In this post, we will see the book Calculus: Basic Concepts for High Schools by Lev Tarasov. Now, many of you must be wondering why a re-post of a book? The answer is that this is not a scan of the original book. But instead, it is a completely electronic version of the book created using LaTeX!

We have used XeLaTeX for typesetting the book, and friends it was fun indeed to do it. With LaTeX the equations are typeset really beautifully. And the final result is a beautifully typeset book which is of the best out there for the given subject. The result was immensely satisfying to see and is aesthetically pleasing as well.

Below are a few sample pages from the book:

Some of the diagrams I have drawn using TiKz.

At other places, I have used the existing diagrams.

For now, I have used the some of the old figures from the scan, but it would be fun to redraw them using TiKz. I have redrawn some of them like the ones above, but I would need some help with doing all of them. let me know if you are ready for volunteering for that. There might be a few typos here and there or the mathematical mistakes. Please point them and I will correct them. What better way to proofread than using 1000s of eyes? We plan to digitise all the important books with LaTeX in the near future, let me know if you want to pitch in.

About the book

The whole book is presented as a relatively free-flowing

dialogue between the AUTHOR and the READER. From one discussion

to another the AUTHOR will lead the inquisitive and receptive

READER to different notions, ideas, and theorems of calculus,

emphasizing especially complicated or delicate aspects, stressing the

inner logic of proofs, and attracting the reader’s attention to special

points. I hope that this form of presentation will help a reader of the

book in learning new definitions such as those of derivative, antiderivative, definite. integral, differential equation, etc. I also expect that

it will lead the reader to better understanding of such concepts as

numerical sequence, limit of sequence, and function. Briefly, these

discussions are intended to assist pupils entering a novel world of

calculus. And if in the long run the reader of the book gets a feeling

of the intrinsic beauty and integrity of higher mathematics or even

is appealed to it, the author will consider his mission as successfully

completed.

Thanks to Anish.dot for the original scan.

The Internet Archive link.

Link to the old scan.

Contents

Preface v

1 INFINITE NUMERICAL SEQUENCE 1

2 LIMIT OF SEQUENCE 17

3 CONVERGENT SEQUENCE 29

4 FUNCTION 45

5 MORE ON FUNCTION 61

6 LIMIT OF FUNCTION 85

7 MORE ON THE LIMIT OF FUNCTION 103

8 VELOCITY 115

9 DERIVATIVE 129

10 DIFFERENTIATION 147

11 ANTIDERIVATIVE 169

12 INTEGRAL 185

13 DIFFERENTIAL EQUATIONS 199

14 MORE ON DIFFERENTIAL EQUATIONS 215

PROBLEMS 227

Hi,

It is a great idea to typeset old books using LaTeX. I have some experience in typesetting mathematical texts using LaTeX and TikZ and will be happy to contribute. Let me know if you have started a project in github or similar places.

Regards,

Mainak

Hi Mitr, I will be happy to LaTeX’em too if you are planning to start a project. I also think it’s a great idea to re-typeset and extend the life of these treasures! Please let me know

— AD

Sure, already have about 5-6 ready to go, with each requiring a little work. Will perhaps start a git kind of repo, or a document on sharelatex or something similar

Sharelatex/overleaf are convenient for such collaborations. I have emailed you [from] my mail address. Let me know when, where and how to begin. Thanks! 🙂

How can I download this new version?

Sent from my iPad

>

the link is given in the post

Awesome job guys !! I grew up on Mir books and was looking around to see if I could get some for my daughter entering 9th grade. Glad I found this site. This book in particular is a gem.

Great job! Thanks a lot. What is the main text font used throughout the book? I know that’s too much but i’ll try: Can you upload tex-file of the book?

I have created a git repo with all the files. l will share the details soon.

WELL DONE ! ^ _ ^

GREAT WORK. KEEP IT DOING. – THANKS

Have you already made a git repo with all the file available (as mentioned above)? I’d be happy to jump in and help with typesetting (even for original Russian ones).

I have created a git repo, but have not added all the files, will surely announce here perhaps sometime next week. Thanks for the gesture!

Have experience in LaTeX and tikz.

Ready to volunteer.

Please intimate me.

Thanks for the gesture. Will post the git repo with sometime next week.