Bartsch Handbook of Mathematical Formulas

1. Auflage 2014
ISBN: 978-1-4832-6742-5
Verlag: Elsevier Science & Techn.
Format: PDF
Kopierschutz: 1 - PDF Watermark

E-Book, Englisch, 528 Seiten, Web PDF

Handbook of Mathematical Formulas presents a compilation of formulas to provide the necessary educational aid. This book covers the whole field from the basic rules of arithmetic, via analytic geometry and infinitesimal calculus through to Fourier's series and the basics of probability calculus. Organized into 12 chapters, this book begins with an overview of the fundamental notions of set theory. This text then explains linear expression wherein the variables are only multiplied by constants and added to constants or expressions of the same kind. Other chapters consider a variety of topics, including matrices, statistics, linear optimization, Boolean algebra, and Laplace's transforms. This book discusses as well the various systems of coordinates in analytical geometry. The final chapter deals with algebra of logic and its development into a two-value Boolean algebra as switching algebra. This book is intended to be suitable for students of technical schools, colleges, and universities.

Autoren/Hrsg.

Bartsch, Hans-Jochen

Inhaltsverzeichnis

1;Front Cover;1
2;Handbook of Mathematical Formulas;4
3;Copyright Page;5
4;Table of Contents;8
5;PREFACE;6
6;Chapter 0. Mathematical Signs and Symbols;16
6.1;0.1. Mathematical signs;16
6.2;0.2. Symbols used in the theory of sets;18
6.3;0.3. Symbols of logic;18
7;Chapter 1. Arithmetic;19
7.1;1.1. Set theory;19
7.2;1.2. Real numbers;21
7.3;1.3. Imaginary or complex numbers;26
7.4;1.4. Proportions;38
7.5;1.5. Logarithms;40
7.6;1.6. Combinatoric analysis;44
7.7;1.7. Per cent calculation, interest calculation;47
7.8;1.8. Sequences and series;49
7.9;1.9. Determinants;58
7.10;1.10. Matrices;67
8;Chapter 2. Equations, functions, vectors;80
8.1;2.1. Equations;80
8.2;2.2. Inequalities;103
8.3;2.3. Functions;104
8.4;2.4. Vector calculus;118
8.5;2.5. Reflection in a circle, inversion;131
9;Chapter 3. Geometry;135
9.1;3.1. General;135
9.2;3.2. Planimetry;141
9.3;3.3. Stereometry;157
9.4;3.4. Goniometry, plane trigonometry, hyperbolic functions;170
9.5;3.5. Spherical trigonometry;205
10;Chapter 4. Analytical geometry;215
10.1;4.1. Analytical geometry of the plane;215
10.2;4.2. Analytical geometry of space;258
11;Chapter 5. Differential calculus;280
11.1;5.1. Limits;280
11.2;5.2. Difference quotient, differential quotient, differential;282
11.3;5.3. Rules for differentiation;284
11.4;5.4. Derivatives of the elementary functions;290
11.5;5.5. Differentiation of a vector function;293
11.6;5.6. Graphical differentiation;294
11.7;5.7. Extrema of functions (maxima and minima);294
11.8;5.8. Mean-value theorems;300
11.9;5.9. Indeterminate expressions;301
12;Chapter 6. Differential geometry;304
12.1;6.1. Plane curves;304
12.2;6.2. Space curves;321
12.3;6.3. Curved surfaces;329
13;Chapter 7. Integral calculus;331
13.1;7.1. Definition of the indefinite integral;331
13.2;7.2. Basic integrals;331
13.3;7.3. Rules of integration;332
13.4;7.4. A few special integrals;342
13.5;7.5. Definite integral;359
13.6;7.6· Line integral;378
13.7;7.7. Multiple integrals;381
14;Chapter 8. Differential equations;390
14.1;8.1, General;390
14.2;8.2. Ordinary differential equations of the first order;394
14.3;8.3. Ordinary differential equations of the second order;403
14.4;8.4. Ordinary differential equations of the third order;419
14.5;8.5. Integration of differential equations by power series;420
14.6;8.6. Partial differential equations;422
15;Chapter 9. Infinite series, Fourier series, Fourier integral, Laplace transformation;426
15.1;9.1. Infinite series;426
15.2;9.2. General statements on Fourier series, Fourier integrals, and Laplace transforms;437
15.3;9.3. Fourier series;440
15.4;9.4. Fourier integral, example of calculation;451
15.5;9.5. Laplace transforms;452
15.6;9.6. Employment of Laplace transforms; solution of differential equations;456
15.7;9.7. Table of correspondences of some rational Laplace integrals;461
16;Chapter 10. Theory of probability; statistics; error calculation; mathematical analysis of observations;464
16.1;10.1. Theory of probability;464
16.2;10.2. Statistics;469
16.3;10.3. Error calculations;474
16.4;10.4. Calculus of observations;475
17;Chapter 11. Linear Optimization;482
17.1;11.1. General;482
17.2;11.2. Graphical procedure;484
17.3;11.3. Simplex procedure (simplex algorithm);486
17.4;11.4. Simplex table;492
18;Chapter 12. Algebra of logic (Boolean algebra);494
18.1;12.1. General;494
18.2;12.2. Arithmetical laws, arithmetical rules;496
18.3;12.3. Further possibilities of interconnecting two input variables (lexigraphic order);497
18.4;12.4. Normal forms;499
18.5;12.5. Karnaugh tables;501
19;APPENDIX;504
20;Index;510