This article is devoted to testing radio components (transistors, diodes, capacitors, etc.) and was published in connection with many requests to me on this matter.
How to check radio components
To check the serviceability of radio components, you will need a measuring device - a multimeter. It is better not to purchase cheap Chinese consumer goods, which not only quickly fail, but are also significantly limited in capabilities due to low current. Ideally, the multimeter should be powered by a Krona battery.
Resistor
With the naked eye you can identify a burnt out resistor - it will turn black. Even if the required resistance remains on it, it should be replaced.
To check, put the multimeter in ohmmeter mode. Then we connect the probes (the polarity does not matter) to the resistor terminals and compare the measured resistance with the nominal one. The value is indicated either on the board or on the resistor itself. Some resistors are marked not with numbers, but with multi-colored stripes, decipherable according to a simple scheme. Deviations within 5% of the nominal value are considered normal.
Capacitor
Just like a resistor, it can visually indicate a malfunction. The capacitor may swell or even explode and leak. It's easy to notice. In this case, no measurements are required - the part is subject to unconditional replacement.
Another simple capacitor test is to check the integrity of the contacts. To do this, the “legs” of the capacitor need to be slightly bent, and then try to turn them or pull them out. If there is even minimal play, the capacitor is faulty.
In other cases, the capacitor is checked with an ohmmeter. The resistance value should be equal to infinity. If not, replace it.
Diode
A diode conducts current in one direction and does not conduct in the opposite direction. It is easy to check this with a dial multimeter in ohmmeter mode. The positive probe goes to the anode, the negative probe goes to the cathode. In this position, current must pass. If you swap the probes, the measurement result will be equivalent to an open circuit.
The digital multimeter is placed in a special diode testing mode. The fixed voltage on a germanium diode should be in the region of 200-300 mV, on a silicon diode - 550 - 700. If the voltage exceeds 2000 mV, the diode is faulty.
Transistor
Bipolar
The easiest way is to imagine a transistor in the form of two “counter” diodes. The test must be appropriate: base-emitter and base-collector. The current must flow in one direction, but not in the other.
The emitter-collector junction should not ring at all! If current flows without voltage at the base, the transistor must be discarded.
Field
Before checking, it is necessary to short-circuit all contacts to discharge the gate capacitance. After this, the ohmmeter should record a resistance equal to infinity at all terminals. Otherwise, the part must be replaced.
Zener diode
Checking the zener diode is a more delicate process. It is not recommended to use a digital multimeter here - it can easily “pierce” a serviceable part in both directions. If you have an analog tester, you can check it in the same way as a diode. If not, yes various ways checks. Let's describe the simplest one.
You will need a power supply with voltage regulation. We connect a resistor with a resistance of 300-500 Ohms to the anode, then connect the power supply. We measure the voltage on the zener diode, raising its value on the power supply. Having reached a certain value (it is better if it is known in advance - stabilization voltage), the voltage should stop growing. If it continues, change the zener diode.
Thyristor
The positive ohmmeter probe goes to the anode, the negative probe goes to the cathode. The resistance must be infinity. If you touch the control electrode to the anode, a resistance of about 100 Ohms should be detected. When the UE is disconnected, this value must remain fixed. If the result at any of these steps is different from what is described, the thyristor must be replaced.
Inductor
The simplest breakdown - a break - can be easily determined with an ohmmeter. There must be resistance. As a rule, several hundred ohms. If the value goes to infinity, it means a break has occurred.
The situation is more complicated with the closure of the turns. As a rule, it is almost impossible to determine it - all methods are imperfect. Therefore, it is better to leave the coil for last, when all other parts are absolutely in good condition, and simply replace it, according to the elimination method.
So you go to the kettle to celebrate with the thought of slamming a mug of tea with a steering wheel in honor of the device you just assembled, but it suddenly stopped working. In this case, there are no visible reasons: the capacitors are intact, the transistors do not seem to smoke, and the diodes too. But the device does not work. What should I do? You can use this simple algorithm troubleshooting:
Installation "snot"
“Snot” is a small drop of solder that creates a short circuit between two different traces on a printed circuit board. During home assembly, such unpleasant drops of solder lead to the fact that the device either simply does not start, or does not work correctly, or, worst of all, expensive parts immediately burn out after switching on.
