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Epsilon

epsilon in the crossword dictionary

New explanatory and derivational dictionary of the Russian language, T. F. Efremova.

epsilon

m. The name of the letter of the Greek alphabet.

Wikipedia

Epsilon

The name epsilon was introduced to distinguish this letter from the consonant combination αι.

Epsilon (launch vehicle)

Epsilon - Japanese three-stage solid-propellant light launch vehicle, also known as ASR designed and constructed by the Japan Aerospace Agency (JAXA) and the IHI Corporation for the launch of light scientific spacecraft. Its development began in 2007 as a replacement for the Mu-5 four-stage solid-propellant launch vehicle, which was discontinued in 2006.

Epsilon (disambiguation)

Epsilon is the fifth letter of the Greek alphabet. It can also mean:

Epsilon is a Latin letter.
Epsilon - Japanese three-stage solid-propellant light launch vehicle
Operation Epsilon is the codename for the Allied Forces operation at the end of World War II
Machine epsilon is a numerical value, less than which it is impossible to set the precision for any algorithm that returns real numbers.
Epsilon-salon - samizdat literary almanac
Epsilon cells - endocrine cells
Epsilon Neighborhood - Sets in functional analysis and related disciplines
Epsilon equilibrium in game theory
Epsilon-net of metric space
Epsilon entropy in functional analysis
Epsilon is a machine-oriented programming language developed in 1967 in the Novosibirsk academic town.
Epsilon is a genus of solitary wasps from the Vespidae family.

Examples of the use of the word epsilon in literature.

And what grace is in the Greek letters pi, epsilon, omega - Archimedes and Euclid would envy them!

Subdivision Epsilon captured one of the shipbuilding yards and assured that the ships located there are completely new and do not need repair at all.

Sines and cosines, tangents and cotangents, epsilons, sigma, phi and psi Arabic script covered the pedestal.

As I understand it, the star they contacted is Epsilon The Toucan of the constellation of the southern sky, replied Mven Mas, is ninety parsecs away, which is close to the limit of our constant communication.

Mven Mas wants to Epsilon Toucan, but I don't care, just to stage an experiment.

She was the last in the usual line of stellar hitchhikers, you know, those who hitchhike everywhere and stand with their thumbs up near the entrance to Kosmostrad, where they leave the highway. Epsilon Eridani.

When I entered Cornell University in 1940, I enrolled in the Delta Corporation there. Epsilon: They had a bar on the ground floor and Dr. Seis painted the walls with his drawings.

Noun., Number of synonyms: 1 letter (103) ASIS Synonym Dictionary. V.N. Trishin. 2013 ... Synonym dictionary

epsilon - epsilon, and (letter name) ... Russian spelling dictionary

epsilon - A designation commonly ascribed to intermetallic, metal metalloid and metal non-metal compounds found in iron alloy systems, for example: Fe3Mo2, FeSi and Fe3P. Mechanical engineering topics in general ... Technical translator's guide

Epsilon (ε) Epsilon (ε). A designation commonly attributed to intermetallic, metal-metalloid and metal-non-metal compounds found in iron alloy systems such as Fe3Mo2, FeSi, and Fe3P. (Source: "Metals and alloys. Handbook." Under ... Dictionary of metallurgical terms

M. The name of the letter of the Greek alphabet. Efremova's explanatory dictionary. T.F. Efremova. 2000 ... Modern explanatory dictionary of the Russian language by Efremova

epsilon - (other Greek. Е, ε έπσίλο.ν). 5th letter of the Greek alphabet; - ε΄ with a prime at the top right denoted 5, Íε with a prime at the bottom left - 5000 ... Dictionary of linguistic terms T.V. Foal

epsilon - (2 m); pl. e / psilons, R. e / psilons ... Spelling dictionary of the Russian language

epsilon - A noun see Appendix II (the name of the letter "Ε, ε" of the Greek alphabet) Information about the origin of the word: The word does not match the stress of the source language: it goes back to the Greek phrase ἐ ψιλόν, where each component has its own stress, in ... ... Dictionary of Russian stresses

Epsilon Salon is a samizdat literary almanac, published in 1985 1989. in Moscow by Nikolai Baytov and Alexander Barash. There were 18 issues, 70 80 pages each, typewritten, with a circulation of 9 copies. According to ... ... Wikipedia

Greek alphabet Α α alpha Β β beta ... Wikipedia

Books

Epsilon Eridani
Epsilon Eridani, Alexey Baron. A new era of humanity has come - the era of colonization of distant worlds. One of these colonies was the planet Campanella of the Epsilon Eridani system ... And one day something happened. The planet fell silent. ...

