Sequence and Author
L. V. TARASOV
Ii'
A
Basic Concepts for High Schools
MAR FUBLISHERS MOSCOW:
L. V. TARASOV
CALCULUS
Basic Concepts for High Schools
Translated from the Russian by V. KISIN and A. ZILBERMAN
MIR PUBLISHERS
Moscow
PREFACE
Many objects are obscure to us not because our perceptions are poor, but simply because these objects
are outside of the realm of our conceptions. Kosma Prutkov
CONFESSION OF THE AUTHOR. My first acquaintance with calculus (or mathematical analysis) dates back to nearly a quarter of a century. This happened in the Moscow Engineering Physics Institute during splendid lectures given at that time by Professor D. A. Vasilkov. Even now I remember that feeling of delight and almost happiness. In the discussions with my classmates I rather heatedly insisted on a simile of higher mathematics to literature, which at that time was to me the most admired subject. Sure enough, these comparisons of mine lacked in objectivity. Nevertheless, my arguments were to a certain extent justified. The presence of an inner logic, coherence, dynamics, as well as the use of the most precise words to express a way of thinking, these were the characteristics of the prominent pieces
of literature. They were present, in a different form of course, in
higher mathematics as well. I remember that all of a sudden elementary mathematics which until that moment had seemed to me very dull and stagnant, turned to be brimming with life and inner motion governed by an impeccable logic.
Years have passed. The elapsed period of time has inevitably
erased that highly emotional perception of calculus which has become a working tool for me. However, my memory keeps intact that unusual happy feeling which I experienced at the time of my initiation to this extraordinarily beautiful world of ideas which we call higher mathematics.
CONFESSION OF THE READER. Recently our professor of mathematics told us that we begin to
Ii'
A
Basic Concepts for High Schools
MAR FUBLISHERS MOSCOW:
L. V. TARASOV
CALCULUS
Basic Concepts for High Schools
Translated from the Russian by V. KISIN and A. ZILBERMAN
MIR PUBLISHERS
Moscow
PREFACE
Many objects are obscure to us not because our perceptions are poor, but simply because these objects
are outside of the realm of our conceptions. Kosma Prutkov
CONFESSION OF THE AUTHOR. My first acquaintance with calculus (or mathematical analysis) dates back to nearly a quarter of a century. This happened in the Moscow Engineering Physics Institute during splendid lectures given at that time by Professor D. A. Vasilkov. Even now I remember that feeling of delight and almost happiness. In the discussions with my classmates I rather heatedly insisted on a simile of higher mathematics to literature, which at that time was to me the most admired subject. Sure enough, these comparisons of mine lacked in objectivity. Nevertheless, my arguments were to a certain extent justified. The presence of an inner logic, coherence, dynamics, as well as the use of the most precise words to express a way of thinking, these were the characteristics of the prominent pieces
of literature. They were present, in a different form of course, in
higher mathematics as well. I remember that all of a sudden elementary mathematics which until that moment had seemed to me very dull and stagnant, turned to be brimming with life and inner motion governed by an impeccable logic.
Years have passed. The elapsed period of time has inevitably
erased that highly emotional perception of calculus which has become a working tool for me. However, my memory keeps intact that unusual happy feeling which I experienced at the time of my initiation to this extraordinarily beautiful world of ideas which we call higher mathematics.
CONFESSION OF THE READER. Recently our professor of mathematics told us that we begin to