To avoid such unpleasant consequences, before turning on the assembled device, you should carefully check the printed circuit board for short circuits between the tracks.
Device diagnostic devices
The minimum set of instruments for setting up and repairing amateur radio structures consists of, a multimeter and. In some cases, you can only get by with a multimeter. But for more convenient debugging of devices, it is still advisable to have oscilloscope.
For simple devices, this set is enough. As for, for example, debugging various amplifiers, then in order to configure them correctly it is advisable to also have signal generator.
Proper nutrition is the key to success
Before drawing any conclusions about the performance of the parts included in your amateur radio design, you should check whether the correct power is supplied. Sometimes it turns out that the problem was due to poor nutrition. If you start checking the device with its power supply, you can save a lot of time on debugging if the problem was in it.
Diode check
If there are diodes in the circuit, then they should be carefully checked one by one. If they are apparently intact, then you should unsolder one terminal of the diode and check it with a multimeter turned on in resistance measurement mode. Moreover, if the polarity of the multimeter terminals coincides with the polarity of the diode terminals (+ terminal to the anode, and - terminal to the cathode), then the multimeter will show approximately 500-600 Ohms, and in reverse connection (- terminal to the anode, and + terminal to the cathode) not It will show nothing at all, as if there is a break there. If the multimeter shows something else, then most likely the diode is faulty and unusable.
Checking capacitors and resistors
Burnt resistors can be seen immediately - they turn black. Therefore, finding a burnt resistor is quite easy. As for capacitors, checking them is more difficult. First, as in the case of resistors, you need to inspect them. If they do not outwardly cause suspicion, then they should be unsoldered and checked using an LRC meter. Electrolytic capacitors usually fail. At the same time, they swell when they burn. Another reason for their failure is time. Therefore, in older devices, all electrolytic capacitors are often replaced.
Checking transistors
Transistors are tested similarly to diodes. First, an external inspection is carried out and if it does not cause suspicion, the transistor is checked using a multimeter. Only the multimeter terminals are connected alternately between the base-collector, base-emitter and collector-emitter. By the way, transistors have an interesting malfunction. When checked, the transistor is normal, but when it is connected to the circuit and power is supplied to it, after a while the circuit stops working. It turns out that the transistor has heated up and in a heated state behaves as if it were broken. This transistor should be replaced.
To a schoolchild about the theory of probability. Lyutikas V.S.
Tutorial By elective course for students in grades 8-10.
2nd ed., add. -M.; Enlightenment, 1983.-127 p.
The purpose of this manual is to outline the most basic information from probability theory, to teach young reader apply them when deciding practical problems.
Format: djvu/zip
Size: 1.7 MB
/Download file
TABLE OF CONTENTS
A word to the reader......................
I. Something from the past of probability theory............. 4
II. Random events and operations on them.............. 10
1. Random event................... -
2. Lots elementary events............ 12
3. Relationships between events............... -
4. Operations on events.................. 14
5. Full group events........................ 21
III. The science of counting the number of combinations - combinatorics... 22
1. General rules combinatorics............... 23
2. Selections of elements................... 24
3. Samples with repetitions.................... 28
4. Complex combinatorics................................. 32
IV. Probability of an event...................... 35
V. Operations on probabilities................................ 42
1. Probability of the sum of incompatible events......... -
2. Probability of the sum of compatible events.......... 44
3. Conditional probabilities......................... 46
4. Product probability independent events....... 48
5. Formula full probability............... 50
VI. Independent retests.........55
1. J. Bernoulli’s formula................. -
2. Moivre-Laplace formula........................ 60
3. Poisson's formula.................... 62
4. Laplace's formula.................... 65
VII. Discrete random variables and their characteristics.. 68
1. Expectation................ 70
2. Variance................................... 76
3. Chebyshev’s inequality and law large numbers....... 80
4. Poisson distribution................... 84
VIII. Continuous random variables and their characteristics. 88
1. Distribution density................90
2. Mathematical expectation................93
3. Dispersion................................... 95
4. Normal distribution................ -
5. The concept of Lyapunov’s theorem................... 98
6. Exponential distribution.............. 102
IX. A little strange, but interesting.......... 104
1. Smart needle (Buffon problem) ............... -
2. Chevalier de Mere's problem.................................. 106
3. Give me my hat................... 108
4. Meteorological paradox 110
5. To keep customers happy............ -
6. Bertrand's paradox...... 111
7. Randomness or system?................................. 11З
8. The crime is solved................... 114
9. "Battle" ...................... 115
10. Visiting grandfather.................................... 116
References........................ 118
Appendix........................... 119
Answers........................... 125
All books can be downloaded for free and without registration.