What icons do you know besides inequality and modulus?

We know the following notation from the algebra course:

- the universality quantifier means - “for any”, “for all”, “for everyone”, that is, the record should be read “for any positive epsilon”;

- existential quantifier, - there is a value belonging to the set of natural numbers.

- a long vertical stick reads like this: “such that”, “such that”, “such that” or “such that”, in our case, obviously, we are talking about a number - therefore “such that”;

- for all "en", greater than;

- the modulus sign means distance, i.e. this entry tells us that the distance between the values \u200b\u200bis less than epsilon.

Determining the Limit of a Sequence

And in fact, let's think a little - how to formulate a strict definition of a sequence? ... The first thing that comes to mind in the light of the practical lesson: "the limit of the sequence is the number to which the members of the sequence are infinitely close."

Ok, let's write the sequence:

It is easy to see that the subsequence is infinitely close to the number –1, and the terms with even numbers - to "one".

Or maybe there are two limits? But then why can't some sequence have ten or twenty? This can go far. In this regard, it is logical to assume that if a sequence has a limit, then it is unique.

Note: the sequence has no limit, however, two subsequences can be distinguished from it (see above), each of which has its own limit.

Thus, the above definition turns out to be untenable. Yes, it works for cases like (which I did not quite correctly use in simplified explanations of practical examples), but now we need to find a strict definition.

Attempt two: "the limit of the sequence is the number to which ALL members of the sequence approach, with the exception, perhaps, of their finite number." This is closer to the truth, but still not entirely accurate. So, for example, in a sequence, half of the terms do not approach zero at all - they are simply equal to it \u003d) By the way, the "flasher" generally takes two fixed values.

The wording is not difficult to clarify, but then another question arises: how to write the definition in mathematical signs? The scientific world struggled with this problem for a long time until the situation was resolved by the famous maestro, who, in essence, formalized classical calculus in all its rigor. Cauchy proposed to operate with neighborhoods, which significantly advanced the theory.

Consider a point and its arbitrary -neighborhood:

The meaning of "epsilon" is always positive, and, moreover, we have the right to choose it ourselves. Suppose that a given neighborhood contains a set of members (not necessarily all) of a certain sequence. How to write down the fact that, for example, the tenth member got into the neighborhood? Let it be on the right side of it. Then the distance between the points should be less than "epsilon":. However, if "x-tenth" is located to the left of point "a", then the difference will be negative, and therefore the modulus sign must be added to it:.

Definition: a number is called the limit of a sequence if for any of its neighborhood (preselected) there is a natural number - SUCH that ALL members of the sequence with higher numbers will be inside the neighborhood:

Or in short: if

In other words, no matter how small the value of “epsilon” we take, sooner or later the “infinite tail” of the sequence will be COMPLETELY in this neighborhood.

So, for example, the "infinite tail" of the sequence will FULLY enter any arbitrarily small -neighborhood of the point. Thus, this value is the limit of the sequence by definition. As a reminder, a sequence whose limit is zero is called infinitely small.

It should be noted that for the sequence it is no longer possible to say “the endless tail will go in” - the members with odd numbers are in fact equal to zero and “do not go anywhere” \u003d) That is why the verb “will turn out” is used in the definition. And, of course, members of such a sequence as also "don't go anywhere." By the way, check if the number is the limit.

Now we will show that the sequence has no limit. Consider, for example, a neighborhood of a point. It is quite clear that there is no such number after which ALL members will be in the given neighborhood - odd members will always "jump out" to "minus one". For a similar reason, there is no limit at a point.

Prove that the limit of the sequence is zero. Specify the number after which all members of the sequence are guaranteed to be inside any arbitrarily small -neighborhood of the point.

Note: for many sequences, the desired natural number depends on the value - hence the notation.

Solution: consider an arbitrary -neighborhood of the point and check if there is a number such that ALL members with larger numbers will be inside this neighborhood:

To show the existence of the desired number, we express through.

