The Fundamentals of Mathematical Analysis: International Series of Monographs in Pure and Applied Mathematics, Volume 72

The Fundamentals of Mathematical Analysis, Volume I is a translation from Russian and used as a textbook that provides a systematic and serious discussion of the fundamentals of mathematical analysis. Differential and integral calculus, which were established in the 17th century; the theory of limits as the foundation of mathematical analysis; and the concept of real numbers as justifying the theory of limits are discussed in the early part of the volume. The concept of the limit of a function related to the concept of continuity of a function as explained by Bolzano and Cauchy is discussed. Fermat's theorem and Taylor's formula in understanding differential calculus are then presented. The book also investigates the value of the function when several independent variables occur, by considering the values of all the independent variables simultaneously. The concept of a primitive function and of an indefinite integral used in science and engineering is noted. Integral calculus, as found in geometric and mechanical applications, and differential calculus, as significant in some geometric application, are then examined. In the last part, the text discusses the works of Newton and Leibniz. The book will serve as a guide and reference for mathematicians, students, and professors of calculus and advanced mathematics.