Differential and Integral Calculus by N. Piskunov


This text is designed as a course of mathematics for higher technical schools. It contains many worked examples that illustrate the theoretical material and serve as models for solving problems. The first two chapters "Number. Variable. Function" and "Limit. Continuity of a Function" have been made as short as possible. Some of the questions that are usually discussed in these chapters have been put in the third and subsequent chapters without loss of continuity. This has made it possible to take up very early the basic concept of differential calculus the derivative which is required in the study of technical subjects. Experience has shown this arrangement of the material to be the best and most convenient for the student.

A large number of problems have been included, many of which illustrate the interrelationships of mathematics and other disciplines. The problems are specially selected (and in sufficient number) for each section of the course thus helping the student to master the theoretical material. To a large extent, this makes the use of a separate book of problems unnecessary and extends the usefulness of this text as a course of mathematics for self-instruction.

The book was translated from the Russian by G. Yankovsky and was published by Mir in 1969. Subsequently it was also republished as a single and two volume format.



Contents



Preface 11

Chapter I NUMBER. VARIABLE. FUNCTION

Chapter II. LIMIT. CONTINUITY OF A FUNCTION

Chapter III. DERIVATIVE AND DIFFERENTIAL

Chapter IV. SOME THEOREMS ON DIFFERENTIABLE FUNCTIONS

Chapter V. INVESTIGATING THE BEHAVIOUR OF FUNCTIONS

Chapter VI. THE CURVATURE OF A CURVE

Chapter VII. COMPLEX NUMBERS. POLYNOMIALS

Chapter VIII. FUNCTIONS OF SEVERAL VARIABLES

Chapter IX. APPLICATIONS OF DIFFERENTIAL CALCULUS TO SOLID GEOMETRY

Chapter X, INDEFINITE INTEGRALS

Chapter XI. THE DEFINITE INTEGRAL

Chapter XII. GEOMETRIC AND MECHANICAL APPLICATIONS OF THE DEFINITE INTEGRAL

Chapter XIII. DIFFERENTIAL EQUATIONS

Chapter XIV. MULTIPLE INTEGRALS

Chapter XV. LINE INTEGRALS AND SURFACE INTEGRALS

Chapter XVI. SERIES

Chapter XVII. FOURIER SERIES

Chapter XVIII. EQUATIONS OF MATHEMATICAL PHYSICS

Chapter XIX. OPERATIONAL CALCULUS AND CERTAIN OF ITS APPLICATIONS

Subject Index