Theoretical minimum
The notion of a limit in relation to number sequences has already been introduced in the topic "".
It is recommended that you first read the material contained therein.
Moving on to the subject of this topic, let us recall the concept of function. The function is another display example. We will consider the simplest case
a real function of one real argument (what is the complexity of other cases - will be discussed later). The function within this topic is understood as
the law according to which each element of the set on which the function is defined is associated with one or more elements
a set called the set of values \u200b\u200bof the function. If each element of the function domain is assigned one element
set of values, then the function is called single-valued, otherwise the function is called multivalued. For simplicity, we will only talk about
unique functions.
I would like to emphasize right away the fundamental difference between a function and a sequence: the sets connected by the mapping in these two cases are significantly different.
To avoid the need to use the terminology of general topology, let us clarify the difference with imprecise reasoning. When discussing the limit
sequence, we talked about only one option: unlimited growth of the sequence element number. With this increase in the number, the elements themselves
the sequences behaved much more varied. They could "accumulate" in a small neighborhood of a certain number; they could grow indefinitely, etc.
Roughly speaking, sequencing is a function setting on a discrete "domain of definition" If we talk about the function, the definition of which is given
at the beginning of the topic, then the concept of the limit should be built more accurately. It makes sense to talk about the limit of a function when her argument tends to a certain value .
This statement of the question did not make sense when applied to sequences. It becomes necessary to introduce some clarifications. They are all related to
how exactly the argument tends to the meaning in question.
Let's look at a few examples - so far in passing:

These functions will allow us to consider a wide variety of cases. Here are the graphs of these functions for greater clarity of presentation.
The function has a limit at any point of the domain of definition - this is understandable intuitively. Whatever point of the domain of definition we take,
you can immediately tell which value the function tends to when the argument tends to the selected value, and the limit will be finite, if only the argument
does not tend to infinity. The function graph has a break. This affects the properties of the function at the break point, but from the point of view of the limit
this point is not highlighted by anything. The function is already more interesting: at the point it is not clear what value of the limit to assign to the function.
If we approach a point on the right, then the function tends to one value, if on the left, the function tends to another value. In previous
examples of this were not. The function, when tending to zero, at least on the left or on the right, behaves the same way, tending to infinity
in contrast to the function, which tends to infinity as the argument tends to zero, but the sign of infinity depends on which
hand we come to zero. Finally, the function behaves at zero is completely incomprehensible.
Let us formalize the concept of a limit using the "epsilon-delta" language. The main difference from the definition of the sequence limit will be the need
to register the tendency of the function argument to a certain value. This requires the concept of the limit point of a set, which is auxiliary in this context.
A point is called a limit point of a set if in any neighborhood contains countless points,
belonging to and other than. A little later it will become clear why such a definition is required.
So, the number is called the limit of the function at the point that is the limit point of the set on which
function if

Let us analyze this definition one by one. Let us highlight here the parts related to the tendency of the argument to the value and to the tendency of the function
to the value. The general meaning of the written statement should be understood, which can be roughly interpreted as follows.
The function tends to at, if taking a number from a sufficiently small neighborhood of the point, we will
get the value of the function from a sufficiently small neighborhood of the number. And the smaller the neighborhood of the point from which the values \u200b\u200bare taken
argument, the smaller the neighborhood of the point where the corresponding values \u200b\u200bof the function will fall.
Let's go back to the formal definition of the limit and read it in the light of what has just been said. A positive number limits the neighborhood
the point from which we will take the values \u200b\u200bof the argument. Moreover, the values \u200b\u200bof the argument, of course, are from the domain of the function and do not coincide with the
point: we are writing aspiration, not coincidence! So if we take the value of the argument from the specified -neighborhood of the point,
then the value of the function will fall into the -neighborhood of the point .
Finally, we bring the definition together. No matter how small we choose the neighborhood of the point, there will always be such a neighborhood of the point,
that when choosing the values \u200b\u200bof the argument from it, we will get into the vicinity of the point. Of course, the size of the neighborhood of the point in this case
depends on which point's neighborhood was specified. If the neighborhood of the function value is large enough, then the corresponding spread of values
the argument will be great. As the neighborhood of the value of the function decreases, the corresponding scatter of the values \u200b\u200bof the argument also decreases (see Fig. 2).
It remains to clarify some details. First, requiring the point to be the ultimate eliminates the need to worry that the point
of the -neighborhood generally belongs to the domain of the function. Second, participation in determining the limit of the condition means
that the argument can tend to the value on both the left and right.
For the case when the function argument tends to infinity, the notion of the limit point should be defined separately. called the limit
point of a set if for any positive number the interval contains an infinite set
points from the set.
Let's go back to the examples. The function is of no particular interest to us. Let's take a closer look at other functions.
Examples.
Example 1. Function graph has a kink.
Function despite the singularity at the point, it has a limit at this point. The feature at zero is the loss of smoothness.
Example 2. One-sided limits.
The function at a point has no limit. As already noted, for the existence of the limit, it is required that when tending
on the left and right, the function tends to the same value. This is obviously not true here. However, the concept of a one-sided limit can be introduced.
If the argument tends to a given value from the side of larger values, then one speaks of a right-hand limit; if from the side of smaller values \u200b\u200b-
about the left-hand limit.
In the case of the function
- right-sided limit However, an example can be given when infinite sine oscillations do not interfere with the existence of a limit (moreover, a two-sided one).
An example is the function ... The graph is shown below; for obvious reasons build it to the end in the neighborhood
the origin is impossible. The limit at is zero.

