We begin with the Little Mathematics Library series once again, after a long break. We first see the book titled *Differentiation Explained* by *V. G. Boltyansky* (*Boltyanskii*).

The author in the Preface says:

High school students, especially those interested in mathematics, physics and engineering, often ask, ‘What is “higher” mathematics?’ Sometimes they discuss this and similar questions at mathematics clubs at schools.

In this book I have tried to explain, in a way a high school pupil would understand, certain concepts of higher mathematics such as the derivative, differential equation, the number e, and natural logarithm (pupils are more apt to be aware of and interested in the latter two concepts). Wherever possible, I have tried to illustrate the concepts with problems taken from physics. In addition, I have tried to show that the concepts of “higher mathematics” are mathematical reflections of actual processes, that mathematics and life are connected, not separated, and that mathematics is a growing, not an unchanging, completed science. Not all proofs and arguments are presented with complete mathematical rigour. Some arguments are presented for illustration. This method seems to me more appropriate for a general book.

The book can be used by mathematics and physics clubs at school. Part of the material is taken from lectures the author gave at the request of the advisers of school mathematics clubs at the Moscow State University.

The book was translated from Russian by *M. Samokhvalov* and was first published by Mir in 1977. You can get the book here. All credits to the original uploader.

Contents

**Author’s Preface 6**

The Problem of a Free Falling Body 7

Statement of the Problem 7

Qualitative Solution of the Problem 9

Formula for the Velocity of a Falling Body The Number *e* 13

**Differentiation 25**

The Concept of the Derivative 25

The Differential Equation 27

Two Problems Leading to Differential Equations 28

Napierian Logarithms 33

**Harmonic Oscillations 34**

The Problem of Small Oscillations of a Pendulum 34

The Differential Equation of Harmonic Oscillations 42

The Oscillatory Circuit 45

Oscillations Produced by the Action of the Elastic Force of a Spring 47

**Some Other Applications of the Concept of the Derivative 52**

Maximum and Minimum Values 52

The Problem of Drawing a Tangent 58

Modelling 60

**Afterword 62**

Password, if needed: *mirtitles*

4-shared link here

Password, if required, for 4shared files:

www.mirtitles.org

Sir, the ebook provided contains a file in djuv format and not in pdf so I annot open it. Can you please provide a link for pdf version of the book.

You can get the appropriate djvu reader from

http://www.djvu.org

D

Another link to this file http://rapidgator.net/file/22338392/Differentiation_Explained_-Boltyansky(1977).djvu.html