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.