Remarks.
1. There is an approach to determining the limit of a function using a sequence limit - the so-called. definition of Heine. There, a sequence of points is constructed, converging to the required value
argument - then the corresponding sequence of function values \u200b\u200bconverges to the function limit at this argument value. Equivalence of Heine's definition and definition in language
"epsilon-delta" is proved.
2. The case of functions of two or more arguments is complicated by the fact that for the existence of a limit at a point it is required that the value of the limit turns out to be the same for any method of aspiration
to the required value. If there is only one argument, then you can strive to the required value from the left or right. With more variables, the number of options rises sharply. Function case
complex variable requires a separate discussion.

● The rate of increase of the chain reaction dN N (k - 1) (k -1) t / T \u003d, whence N \u003d N 0e, dt T where N0 is the number of neutrons at the initial moment of time; N is the number of neutrons at time t; T is the average lifetime of one generation; k is the neutron multiplication factor. APPENDICES Basic physical constants (rounded values) Physical constant Designation Value Normal acceleration g 9.81 m / s2 free fall Gravitational constant G 6.67 ⋅ 10–11 m3 / (kg ⋅ s2) Avogadro constant NA 6.02 ⋅ 1023 mol– 1 Faraday constant F 96.48 ⋅ 103 C / mol Molar gas 8.31 J / mol constant Molar volume of ideal gas at normal Vm 22.4 ⋅ 10–3 m3 / mol conditions Boltzmann constant k 1.38 ⋅ 10– 23 J / K Speed \u200b\u200bof light in vacuum s 3.00 ⋅ 108 m / s Stefan-Boltzmann constant σ 5.67 ⋅ 10–8 W / (m2 ⋅ К4) Wien's displacement law constant b 2.90 ⋅ 10–3 m ⋅ K h 6.63 ⋅ 10–34 J s Planck's constant ħ \u003d h / 2π 1.05 ⋅ 10–34 J s Rydberg constant R 1.10 ⋅ 107 m – 1 Bohr radius а 0.529 ⋅ 10–10 m Mass electron rest mass me 9.11 ⋅ 10–31 kg Proton rest mass mp 1.6726 ⋅ 10–27 kg Neutron rest mass mn 1.6750 ⋅ 10–27 kg α-particle rest mass mα 6.6425 ⋅ 10–27 kg Atomic unit of mass amu 1.660 ⋅ 10–27 kg Ratio of mass mp / me 1836.15 proton to electron mass Elementary charge e 1.60 ⋅ 10–19 C Ratio of electron charge to its mass e / me 1.76 ⋅ 1011 C / kg Compton wavelength of an electron Λ 2.43 ⋅ 10–12 m Ionization energy of a hydrogen atom Ei 2.18 ⋅ 10–18 J (13.6 eV) Bohr magneton µV 0.927 ⋅ 10–23 A ⋅ m2 Electrical constant ε0 8.85 ⋅ 10–12 F / m Magnetic constant µ0 12.566 ⋅ 10–7 Gn / m Units and dimensions of physical quantities in SI Value Unit Expression in terms of basic and additional designations Name Dimension Unit name Basic units Length L meter m Weight M kilogram kg Time T second s Electric force - I ampere A current Thermodynamic - Θ kelvin K temperature Amount N mol mol of substance Luminous intensity J candela cd Additional units Plane angle - radian rad Solid angle - steradian av Derivative units Frequency T –1 hertz Hz s – 1 –2 Force, weight LMT newton N m ⋅ kg ⋅ s – 2 Pressure, mechan- L – 1MT –2 pascal Pa m– 1 ⋅ kg ⋅ s – 2 electrical voltage Energy, work, L2MT –2 joule J m2 ⋅ kg ⋅ s – 2 amount of heat Power, flow L2MT –3 watts W m2 ⋅ kg ⋅ s – 3 energy Number of elec- TI coulomb Cl s ⋅A tricity (electric charge) Electric L2MT –3I –1 volt V m2 ⋅ kg ⋅ s – 3 ⋅ A – 1 voltage, electric potential, electric potential difference, electric force Electric L – 2M - 1T 4I 2 farad F m – 2 ⋅ kg – 1 ⋅ s4 ⋅ A2 capacitance Electrical L2MT –3I –2 ohm Ohm m2 ⋅ kg ⋅ s – 3 ⋅ A – 2 resistance Electrical L – 2M –1T 3I 2 siemens S m – 2 ⋅ kg – 1 ⋅ s3 ⋅ A2 conductivity Magnetic flux L2MT –2I –1 weber Wb m2 ⋅ kg ⋅ s – 2 ⋅ A – 1 Magnetic induction - MT –2I –1 Tesla Tl kg ⋅ s – 2 ⋅ A – 1 Inductance , L2MT –2I –2 henry H m2 ⋅ kg ⋅ s – 2 ⋅ A – 2 mutual inductance Luminous flux J lumen lm cd ⋅ sr Illumination L – 2J lux lx m – 2 ⋅ cd ⋅ sr Isotope activity T –1 becquerel Bq s – 1 pa (activity of a nuclide in a radioactive source) Absorbed dose of L – 2T –2 gray Gy m – 2 ⋅ s – 2 radiation Ratios I between SI units and some units of other systems, as well as non-systemic units Physical quantity Ratios Length 1 Е \u003d 10–10 m Mass 1 amu. \u003d 1.66⋅10–27 kg Time 1 year \u003d 3.16⋅107 s 1 day \u003d 86 400 s Volume 1 l \u003d 10–3 m3 Speed \u200b\u200b1 km / h \u003d 0.278 m / s Angle of rotation 1 rev \u003d 6, 28 rad Force 1 dyn \u003d 10-5 N 1 kg \u003d 9.81 N Pressure 1 dyn / cm2 \u003d 0.1 Pa 1 kg / m2 \u003d 9.81 Pa 1 atm \u003d 9.81⋅104 Pa 1 atm \u003d 1, 01⋅105 Pa 1 mm Hg. st \u003d 133.3 Pa Work, energy 1 erg \u003d 10–7 J 1 kg⋅m \u003d 9.81 J 1 eV \u003d 1.6⋅10–19 J 1 cal \u003d 4.19 J Power 1 erg / s \u003d 10 –7 W 1 kg⋅m / s \u003d 9.81 W Charge 1 SGSE q \u003d 3.33⋅10–10 C Voltage, emf 1 SGSEU \u003d 300 V Electrical capacity 1 cm \u003d 1.11⋅10–12 F Magnetic strength 1 E \u003d 79.6 A / m of the field Astronomical values \u200b\u200bPeriod Cosmic-Average Average rotation Mass, kg density, radius, m around the axis, body g / cm3 day Sun 6.95 ⋅ 108 1.99 ⋅ 1030 1.41 25.4 Earth 6.37 ⋅ 10 6 5.98 ⋅ 1024 5.52 1.00 Moon 1.74 ⋅ 10 6 7.35 ⋅ 1022 3.30 27.3 Distance from the center of the Earth to the center of the Sun: 1.49 ⋅ 1011 m.Distance from the center of the Earth to the center of the Moon: 3.84 ⋅ 108 m.Period Average planet of revolution Mass in the distance of the Solar around units of mass from Sun, solar systems, Earth 106 km in years Mercury 57.87 0.241 0.056 Venus 108.14 0.615 0.817 Earth 149.50 1.000 1.000 Mars 227.79 1.881 0.108 Jupiter 777.8 11.862 318.35 Saturn 1426.1 29.458 95.22 Uranium 2867.7 84.013 14.58 Neptune 4494 164.79 17.26 Densities of substances Solid g / cm3 Liquid g / cm3 Diamond 3.5 Benzene 0.88 Aluminum 2.7 Water 1.00 Tungsten 19.1 Glycerin 1, 26 Graphite 1.6 Castor oil 0.90 Jelly zo (steel) 7.8 Kerosene 0.80 Gold 19.3 Mercury 13.6 Cadmium 8.65 Carbon disulfide 1.26 Cobalt 8.9 Alcohol 0.79 Ice 0.916 Heavy water 1.1 Copper 8.9 Ether 0.72 Molybdenum 10.2 Gas Sodium 0.97 (at normal kg / m3 conditions) Nickel 8.9 Tin 7.4 Nitrogen 1.25 Platinum 21.5 Ammonia 0.77 Plug 0.20 Hydrogen 0.09 Lead 11.3 Air 1.293 Silver 10.5 Oxygen 1.43 Titanium 4.5 Methane 0.72 Uranium 19.0 Carbon dioxide 1.98 Porcelain 2.3 Chlorine 3.21 Zinc 7.0 Elastic constants. Tensile strength Coefficients Modulus Modulus Compressive strength