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Intro
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there are three scientific languages I
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guess other than English
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and they are French German and the third
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is Russian
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and what I mean by that is if you go to
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graduate school if you go to a good
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graduate school for mathematics
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oftentimes one of the requirements is
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that you learn a foreign language that
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you have to pass some tests some type of
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proficiency test
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in French German or Russian
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and it’s because a lot of mathematics
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was produced in those languages
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in this video we’re going to look at a
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book that was originally published in
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Russian
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so this is a book let me show you the
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cover here and be very careful with it
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this is a very rare book
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multiple integrals field Theory and
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series by B and budok and SV fomen you
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can hear it see it says mirror
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Publishers Moscow it’s pronounced near I
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believe
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really nice book let’s look at the back
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here about the Publishers this is really
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interesting mere Publishers of Moscow
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publish Soviet scientific and technical
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literature in 11 languages English
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German French Italian Spanish Czech
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cerebral croat Slovak Hungarian
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Mongolian and Arabic
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titles include textbooks for higher
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technical schools and vocational schools
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literature on the Natural Sciences in
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medicine including textbooks for medical
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schools Popular Science and science
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fiction
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the contributors to near Publishers list
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are leading Soviet scientists and
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engineers in all fields of Science and
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Technology and include more than 40
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members and corresponding members of the
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USSR Academy of Sciences
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skill to translators provide a high
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standard of translation from the
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original Russian
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many of the titles already issued by
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mere Publishers have been adopted as
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textbooks and manuals at educational
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establishments in France Cuba Egypt
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India and many other countries I
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actually have some books that were
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published that are that were used in
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Cuba by mere Publishers I have I think I
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have one or two and they’re in Spanish
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though but
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I had some some I received those from
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Cuba mere publishes books in foreign
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languages are exported by vo and then
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has a name there I can’t read that and
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can be
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purchased or ordered through booksellers
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in their country dealing with v slash o
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and then it has something there just
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have to smell this because this is a
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classic
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ah smells so good so these books are
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really hard to get in the United States
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very rare I’ve been told that
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um someone told me once that this was
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the comment I got when the Soviet Union
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fell so it’s no longer the Soviet Union
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but when it was when it went away people
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were selling these books like on the
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streets for dollars I don’t know if
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that’s true or not uh that’s just what I
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heard this one’s signed Bhatia let’s see
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what it says here about this particular
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book
Authors
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this book covers branches of mathematics
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increasingly required by physicists such
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as multiple line and improper integrals
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the theory of fields and power and
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trigonometric series based on lectures
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read by the authors and physics faculty
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of Moscow University the book Endeavors
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to show the connection between various
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mathematical Concepts and their
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applications and wherever possible their
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physical sense as well let me see if
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there’s anything on the back flap here
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be very careful with this
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I hear it talks about the authors
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the authors of this text are BM budak
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and then professor fomen formerly of
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Moscow State University
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budak was the assistant professor and
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math at the math chair of the physics
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department was active mainly in the
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field of computational mathematics he is
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the author of over a hundred
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Publications wow on different methods
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for solving differential equations
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methods of solving optimal control
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problems stochastic problems methods of
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solving ill-condition problems fulman
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was a lecturer at the department of
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mechanics and Mathematics
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as principal lines of research were
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topology functional analysis and
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mathematical aspects of biology wow
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wow he is the author of over 70
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Publications among them textbooks and
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manuals for college and university
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students several have been translated
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into foreign languages so this book is
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written by Leading researchers these are
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some of the best people in the world
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right and this book was originally
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written in Russian let’s go ahead and go
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through it very carefully look at the
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topics and stuff
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there’s the inside cover it says
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something here which I can’t read I
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don’t speak Russian
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and then here it says translated from
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the Russian by VM volosov DSC mere
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Publishers Moscow so the fact that it
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was translated already is epic I think
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it is a Monumental task to translate a
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math book to any language from any
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language it’s just very very impressive
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an advanced course in higher mathematics
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so this is the second printing first
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published in 73 it says and this one was
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in 78.