NEW. Korolyuk V.S., Portenko N.I., Skorokhod A.V. Turbin A.F. Handbook of probability theory and mathematical statistics. 2nd ed. reworked add. 1985 640 pp. djvu. 13.2 MB.
The reference book is an expanded and revised edition of the book “Handbook of Probability Theory and Mathematical Statistics” edited by V. S. Korolyuk, published in 1978 by the Naukova Dumka publishing house. By the breadth of coverage of main ideas, methods and specific results modern theory probabilities, theories random processes and partly mathematical statistics "Handbook" is the only publication of its kind.
For scientists and engineers.
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NEW. F. Mosteller, R. Rourke, J. Thomas. Probability. 1969 432 pp. pdf. 12.6 MB.
This book, written by a group of famous American mathematicians and educators, is an elementary introduction to probability theory and statistics - branches of mathematics that are now increasingly greater application in science and practical activities. Written by the living and bright language, it contains many examples taken mostly from the sphere of everyday life. Despite the fact that a high school level of mathematics is sufficient to read the book, it is a completely correct introduction to probability theory. I read in this book what I had never seen in others.
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Andronov A.M., Kopytov E.A., Gringlaz L.Ya. Probability theory and mathematical statistics. 2004 460 pp. djvu. 6.7 MB.
From the publisher:
Here is an extended textbook on probability theory and mathematical statistics. The traditional material is supplemented with such questions as the probabilities of combinations of random events, random walks, linear transformations random vectors, numerical determination of non-stationary probabilities of states of discrete Markov processes, application of optimization methods to solve problems of mathematical statistics, regression models. The main difference between the proposed book and well-known textbooks and monographs on probability theory and mathematical statistics is its focus on constant use personal computer when studying the material. The presentation is accompanied by numerous examples of solving the problems under consideration in the environment of the Mathcad and STATISTICA packages. The book is written on the basis of more than thirty years of experience of the authors in teaching the disciplines of probability theory, mathematical statistics and the theory of random processes for students of various higher specialties educational institutions. It is of practical interest both for students and university teachers, and for anyone interested in the application of modern probabilistic and statistical methods.
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Agekyan. Probability theory for astronomers and physicists. 260 pages. Size 1.7 MB. The book contains material so that physicists and astronomers can use it when processing measurement results. Useful book when calculating errors.
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I.I. Bavrin. Probability theory, mathematical statistics. 2005 161 pp. djv. 1.7 MB.
The fundamentals of probability theory and mathematical statistics are outlined in application to physics, chemistry, biology, geography, ecology, and exercises are given for independent work All basic concepts and provisions are illustrated with analyzed examples and tasks
For students of natural sciences pedagogical universities Can be used by students of other universities
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Borodin A. N. Elementary course in the theory of probability and mathematical statistics. 1999 224 pp. djvu. 3.6 MB.
The textbook contains a systematic presentation of the main sections elementary course probability theory and mathematical statistics. One new section has been added to the traditional sections - “Recurrent Estimation Procedure”, due to the special importance of this procedure for applications. Theoretical material is accompanied a large number examples and problems from different areas knowledge.
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Bocharov P. P., Pechinkin A. V. Probability theory. Mathematical statistics. 2005 296 pp. djvu. 2.8 MB.