Young's material E, shear G, Poisson tensile strength β, GPa GPa GPa – 1 µ σm, GPa Aluminum 70 26 0.34 0.10 0.014 Copper 130 40 0.34 0 , 30 0.007 Lead 16 5.6 0.44 0.015 0.022 Steel (iron) 200 81 0.29 0.60 0.006 Glass 60 30 0.25 0.05 0.025 Water - - - - 0.49 Thermal constants of solids Specific Tempe - Specific Debye heat temperature heat Substance temperature bone of melting, melting θ, K s, J / (g ⋅ K) ° C q, J / g Aluminum 0.90 374 660 321 Iron 0.46 467 1535 270 Ice 2.09 - 0 333 Copper 0.39 329 1083 175 Lead 0.13 89 328 25 Silver 0.23 210 960 88 Note. The values \u200b\u200bof the specific heat capacities correspond to normal conditions. Thermal conductivity coefficient Substance χ, J / (m ⋅ s ⋅ K) Water 0.59 Air 0.023 Wood 0.20 Glass 2.90 Some permanent liquids Surface specific specific heat Viscosity η Liquid heat capacity of vaporization η, mPa ⋅ s tension s, J / (g ⋅ K) q, J / (g ⋅ K) α, mN / m Water 10 73 4.18 2250 Glycerin 1500 66 2.42 - Mercury 16 470 0.14 284 Alcohol 12 24 2.42 853 P r Note. The given values \u200b\u200bof the quantities correspond to: η and α - room temperature (20 ° С), c - normal conditions, q - normal atmospheric pressure. Constants of gases Constants Viscosity η, μPa ⋅ s Molecule diameter Heat - Van der Waals Gas wire - (relative CP d, nm γ \u003d molecular weight CV a, b, mW mass) χ, m ⋅K Pa⋅m 6 −6 m3 10 mol 2 mol He (4) 1.67 141.5 18.9 0.20 - - Ar (40) 1.67 16.2 22.1 0.35 0.132 32 H2 (2) 1.41 168, 4 8.4 0.27 0.024 27 N2 (28) 1.40 24.3 16.7 0.37 0.137 39 O2 (32) 1.40 24.4 19.2 0.35 0.137 32 CO2 (44) 1 , 30 23.2 14.0 0.40 0.367 43 H2O (18) 1.32 15.8 9.0 0.30 0.554 30 Air (29) 1.40 24.1 17.2 0.35 - - P Note. The values \u200b\u200bof γ, χ and η are under normal conditions. Pressure of water vapor saturating space at different temperatures t, ° C pn, Pa t, ° C pn, Pa t, ° C pn, Pa –5 400 8 1070 40 7 335 0 609 9 1145 50 12 302 1 656 10 1225 60 19 817 2 704 12 1396 70 31 122 3 757 14 1596 80 47 215 4 811 16 1809 90 69 958 5 870 20 2328 100 101 080 6 932 25 3165 150 486240 7 1025 30 4229 200 1 549 890 Dielectric constants Dielectric ε Dielectric ε Water 81 Polyethylene 2.3 Air 1.00058 Mica 7.5 Wax 7.8 Alcohol 26 Kerosene 2.0 Glass 6.0 Paraffin 2.0 Porcelain 6.0 Plexiglass 3.5 Ebonite 2.7 Resistivity of conductors and insulators Specific Specific Temperature Resistance - Conductor (at 20 ° C), coefficient a, Insulation, kK – 1 nΩ m Ohm ⋅ m Aluminum 25 4.5 Paper 1010 Tungsten 50 4.8 Paraffin 1015 Iron 90 6.5 Mica 1013 Gold 20 4.0 Porcelain 1013 Copper 16 4.3 Shellac 1014 Lead 190 4.2 Ebonite 1014 Silver 15 4.1 Amber 1017 Magnetic susceptibility of para- and diamagnets Paramagnet d - 1, 10–6 Diamagnet d - 1, 10–6 Nitrogen 0.013 Hydrogen –0.063 Air 0.38 Benzyl –7.5 Oxygen 1.9 Water –9.0 Ebonite 14 Copper –10.3 Aluminum 23 Glass –12.6 Tungsten 176 Rock salt –12 , 6 Platinum 360 Quartz –15.1 Liquid oxygen 3400 Bismuth –176 Refractive indices n Gas n Liquid n Solid n Nitrogen 1.00030 Benzene 1.50 Diamond 2.42 Quartz Air 1.00029 Water 1.33 1.46 fused Glass Oxygen 1,00027 Glycerin 1.47 1.50 (regular) Carbon disulfide 1.63 Note. Refractive indices also depend on the