Soviet Era Math Book for Beginners and Mathematical Experts

This book states that it is written with beginners in mind but it can also be of use to expert mathematicians. The first half of the book is on Differential Equations and the second half is on the Calculus of Variations. In this video I will show you this book and I will also solve a differential equation from the book near the end of the video. I purposely picked one that was really simple so if you know some calculus you should be able to follow along or solve it yourself. Originally this book was written in Russian but it was translated to English and published by Mir Publishers. Mir Publishers was/is a publishing company that translates Russian books to various languages. I first heard of Mir from the comments here on the channel so thank you to everyone for the book suggestions! The book is called Differential Equations and the Calculus of Variations and it was written by Lev Elsgolts.

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0:00 The Book
7:43 The Problem
13:22 Finishing Up
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[corbinwilson]

My math teacher learnt math in the Soviet Union. He’s Cuban and went there for university. He is unbelievably smart.

[cesarmaldonadomercad]

My PhD supervisor was born and educated in the Soviet Union. He was and still is a superb mathematician. He told me he learnt all this stuff of differential equations when he was 14. By the way, I have this book in Spanish and I love it.

[maksimluzin]

I have studied the Pure Mathematics in UK Open University. My tutor was British, of course, but he said me he has learn Russian language just to read Russian Math books! 🙄 He was not good in Russian ordinal conversations with me at all, but he could read the math books in Russian quite well and fast, I was really very excited about it! I didn't expect that!

[razendra]

I did my MSc in Engineering from the Soviet Union 33 years ago. I still use those excellent textbooks as a reference.

[Fazz]

Soviet math books are pretty good.

My calculus teacher always told his students "the older the textbook, the better", soviet math books is a good example of this.

[meteor]

I have a lot of URSS math books in Russian, they are very hardcore. Also there is a legendary exercise book for analysis by Boris Demidovich. I know 100% that there are translations of it in English, if you have the possibility buy it, you won't regret. Here where I live, soviet era books cost something like 1-3$

[Lena-szyt]

I own a book by Soviet mathematician Boris Demidovich. It's called Collection of problems in mathematical analysis (Сборник задач и упражнении по математическом анализи). My father used that book while he was at University and now I used it for my postgradueted studies in math. The book that I own is published in 1969 and is a real treasure, it has over a 4.000 problems with answers. Here where I live theese old editions are about 3 to 5 euro.

[johnnath]

Another great Soviet era text is Landau and Lifshitz's Course of Theoretical Physics, which Landau referred to as the "theoretical minimum". This book is permeated throughout by deep physical insights. I believe this work is well worth a review by an expert.

[justinnamuco]

The fact that it has many example problems, many exercises, and answers for all exercises, that's just beautiful

[vladimirdb]

Countries like Peru and Mexico increased exponentially their level in math due to the soviet professors that came to teach at colleges. Till this day there are various courses that their syllabus is based pretty much in translated soviet textbooks. Those textbooks have an amazing level

[IVANKOVALE]

Thank you for excellent review. For us in USSR MIR (translated both as 'Peace' and 'World') publisher was the main source of the excellent foreign books translated from English, German and other languages. For example, it was 'MIR' who published 'Feynman Lectures in Physics' in Russian and many other very good books.

[watermelonguy]

It's nice to feel that our textbooks are appreciated in the world. I am studying at the university to be an applied mathematician and programmer.
Soviet textbooks have always had a charm for me. They always have excellent explanations that always help me to deal with complex topics, but the most pleasant thing for me is the illustrations. They are always made as aesthetically pleasing as possible. Looking at them you see the beauty of mathematics.
You treat this textbook with such attention that I feel ashamed that I don't appreciate these beautiful textbooks enough :)
They also sometimes contain mathematical jokes :D. I really hope that they are left in translation

[viata.]

I grew up learning math and physics from soviet union books. MIR publisher is pretty much part of my childhood. I recommend any math and physics book from them.

[Andrey]

I finished the DE course at the Moscow State University (exactly where the author worked at the time) 2 years ago and our professors still recommend this book as the main textbook for this course

[ivan.i.gerasimov]

My family moved from Russia in 2017 and we brough this book and the next 2 parts of it with us. It helped my father through his university years and he lended it to many of our family's friends to help them as well. What a great piece of literature.

[SamManso]

Mir Publishers also put out a series of booklets, written by outstanding Soviet mathematicians, meant for talented high school students and teachers under the title: Little Mathematics Library. Some of the titles (and there was many) are:
The Euler Characteristics by Shashkin; The Method of Mathematical Induction by Sominsky; The Monte Carlo Method by Sobol; Godel's Incompletness Theorem by Uspensky; and so on...lots and lots of titles. They all have Problems and hints and solutions and a bibliography. I learned a ton of math from these little booklets. They cost pennies in my old country and they were very much appreciated unlike the money-grubbing publishers of today (we all know who they are).

[phillipphil]

Mir publishing (Mir means "peace" in Russian) I still have a few from university in France. They were dirt cheap and fantastic, with some amusing comments, for example a page on how Einstein's relativity was consistent with materialistic dialectic and Marxism.

[jedediahjehoshaphat]

You can bet Mir Publisher books were really popular here in India too, owing to the good bilateral ties between India and Soviet Union there was a widespread circulation of their textbooks here during the era of the older academia.

[sanjaybhatikar]

We got books on math and science from the USSR at heavily discounted prices in India in the days of the Soviet Union. I had my school texts but almost always studied from these books from Mir publishers and Raduga publishers because they were so good for mastery of a subject. Mir means friendship in Russian.

[GCKteamKrispy]

I really love how they explain math and physics in soviet union (I am from post-soviet country). And now, they teach math in schools by totally different books that are very bad