The first part examines the basic concepts of probability theory, using relatively simple mathematical constructions, but, nevertheless, the presentation is based on axiomatic construction, proposed by academician A. N. Kolmogorov. The second part outlines the basic concepts of mathematical statistics. The most common assessment problems are considered unknown parameters and testing statistical hypotheses and describes the main methods for solving them. Each of the above provisions is illustrated with examples. The material presented generally corresponds to the state educational standard.
Students, graduate students and university teachers, researchers in various specialties and those wishing to get a first idea of probability theory and mathematical statistics.
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V.N. Vapnik. Recovering dependencies from empirical data. 1979 449 pp. djvu. 6.3 MB.
The monograph is devoted to the problem of recovering dependencies based on empirical data. It examines the method of minimizing risk on samples of limited volume, according to which, when restoring a functional dependence, one should choose a function that satisfies a certain compromise between the value characterizing its “complexity” and the value characterizing the degree of its approximation to the totality of empirical data. The application of this method to three main problems of dependency recovery is considered: the problem of learning pattern recognition, regression recovery, and interpretation of the results of indirect experiments. It is shown that taking into account the limited volume of empirical data allows solving problems of pattern recognition with a large dimension of the feature space, restoring regression dependencies in the absence of a model of the function being restored, and obtaining stable solutions to ill-posed problems of interpreting the results of indirect experiments. The corresponding dependency recovery algorithms are presented.
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A.I. Volkovets, A.B Gurinovich. Probability theory and mathematical statistics. Lecture notes. 2003 84 pp. PDF. 737 KB.
Lecture notes for the course “Probability Theory and Mathematical Statistics” include 17 lectures on topics defined by the standard work program studying this discipline. The purpose of the study is to master the basic methods of formalized description and analysis random phenomena, processing and analysis of the results of physical and numerical experiments. To study this discipline, the student needs the knowledge gained from studying the sections “Series”, “Sets and operations on them”, “Differential and integral calculus” of the course higher mathematics.
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Volodin. Lectures on probability theory and mathematical statistics. 2004 257 pages. Size 1.4 MB. PDF. The theory focuses on methods for constructing probabilistic models and the implementation of these methods on real problems natural sciences. Statistics focuses on methods for calculating the risk of specific statistical rules.
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Ventzel, Ovcharov. Probability theory and its engineering applications. 2000 480 pp. djvu. 10.3 MB.
The book provides a systematic presentation of the foundations of probability theory from the point of view of their practical applications in specialties: cybernetics, applied mathematics, computers, automated control systems, theory of mechanisms, radio engineering, reliability theory, transport, communications, etc. Despite the variety of areas to which the applications relate, they are all imbued with a single methodological basis.
For students of higher technical educational institutions. It may be useful for teachers, engineers and scientists of various profiles who, in their practical activities, are faced with the need to pose and solve problems related to the analysis of random processes.
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Ventzel, Ovcharov. Probability theory. 1969 365 pp. djvu. 8.3 MB.
The book is a collection of tasks and exercises. All problems have an answer, and most have solutions.
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N. Y. VILENKIN, V. G. POTAPOV. PRACTICAL PROBLEM ON PROBABILITY THEORY WITH ELEMENTS OF COMBINATORICS AND MATHEMATICAL STATISTICS. Textbook. 1979 113 pp. djvu. 1.3 MB.
The book brought to the attention of the reader is a practical problem book for the course “Probability Theory”. The problem book consists of three chapters, which in turn are divided into paragraphs. At the beginning of each paragraph, the main theoretical information, then detailed typical examples are given and, finally, tasks for independent decision, complete with answers and directions. The book also contains texts laboratory work, the implementation of which will help the part-time student to better understand the basic concepts of mathematical statistics.
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Gmurman. Probability theory and mathematical statistics. 2003 480 pp. DJVU. 5.8 MB.
The book contains basically all the program material on probability theory and mathematical statistics. Much attention devoted to statistical methods for processing experimental data. At the end of each chapter there are problems with answers. Intended for university students and individuals using probabilistic and statistical methods when solving practical problems.
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Kolmogorov. Probability theory. Size 2.0 MB.