wavelength of light; therefore, the values \u200b\u200bof n given here should be regarded as conditional. For birefringent crystals Length Icelandic spar Quartz wavelength λ, Color nm ne no ne no 687 Red 1.484 1.653 1.550 1.541 656 Orange 1.485 1.655 1.551 1.542 589 Yellow 1.486 1.658 1.553 1.544 527 Green 1.489 1.664 1.556 1.547 486 Light blue 1.491 1.688 1.559 1.550 431 Blue -violet 1.495 1.676 1.564 1.554 400 Violet 1.498 1.683 1.568 1.558 Rotation of the plane of polarization Natural rotation in quartz Wavelength λ, nm Rotation constant α, deg / mm 275 120.0 344 70.6 373 58.8 405 48.9 436 41, 5 49 31.1 590 21.8 656 17.4 670 16.6 Magnetic rotation (λ \u003d 589 nm) Liquid Verde constant V, ang. min / A Benzene 2.59 Water 0.016 Carbon disulfide 0.053 Ethyl alcohol 1.072 Note. The given values \u200b\u200bof the Verdet constant correspond to room temperature Work function of the electron from metals Metal A, eV Metal A, eV Metal A, eV Aluminum 3.74 Potassium 2.15 Nickel 4.84 Barium 2.29 Cobalt 4.25 Platinum 5.29 Bismuth 4.62 Lithium 2.39 Silver 4.28 Tungsten 4.50 Copper 4.47 Titanium 3.92 Iron 4, 36 Molybdenum 4.27 Cesium 1.89 Gold 4.58 Sodium 2.27 Zinc 3.74 Ionization energy Matter Ei, J Ei, eV Hydrogen 2.18 ⋅ 10 –18 13.6 Helium 3.94 ⋅ 10 –18 24 , 6 Lithium 1.21 ⋅ 10 –17 75.6 Mercury 1.66 ⋅ 10 –18 10.4 Mobility of ions in gases, m2 / (V ⋅ s) Gas Positive ions Negative ions Nitrogen 1.27 ⋅ 10 –4 1 , 81 ⋅ 10–4 Hydrogen 5.4 ⋅ 10–4 7.4 ⋅ 10–4 Air 1.4 ⋅ 10–4 1.9 ⋅ 10–4 Edge of the K absorption band Z Element λк, pm Z Element λк, pm 23 Vanadium 226.8 47 Silver 48.60 26 Iron 174.1 50 Tin 42.39 27 Cobalt 160.4 74 Tungsten 17.85 28 Nickel 148.6 78 Platinum 15.85 29 Copper 138.0 79 Gold 15.35 30 Zinc 128.4 82 Lead 14.05 42 Molybdenum 61.9 92 Uranium 10.75 Mass attenuation coefficients (X-rays, narrow beam) Mass attenuation coefficient e / ρ, cm2 / g λ, pm Air Water Aluminum Copper Lead 10 0.16 0.16 0.36 3.8 20 0.18 0.28 1.5 4.9 30 0.29 0.47 4.3 14 40 0.44 1D 9.8 31 50 0, 48 0.66 2.0 19 54 60 0.75 1.0 3.4 32 90 70 1.3 1.5 5.1 48 139 80 1.6 2.1 7.4 70 90 2D 2.8 11 98 100 2.6 3.8 15 131 150 8.7 12 46 49 200 21 28 102 108 250 39 51 194 198 Constants of diatomic molecules Internuclear Frequency Internuclear Frequency Mole - distance of vibrations Mole - distance of vibrations of the coil d, 10–8 cm ω, 1014 s – 1 d, 10–8 cm ω, 1014 s – 1 H2 0.741 8.279 HF 0.917 7.796 N2 1.094 4.445 HCl 1.275 5.632 O2 1.207 2.977 HBr 1.413 4.991 F2 1.282 2.147 HI 1.604 4.350 S2 1.889 1.367 CO 1.128 4.088 Cl2 1.988 1.064 NO 1.150 3.590 Br2 2.283 0.609 OH 0.971 7.035 I2 2.666 0.404 Half-lives of radionuclides Cobalt 60Co 5.2 years (β) Radon 222Rn 3.8 days (α) Strontium 90Sr 28 years (β) Radium 226Ra 1620 years (α) Polonium 10Ро 138 days (α) Uranium 238U 4.5 ⋅ 109 years (α) Masses of light nuclides Excess mass Excess mass Z Nuclide M – A, Z Nuclide of nuclide М – А, amu a.u. 11 0 n 0.00867 6 С 0.01143 1 12 1 Н 0.00783 С 0 2 13 Н 0.01410 С 0.00335 3 13 Н 0.01605 7 N 0.00574 3 14 2 Н 0.01603 N 0 , 00307 4 15 Not 0.00260 N 0.00011 6 15 3 Li 0.01513 8 O 0.00307 7 16 Li 0.01601 O –0.00509 7 17 4 Be 0.01693 O –0.00087 8 19 Be 0.00531 