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
Thanks to Anish.dot for the original scan.
The Internet Archive link.
Link to the old scan.
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