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Kibzun et al. Probability theory and mathematical statistics. Uch. allowance. Basic course with examples and tasks. Size 1.7 MB. djvu. 225 pp.
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M. Katz. Statistical independence in probability theory, analysis and number theory. 152 pages djv. 1.3 MB.
The book presents in a very accessible and in a fun way application of some ideas of probability theory in other areas of mathematics. The bulk of the book is devoted to the concept of statistical independence.
The book will be useful and interesting for students, mathematicians, physicists, and engineers.
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M. Katz. Probability and related issues in physics. 408 pp. djv. 3.8 MB.
The author is familiar to Soviet readers from the translation of his work “Statistical independence in probability theory, analysis and number theory” (IL, 1963). His new book mainly dedicated to one of the the most interesting tasks physics: describe how a system of very large number particles (gas in a vessel) comes to a state of equilibrium, and explain how the irreversibility of this process in time is consistent with the reversibility in time original equations. Most attention focuses on the probabilistic aspect of the problem; statistical models that simulate the main features of the problem are considered. The first two chapters are also of independent interest - using well-chosen examples, the author shows how the concept of probability arises in mathematical and physical problems and what analytical apparatus is used by probability theory. This edition includes articles by Katz and other authors related to the issues raised in the book.
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Kendall. Stewart. Multidimensional statistical analysis and time series. 375 pp. DJVU. 8.2 MB.
The book is the last volume three-volume course of statistics by M. Kendall and A. Stewart, the first volume of which was published in 1966 under the title “Theory of Distributions:”, and the second in 1973 under the title “Statistical Inferences and Connections”.
The book contains information on analysis of variance, experimental design, sampling theory, multivariate analysis, and time series.
Like the first two volumes, the book contains a lot practical recommendations and examples of their application, and the presentation combines a more or less detailed summary of the main results with a relatively brief listing large quantity more private information.
The book will be of interest to undergraduate and graduate students specializing in the field of mathematical statistics, as well as to wide range scientists dealing with its applications.
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Kendall. Stewart. THEORY OF DISTRIBUTIONS. Volume 1. 590 pp. 10.3 MB. 6.1 MB.
Contents: Frequency distributions. Measures of location and dispersion. Moments and semi-invariants. Characteristic functions. Standard distributions. Probability calculus. Probability and statistical inference. Random selection. Standard errors. Exact sampling distributions. Approximation of sample distributions. Approximation of sample distributions. Ordinal statistics. Multivariate normal distribution and quadratic forms. Distributions associated with normal.
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Kendall. Stewart. STATISTICAL FINDINGS AND CONNECTIONS. Volume 2. 900 pp. djvu. 10.3 MB.
The book contains information on estimation theory, hypothesis testing, correlation analysis, regression, nonparametric methods, and sequential analysis.
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N.Sh. Kremer. Probability theory and mathematical statistics. Textbook. 2nd ed., revised. add. 2004 575 pp. djvu. 12.2 MB.
This is not only a textbook, but also quick guide to solving problems. The fundamentals of probability theory and mathematical statistics presented are accompanied by a large number of problems (including economic ones), presented with solutions and for independent work. In this case, the emphasis is on the basic concepts of the course, their theoretical and probabilistic meaning and application. Examples are given of the use of probabilistic and mathematical-statistical methods in problems queuing and financial market models.
For undergraduate and graduate students of economic specialties and areas, as well as university teachers, researchers and economists.
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Kobzar A.I. Applied mathematical statistics. For engineers and scientists. 2006 814 pp. djvu. 7.7 MB.
The book discusses ways to analyze observations using mathematical statistics methods. Consistently, in a language accessible to a specialist - not a mathematician, are presented modern methods analyzing probability distributions, estimating distribution parameters, testing statistical hypotheses, assessing relationships between random variables, planning a statistical experiment. The main attention is paid to explaining examples of the application of methods of modern mathematical statistics.
The book is intended for engineers, researchers, economists, doctors, graduate students and students who want to quickly, economically and at a high professional level use the entire arsenal of modern mathematical statistics to solve your applied problems.
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M.L. Krasnov. Probability theory. Textbook. 2001 296 pp. djvu. 3.9 MB.