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nice here’s the preface
Contents
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the present book is based on lectures
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given by the authors at the physical
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Department of the lamanasa of State
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University of Moscow
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in the presentation of the material much
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emphasis has been placed on the physical
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meaning of mathematical Notions
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and their interrelation as well as on
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the applications and computational
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aspects then here it talks a little bit
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about the the book and the chapters
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let’s skip that and just go to
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the topics
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so this is the contents double intervals
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that’s where it starts wow so it starts
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with double integrals so double
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integrals are something you would see in
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a calc 3 class right wow the concept of
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measure this book does not they don’t
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mess around these old Russian texts are
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just so hardcore I just love it
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definition and basic properties of
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double integral and I feel like you find
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math and explanations in these books
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that you don’t find in other books I’ve
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often seen techniques and just
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explanations that are just not in modern
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books so it’s kind of interesting
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additive set functions derivative of a
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set function with respect to area
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some physical and geometric geometrical
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applications of the double integral so a
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lot of stuff on double integrals here
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right just tons of stuff here
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spending a lot of time on that
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then here we have some more topics
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reducing double integral to a two-fold
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iterated integral
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change of variables in double integral
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chapter 2 is triple integrals and
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multiple integrals of higher order just
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a lot of a lot of information on double
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and triple integrals right I mean that
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is
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multiple integrals that is that is one
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of the titles of the book right so it
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just spends an incredible amount of time
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on that which is nice because not a lot
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of time is spent in a calculus clause
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and not not as much as this
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not as much as this because you just
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don’t have time elements of differential
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geometry that’s cool so differential
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geometry you could study today in
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college if you wanted to if you’re if
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your school offers it a lot of times
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it’s a course that is simply not taught
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or it’s an elective and it’s not offered
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very often
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you can see some of the more interesting
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topics there let’s turn the page
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more integration line integrals another
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calc 3 topic definition of line integral
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of the first type
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properties of line integrals some
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applications of line integrals of the
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first type
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line integrals of the second type they
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have greens formula
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you have surface integrals
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Stokes theorem
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field Theory
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so Vector Fields so by field Theory they
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don’t mean like
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um you know fields from abstract algebra
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okay they don’t mean that type of field
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this is stuff that’s related mostly to
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physics
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then we have tensors down here
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this is something again that again you
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could study this in a course on tensors
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as an undergrad typically it’s an
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elective type course if you were to get
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like an applied math degree it would
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probably be required
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they have functional sequences in series
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so uniform convergence
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a lot of information in this book right
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it’s very dense when we look at the book
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in a minute you’re going to see how
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quickly it goes to material but that’s
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why it covers so many topics and proper
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integrals
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integrals dependent on parameter
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Fourier series and Fourier integral
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look at this it just keeps going
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it’s gonna go slow here so you can read
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some of these topics
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there’s an incredible amount of
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information
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and then that’s pretty much it’s got a
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couple appendices and some supplements
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basic types of computer that’s cool
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right representing numbers with any
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computers it goes into some
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computational stuff like you know with
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computers
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basic operations actually executed by a
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computer elements of programming
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yeah this is this is from the 70s right
Programming
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they’re talking about programming so
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this is pretty you know forward-looking
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here we go let’s read this definite
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integrals the definite integral f of x
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with respect to X from A to B is
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connected with the problems of
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determining the distance past or for a
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given speed Computing the area of a
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curved linear trapezoid
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Etc there are many similar problems
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involving functions of dependent
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not on one but on many arguments a
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typical problem of this kind is to find
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the volume of a curved linear cylinder
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which is a three-dimensional analog of a
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curved linear trapezoid
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then here it gives you the curve linear
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so that’s a pretty good picture by the
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way that’s a really good picture it
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looks like it’s hand drawn
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let me zoom in so you can see that it’s
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pretty impressive
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yeah that totally looks hand-drawn to me
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yeah I don’t know how they made these
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books back then but you can see how how
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to the point it is
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and it’s pretty Advanced right it’s
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pretty Advanced
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um I cannot see this being used today as
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a book in an undergrad course unless it
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was like you know specifically used for
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advanced undergrads and obviously you
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would have to have a lecture and stuff
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and notes and you know a teacher to help
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you you know dissect the information to
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give you their version of what’s in the
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book and try to fill in missing details
