 Tables of transforms......Page 532
Chapter 7. Probability and Statistics......Page 548
7.1 Probability theory......Page 550
7.2 Classical probability problems......Page 560
7.3 Probability distributions......Page 568
7.4 Queuing theory......Page 577
7.5 Markov chains......Page 580
7.6 Random number generation......Page 583
7.7 Random matrices......Page 589
7.8 Control charts and reliability......Page 590
7.9 Statistics......Page 595
7.10 Confidence intervals......Page 603
7.11 Tests of hypotheses......Page 610
7.12 Linear regression......Page 624
7.13 Analysis of variance (ANOVA......Page 628
7.14 Sample size......Page 635
7.15 Contingency tables......Page 638
7.16 Acceptance sampling......Page 641
7.17 Probability tables......Page 643
Chapter 8. Scientific Computing......Page 660
8.1 Basic numerical analysis......Page 661
8.2 Numerical linear algebra......Page 674
8.3 Numerical integration and differentiation......Page 683
8.4 Programming techniques......Page 703
Chapter 9. Mathematical Formulas from the Sciences......Page 704
9.1 Acoustics......Page 706
9.2 Astrophysics......Page 707
9.3 Atmospheric physics......Page 709
9.4 Atomic Physics......Page 710
9.5 Basic mechanics......Page 711
9.6 Beam dynamics......Page 713
9.7 Biological Models......Page 714
9.8 Chemistry......Page 715
9.9 Classical mechanics......Page 716
9.10 Coordinate systems – Astronomical......Page 717
9.11 Coordinate systems – Terrestrial......Page 718
9.12 Earthquake engineering......Page 719
9.13 Economics (Macro......Page 720
9.14 Electromagnetic Transmission......Page 722
9.15 Electrostatics and magnetism......Page 723
9.16 Electromagnetic Field Equations......Page 724
9.17 Electronic circuits......Page 725
9.18 Epidemiology......Page 726
9.19 Fluid mechanics......Page 727
9.20 Human body......Page 728
9.21 Modeling physical systems......Page 729
9.22 Optics......Page 730
9.23 Population genetics......Page 731
9.24 Quantum mechanics......Page 732
9.25 Quaternions......Page 734
9.26 Radar......Page 735
9.27 Relativistic mechanics......Page 736
9.28 Solid mechanics......Page 737
9.29 Statistical mechanics......Page 738
9.30 Thermodynamics......Page 739
Chapter 10. Miscellaneous......Page 740
10.1 Calendar computations......Page 742
10.2 Cellular automata......Page 743
10.3 Communication theory......Page 744
10.4 Control theory......Page 749
10.5 Computer languages......Page 751
10.6 Compressive Sensing......Page 752
10.7 Constrained Least Squares......Page 753
10.8 Cryptography......Page 754
10.9 Discrete dynamical systems and chaos......Page 755
10.10 Elliptic curves......Page 758
10.11 Financial formulas......Page 761
10.12 Game theory......Page 769
10.13 Knot theory......Page 772
10.14 Lattices......Page 774
10.15 Logic......Page 776
10.16 Moments of inertia......Page 781
10.17 Music......Page 782
10.18 Operations research......Page 784
10.19 Proof Methods......Page 796
10.20 Recreational mathematics......Page 797
10.21 Risk analysis and decision rules......Page 798
10.22 Signal processing......Page 800
10.23 Units......Page 809
10.24 Voting power......Page 816
10.27 Morse code......Page 818
10.28 Bar Codes......Page 819
List of References......Page 820
List of Figures......Page 824
List of Notations......Page 826
Index......Page 834

✦ Subjects

Mathematical analysis;Mathematics;Electronic books;Mathematical formulae;Mathematics -- Formulae