When studying various phenomena in nature and society, the researcher is faced with two types of experiments - those whose results are unambiguously predicted under given conditions, and those whose results under conditions controlled by the researcher cannot be unambiguously predicted, but one can only make an assumption about the range of possible results. In the first case, we talk about deterministic phenomena, in the second, about phenomena that are random in nature. At the same time, they mean that a priori (in advance, before conducting an experiment or completing observation of a phenomenon), in the first case we are able to predict the result, but in the second - not. For what follows, it is unimportant what causes such unpredictability - the laws of nature underlying the phenomenon being studied or the incompleteness of information about the processes causing this phenomenon. An important circumstance is the presence of the very fact of unpredictability. The theory of probability, the foundations of which this section is devoted to, is intended to give the researcher the opportunity to describe such experiments and phenomena and provides him with reliable tool to study reality in situations where deterministic description is impossible.
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E.L. Kuleshov. Probability theory. Lectures for physicists. 2002 116 pp. djvu. 919 KB.
For senior students.
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Lazakovich, Stashulenok, Yablonsky. Probability theory course. Study guide. 2003 322 pp. PDF. 2.9 MB.
The textbook is based on a year-long course of lectures, which the authors read for a number of years for students of the Faculty of Mechanics and Mathematics of the Belarusian State University. state university. The book contains the following sections: probability spaces, independence, random variables, numerical characteristics random variables characteristic functions, limit theorems, fundamentals of the theory of random processes, elements of mathematical statistics and applications that contain tables of basic probability distributions and the values of some of them. Most chapters include appendices that include auxiliary material and topics for self-study.
The presentation is accompanied by a large number of examples, exercises and problems that illustrate the basic concepts and explain possible applications proven statements.
For university students of mathematical specialties.
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Loev M. Theory of Probability. 1962 449 pp. djvu. 6.2 MB.
The book is an extensive systematic course in modern probability theory, written in a high theoretical level. Based on measure theory, the author studies random events, random variables and their sequences, distribution functions and characteristic functions, limit theorems of probability theory and random processes. The presentation is accompanied by a large number of tasks varying degrees difficulties.
A book for undergraduate and graduate students of mathematics studying theory.
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Lvovsky B.N. Statistical construction methods empirical formulas: Textbook. allowance. 2nd ed., revised. add. 1988 239 pp. djvu. 2.3 MB.
The 2nd edition of the manual outlines the main methods for processing experimental data. Methods for preliminary processing of observation results are described in detail. Statistical methods for constructing empirical formulas, the maximum likelihood method, the method of averages and cofluent analysis are considered. The methodology for planning and processing active experiments is covered. Basics given analysis of variance.
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Yu.D. Maksimov editor. Probabilistic branches of mathematics. Textbook. 2001 581 pp. djvu. 7.4 MB.
Sections: !. Probability theory. 2. Mathematical statistics. 3. Theory of random processes. 4. Queuing theory.
Textbook for bachelors of technical science.
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Maksimov Yu.D. Mathematics. Vishusk 9. Probability theory. Detailed outline. Handbook of One-Dimensional continuous distributions. 2002 98 pp. djv. 4.3 MB.
The manual complies with the state educational standard and the current programs of the discipline “Mathematics” for bachelor’s training in all general technical and economic areas. It is a detailed lecture notes on probability theory, basically corresponding to the reference notes (issue 7 of the series supporting notes in mathematics, published by SPBPU publishing house). In contrast to the basic synopsis, here are proofs of theorems and derivations of formulas omitted in the basic synopsis, and a reference book on one-dimensional continuous distributions is given. The manual is intended for students of the Bоporo course of general technical faculties and economic specialties. Can also be used to direct " Technical physics».
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J. Neveu. Mathematical Basics probability theory. 1969 310 pp. djv. 3.0 MB.
The author of the book is known for his work on the application of methods of functional analysis and measure theory to problems in probability theory. This masterfully written book contains a compact and at the same time complete presentation of the foundations of probability theory. Lots included useful additions and exercises.
The book can serve good textbook for undergraduate and graduate students who want to seriously study the theory of random processes, and an excellent reference for specialists.