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uh and things like that but you can see
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these these old these old Soviet era
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books are really hardcore
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and I don’t know I just kind of like
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that it’s just different it’s a piece of
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history as a collector of of math books
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um you know I think it’s amazing right A
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Book Like This is very very rare very
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hard to get I don’t believe let’s see
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let’s go back to the um let’s go back to
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the content here I want to check
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something
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yeah has a name index subject index
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yeah let’s go to the end of the first
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chapter here so chapter one
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so you see there’s I don’t see
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we don’t see exercises
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right I don’t see exercises in this book
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so some of these books have exercises
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some of them don’t this has a lot of
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examples
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um yeah really beautiful I gotta smell
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it one more time here just just
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ah let’s skip ahead to like a random
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section so you can see some more stuff
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here oh absolute convergence I mean
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that’s something you hear about in a
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calc 2 class in some sense right with
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series
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here they’re talking about a double
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integral said to be absolute convergent
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if this integral converges right if the
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absolute value yeah same thing with
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Series right if you have an infinite sum
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it’s the same thing you’ll see the sum
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converges if if it converges and apps it
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converges absolutely if it converges an
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absolute value that’s what they’re
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saying here so that’s just very very
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similar
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test for absolute convergence the
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general comparison test that’s cool you
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have comparison tests for series as well
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so you see a lot of analogs between
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other areas of math
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really beautiful
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wow
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equivalence of convergence and absolute
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convergence in the case of improper
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multiple integral
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yeah sometimes the English is not
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100 right because it’s a translation
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let’s take a look at the appendices see
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what we have back here supplement
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asymptotic expansions
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um
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beautiful
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that’s the first supplement see what the
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second one is
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that’s supplement one being careful here
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with my pages I don’t want to damage
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this book supplement two oh universal
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digital computers oh cool this is the
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computer stuff
Computers
13:04
this supplement provides an introduction
13:05
to Modern digital computers they’re
13:08
operation in use it cannot be regarded
13:10
as a systematic account of the computer
13:11
Theory and programming methods and for
13:13
greater detail we refer the reader to
13:15
special books
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that’s so cool computers wow
13:19
introduction many problems of modern
13:21
science and engineering require
13:22
extensive calculations to obtain results
13:24
of practical importance the amount of
13:27
work may be so large that the
13:28
calculations either cannot be carried
13:30
out manually or take so much time the
13:32
result becomes useless
13:34
for example it makes no sense to
13:36
forecast the next day’s weather by
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applying a method that takes a month of
13:39
computational work that’s a good that’s
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a good example
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yeah it talks about the basic types of
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computer Computing machines are divided
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into two basic classes Machines of
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discrete operation referred to
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as digital and Machines of continuous
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operation called analog a digital
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computer operates with numbers
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represented in a positional number
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system and analog computer represents
14:03
variables by means of some physical
14:04
processes and quantities such as
14:06
electric currents voltages mechanical
14:08
displacements and so on that may very
14:10
continuously interesting and analog
14:13
computers only the final results take
14:14
the digital form analog computers are
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widely
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applied mostly when high accuracy is not
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required but in modern computational
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mathematics they are of less importance
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than digital machines this reminds me of
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other books published by mirror
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Publishers I saw a book once I don’t own
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this one it was on like I think it was
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on like refrigerators or like the
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microwave or something and it talks
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about like microwaves and how microwaves
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are made it’s just they have books on
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everything right all the Sciences not
14:39
just mathematics have a book on bees and
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people it talks about like bees and how
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people are related to them and you know
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it’s really scientific it’s called it’s
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actually called bees and people
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so they have a lot of really interesting
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books on all areas of science they have
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some that are not science I actually
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have a cookbook that was published by
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mere Publishers so
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yeah quite interesting anyways I just
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wanted to show you this really rare book
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there’s other books like this by mere
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Publishers they’re all very very rare
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and the prices very wildly
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um I forgot when I bought this it’s been
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a while oh let’s take the dust jacket
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off
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oh look at that look how blue that is
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wow
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wow look at that it’s fancy looking it’s
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almost like glitter it’s in such good
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condition this is a masterpiece
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yeah you can tell I’m a collector
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so I love stuff like this I collect all
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kinds of things but this is a nice book
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anyways uh that’s it that’s wanted to
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show you this book if you found any
15:46
value in this content at all and you
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know feel free to subscribe if you want
15:50
to if you want to learn mathematics I do
15:52
have courses they’re on my website
15:55
mathsourcerer.com they’re actually on
15:57
the udb platform but if you get them
16:00
please use my website as it helps me and
16:02
I have courses on algebra calculus
16:04
differential equations some Advanced
16:05
calculus some abstract algebra stuff
16:07
like that
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and yeah I set the prices to be really
16:10
low so if you use my website if you use
16:12
those links not only does it help me but
16:13
I’m pretty sure you get like a really
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low price because I I lowered it to the
16:16
minimum
16:17
but yeah mere Publishers if you take
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anything away from this video it’s that
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um these are really rare books at least
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here in the US I know in other countries
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people have them
16:27
um I have a YouTube channel in Spanish
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and people are always going on about
16:30
like oh yeah it’s they’re they’re cheap
16:32
here but it’s all about shipping too
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right A lot of times like the shipping
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is expensive so
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yeah
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anyways until next time good luck take
16:40
care keep doing mathematics