9 F –0.00160 9 20 Be 0.01219 10 Ne –0.00756 10 23 Be 0.01354 11 Na –0.01023 10 24 5 Be 0.01294 Na –0.00903 11 24 Be 0, 00930 12 Mg –0.01496 Note. Here M is the mass of the nuclide in amu, A is the mass number. Multipliers and prefixes for the formation of decimal multiples and sub-multiples of units Designation Designation Multiple prefixes Multiple prefixes Prefixes- Appli- cation inter- Russian inter- Russian folk folk 10-18 atto a а 101 deca da yes 10–15 femto f f 102 hecto h g 10–12 pico p p 103 kilo k k 10–9 nano n n 106 mega M M 10–6 micro µ μ 109 giga G G 10–3 milli m m 1012 tera T T 10–2 centi c s 1015 peta P P 10–1 deci d d 1018 exa E E Greek alphabet Symbols Designations Name of letters Name of letters of letters of letters Α, α alpha Ν, ν nu Β, β beta Ξ, ξ xi Γ, γ gamma Ο, ο omicron ∆, δ delta Π, π pi Ε, ε epsilon Ρ, ρ ro Ζ, ζ zeta Σ, σ sigma Η, η eta Τ, τ tau Θ, θ, ϑ theta Υ, υ upsilon Ι, ι iota Φ, φ phi Κ, κ kappa Χ, χ chi Λ, λ lambda Ψ, ψ psi Μ, µ mu Ω, ω omega CONTENTS SCHOOL MATHEMATICS ………………… 3 HIGHER MATHEMATICS ………………… … .. 13 MEASUREMENT ERRORS ……………… 28 PHYSICS …………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………… 29 1.1. Elements of kinematics …………………… 29 1.2. Dynamics of a material point and translational motion of a rigid body 31 1.3. Work and energy …………………………. 32 1.4. Rigid Body Mechanics …………………. 35 1.5. Gravitation. Elements of field theory ……… 39 1.6. Elements of fluid mechanics ………… 41 1.7. Elements of the special (particular) theory of relativity …………………………. 44 2. BASICS OF MOLECULAR PHYSICS AND THERMODYNAMICS ………………………… 47 2.1. Molecular-kinetic theory of ideal gases ………………………… .. 47 2.2. Fundamentals of Thermodynamics …………………. 52 2.3. Real gases, liquids and solids 55 3. ELECTRICITY AND MAGNETISM ………. 59 3.1. Electrostatics ………………………… ... 59 3.2. Direct electric current ………… 66 3.3. Electric currents in metals, vacuum and gases …………………………………… .. 69 3.4. Magnetic field ………………………… .. 70 3.5. Electromagnetic induction ……………. 75 3.6. Magnetic properties of matter ………… .. 77 3.7. Bases Maxwell's theory for electromagnetic field ..................... 79 4. Vibrations and Waves ......................... 80 4.1. Mechanical and electromagnetic vibrations …………………………………. 80 4.2. Elastic waves …………………………… 85 4.3. Electromagnetic waves ……………… .. 87 5. OPTICS. THE QUANTUM NATURE OF RADIATION …………………………………. 89 5.1. Elements of geometric and electronic optics …………………………………… .. 89 5.2. Light interference ……………………. 91 5.3. Light diffraction …………………………. 93 5.4. Interaction of electromagnetic waves with matter ………………………………. 95 5.5. Light polarization ……………………… .. 97 5.6. The quantum nature of radiation ………… ... 99 6. ELEMENTS OF QUANTUM PHYSICS OF ATOMS, MOLECULES AND SOLIDS…. 102 6.1. Bohr's theory of hydrogen atoms ……… .. 102 6.2. Elements of quantum mechanics …………. 103 6.3. Elements of modern physics of atoms and molecules …………………………………… 107 6.4. Elements of quantum statistics ……… ... 110 6.5. Elements of solid state physics ……… ... 112 7. ELEMENTS OF ATOMIC NUCLEI PHYSICS 113 7.1. Elements of physics of the atomic nucleus ……… .. 113 APPENDICES ………………………………… .. 116