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D.T. Writing. Lecture notes on probability theory and mathematical statistics. 2004 256 pp. djvu. 1.4 MB.
This book is a course of lectures on probability theory and mathematical statistics. The first part of the book contains basic concepts and theorems of probability theory, such as random events, probability, random functions, correlation, conditional probability, the law of large numbers and limit theorems. The second part of the book is devoted to mathematical statistics, it outlines the fundamentals of the sampling method, estimation theory and hypothesis testing. Presentation theoretical material accompanied by a consideration of a large number of examples and problems, conducted in accessible, as strict as possible, language.
Designed for students of economics and technical universities.
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Poddubnaya O.N. Lectures on probability theory. 2006 125 pp. pdf. 2.0 MB.
Clearly written. The advantages of the course, for example, include the fact that theoretical statements are explained with examples.
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Yu.V. Prokhorov, Yu.A. Rozanov. Probability theory. Basic concepts. Limit theorems. Random processes. 1967 498 pp. djvu. 7.6 MB.
The book was written by famous American mathematicians and is dedicated to one of the important modern trends probability theory, which is not sufficiently reflected in the literature in Russian. The authors gravitate toward meaningful results rather than maximum generality; they consider a number of examples and applications. The book successfully combines high scientific level presentation and at the same time accessibility for the student audience.
For specialists in probability theory, physicists, engineers, graduate students and university students.
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Poincaré A. Theory of Probability. 1999 284 pp. djv. 700 KB.
The book is one of the parts of a course of lectures by A. Poincaré. It discusses how general basics probability theory and non-traditional questions that are practically not contained in any course. Various applications to physics, mathematics and mechanics are considered.
The book is useful to a wide range of readers - physicists, mathematicians, historians of science.
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Pytyev Yu. P. Shishmarev I. A. Course in probability theory and mathematical statistics for physicists. Textbook allowance. Moscow State University 1983. 256 pp. djvu. 4.6 MB.
The book is based on a six-month course of lectures, readable by authors at the Faculty of Physics. Much attention is paid to the theory of random processes: Markov and stationary. The presentation is mathematically rigorous, although not based on the use of the Lebesgue integral. The part of the course devoted to mathematical statistics contains sections focused on applications to automation problems, planning, analysis and interpretation physical experiments. The statistical theory of the measuring and computing complex “device + computer” is presented, which makes it possible to significantly improve the parameters of real experimental equipment by processing data on a computer. Includes elements of the theory of statistical hypothesis testing used in the task of interpreting experimental data.
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Savelyev. Elementary theory probabilities. Textbook, Novosibirsk State University, 2005.
Part 1 is devoted to theory. Size 660 KB. Part 2 is devoted to the analysis of examples. Size 810 KB. Part 3. Riemann and Stieltjes integrals. 240 pp. djvu. 5.0 MB. Part 3 of the manual describes in detail the elements of differential and integral calculus, which were used in part I. Material from the author’s manuals “Lectures on mathematical analysis, 2.1" (Novosibirsk, NSU, 1973) and "Integration of uniformly measurable functions" (Novosibirsk, NSU, 1984). The main object is the Stieltjes integral. It is defined as a bounded linear functional on the space of functions without complex discontinuities, which was discussed in Part 1. The Stieltjes integral is widely used not only in probability theory, but also in geometry, mechanics and other areas of mathematics. The appendix in part 3 of the manual complements the appendix in part 2. For completeness of presentation, some passages from part 1 are repeated in part 3. The appendix retains the numbering of pages and paragraphs in the manual by the author of “Lectures on Mathematical Analysis”.
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Savrasov Yu.S. Optimal solutions. Lectures on measurement processing methods. 2000 153 pp. djvu. 1.1 MB.
Methods for processing measurements that provide the most complete extraction are considered. useful information about measured parameters or observed phenomena. The methods presented relate to the field of probability theory, mathematical statistics, decision theory, utility theory, filtering theory for dynamic systems with discrete time. The book's material is based on lectures that the author gave in 1994-1997. third year students basic department"Radiophysics" Moscow Institute of Physics and Technology. In the form presented, the book will be useful to students of physics and technical specialties, engineers in the field of radar, information processing and automated systems management.
