Handbook of Mathematical Formulas (eBook)

Front Cover 1
Handbook of Mathematical Formulas 4
Copyright Page 5
Table of Contents 8
PREFACE 6
Chapter 0. Mathematical Signs and Symbols 16
0.1. Mathematical signs 16
0.2. Symbols used in the theory of sets 18
0.3. Symbols of logic 18
Chapter 1. Arithmetic 19
1.1. Set theory 19
1.2. Real numbers 21
1.3. Imaginary or complex numbers 26
1.4. Proportions 38
1.5. Logarithms 40
1.6. Combinatoric analysis 44
1.7. Per cent calculation, interest calculation 47
1.8. Sequences and series 49
1.9. Determinants 58
1.10. Matrices 67
Chapter 2. Equations, functions, vectors 80
2.1. Equations 80
2.2. Inequalities 103
2.3. Functions 104
2.4. Vector calculus 118
2.5. Reflection in a circle, inversion 131
Chapter 3. Geometry 135
3.1. General 135
3.2. Planimetry 141
3.3. Stereometry 157
3.4. Goniometry, plane trigonometry, hyperbolic functions 170
3.5. Spherical trigonometry 205
Chapter 4. Analytical geometry 215
4.1. Analytical geometry of the plane 215
4.2. Analytical geometry of space 258
Chapter 5. Differential calculus 280
5.1. Limits 280
5.2. Difference quotient, differential quotient, differential 282
5.3. Rules for differentiation 284
5.4. Derivatives of the elementary functions 290
5.5. Differentiation of a vector function 293
5.6. Graphical differentiation 294
5.7. Extrema of functions (maxima and minima) 294
5.8. Mean-value theorems 300
5.9. Indeterminate expressions 301
Chapter 6. Differential geometry 304
6.1. Plane curves 304
6.2. Space curves 321
6.3. Curved surfaces 329
Chapter 7. Integral calculus 331
7.1. Definition of the indefinite integral 331
7.2. Basic integrals 331
7.3. Rules of integration 332
7.4. A few special integrals 342
7.5. Definite integral 359
7.6· Line integral 378
7.7. Multiple integrals 381
Chapter 8. Differential equations 390
8.1, General 390
8.2. Ordinary differential equations of the first order 394
8.3. Ordinary differential equations of the second order 403
8.4. Ordinary differential equations of the third order 419
8.5. Integration of differential equations by power series 420
8.6. Partial differential equations 422
Chapter 9. Infinite series, Fourier series, Fourier integral, Laplace transformation 426
9.1. Infinite series 426
9.2. General statements on Fourier series, Fourier integrals, and Laplace transforms 437
9.3. Fourier series 440
9.4. Fourier integral, example of calculation 451
9.5. Laplace transforms 452
9.6. Employment of Laplace transforms solution of differential equations
9.7. Table of correspondences of some rational Laplace integrals 461
Chapter 10. Theory of probability statistics
10.1. Theory of probability 464
10.2. Statistics 469
10.3. Error calculations 474
10.4. Calculus of observations 475
Chapter 11. Linear Optimization 482
11.1. General 482
11.2. Graphical procedure 484
11.3. Simplex procedure (simplex algorithm) 486
11.4. Simplex table 492
Chapter 12. Algebra of logic (Boolean algebra) 494
12.1. General 494
12.2. Arithmetical laws, arithmetical rules 496
12.3. Further possibilities of interconnecting two input variables (lexigraphic order) 497
12.4. Normal forms 499
12.5. Karnaugh tables 501
APPENDIX 504
Index 510