Many examples have been discussed.
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Samoilenko N.I., Kuznetsov A.I., Kostenko A.B. Probability theory. Textbook. 2009 201 pp. PDF. 2.1 MB.
The textbook introduces the basic concepts and methods of probability theory. The methods given are illustrated typical examples. Every topic ends practical section for independent acquisition of skills in using methods of probability theory in solving stochastic problems.
For students of higher educational institutions.
Examples from the textbook: tossing a coin - experience, falling heads or tails - events; drawing a card from a preference deck - experience, the appearance of a red or black suit - events; holding a lecture is an experience; the presence of a student at a lecture is an event.
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Székely. Paradoxes of probability theory and mathematical statistics. Size 3.8 MB. djv. 250 pp.
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Sevastyannov B.A. Course on probability theory and mathematical statistics. Textbook. 1982 255 pp. djvu. 2.8 MB.
The book is based on a year-long course of lectures given by the author over a number of years at the mathematics department of the Faculty of Mechanics and Mathematics of Moscow State University. Basic concepts and facts of probability theory are introduced initially for the final scheme. Mathematical expectation in general case is defined in the same way as the Lebesgue integral, but the reader is not assumed to have any prior knowledge of Lebesgue integration.
The book contains the following sections: independent tests and Markov chains, limit theorems of Moivre - Laplace and Poisson, random variables, characteristic and generating functions, the law of large numbers, central limit theorem, basic concepts of mathematical statistics, testing statistical hypotheses, statistical estimates, confidence intervals.
For junior university and college students studying probability theory.
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A.N. Sobolevsky. Probability theory and mathematical statistics for physicists. 2007 47 pp. djv. 515 KB.
The textbook contains a presentation of the fundamentals of probability theory and mathematical statistics for students of physics of theoretical specialization. Along with the classical material (diagram independent tests Bernoulli, finite homogeneous Markov chains, diffusion processes), considerable attention is paid to such topics as the theory of large deviations, the concept of entropy in its various variants, stable laws and probability distributions with power-law decay, stochastic differential calculus. The textbook is intended for students specializing in various sections of theoretical and mathematical physics.
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Tarasov L. V. Patterns of the surrounding world. In 3 books. 2004 djvu.
1. Chance, necessity, probability. 384 pp. 6.8 MB.
This book is a fairly popular and at the same time strictly scientific, detailed introduction to probability theory, including detailed analysis the problems under consideration, broad generalizations of a philosophical nature, digressions of a historical nature. The book has a clearly expressed educational character; its material is strictly structured, built on an evidence-based basis, equipped with a large number of graphs and diagrams; given significant amount original problems, some of which are discussed in the book, and some are offered to the reader for independent solution. The book is a complete work and at the same time is the first book in a three-volume series by the author.
2. Probability in modern society. 360 pp. 4.5 MB.
This book demonstrates the fundamental role of probability theory in modern society, which is based on highly developed information technology. The book is a fairly popular and at the same time strictly scientific, detailed introduction to operations research and information theory. It has a clearly defined educational character; its material is strictly structured, built on an evidence-based basis, equipped with a large number of graphs and diagrams; a significant number of problems are presented, some of which are discussed in the book, and some are offered to the reader for independent solution.
3. 440 pages 7.5 MB. Evolution of natural scientific knowledge.
Here evolution is analyzed in a popular and systematic way natural science paintings world: from scientific programs antiquity to the mechanical picture, then to the electromagnetic picture and, finally, to modern painting. The transition from dynamic (rigidly determined) patterns to statistical (probabilistic) patterns is demonstrated as man's scientific comprehension of the surrounding world gradually deepens. The evolution of ideas is examined in sufficient detail quantum physics, physicists elementary particles, cosmology. In conclusion, the ideas of self-organization of open nonequilibrium systems (the emergence of dissipative structures) are discussed.
For a wide range of readers and primarily for high school students (starting from the 9th grade), as well as for students of technical schools and higher educational institutions.
