G. M. Fikhtengol'ts – författare
Visar alla böcker från författaren G. M. Fikhtengol'ts. Handla med fri frakt och snabb leverans.
3 produkter
3 produkter
E-bok
PDF, Engelska, 2014979 kr
Läs direkt efter köp
The Fundamentals of Mathematical Analysis, Volume 1 is a textbook that provides a systematic and rigorous treatment of the fundamentals of mathematical analysis. Emphasis is placed on the concept of limit which plays a principal role in mathematical analysis. Examples of the application of mathematical analysis to geometry, mechanics, physics, and engineering are given. This volume is comprised of 14 chapters and begins with a discussion on real numbers, their properties and applications, and arithmetical operations over real numbers. The reader is then introduced to the concept of function, important classes of functions, and functions of one variable; the theory of limits and the limit of a function, monotonic functions, and the principle of convergence; and continuous functions of one variable. A systematic account of the differential and integral calculus is then presented, paying particular attention to differentiation of functions of one variable; investigation of the behavior of functions by means of derivatives; functions of several variables; and differentiation of functions of several variables. The remaining chapters focus on the concept of a primitive function (and of an indefinite integral); definite integral; geometric applications of integral and differential calculus. This book is intended for first- and second-year mathematics students.
E-bok
PDF, Engelska, 2014979 kr
Läs direkt efter köp
The Fundamentals of Mathematical Analysis, Volume 2 is a continuation of the discussion of the fundamentals of mathematical analysis, specifically on the subject of curvilinear and surface integrals, with emphasis on the difference between the curvilinear and surface ""integrals of first kind"" and ""integrals of second kind."" The discussions in the book start with an introduction to the elementary concepts of series of numbers, infinite sequences and their limits, and the continuity of the sum of a series. The definition of improper integrals of unbounded functions and that of uniform convergence of integrals are explained. Curvilinear integrals of the first and second kinds are analyzed mathematically. The book then notes the application of surface integrals, through a parametric representation of a surface, and the calculation of the mass of a solid. The text also highlights that Green''s formula, which connects a double integral over a plane domain with curvilinear integral along the contour of the domain, has an analogue in Ostrogradski''s formula. The periodic values and harmonic analysis such as that found in the operation of a steam engine are analyzed. The volume ends with a note of further developments in mathematical analysis, which is a chronological presentation of important milestones in the history of analysis. The book is an ideal reference for mathematicians, students, and professors of calculus and advanced mathematics.
E-bok
PDF, Engelska, 1965870 kr
Läs direkt efter köp
The Fundamentals of Mathematical Analysis, Volume 2 focuses on the fundamental concepts of mathematical analysis. This book discusses the theorems on the comparison of series, condition for uniform convergence, and application of the fundamental formula of integral calculus. The differentiation under the integral sign, Lagrange''s method of undetermined multipliers, and definition of curvilinear integrals of the second kind are also elaborated. This text likewise covers the transformation of plane domains, case of a piece-wise smooth surface, and problem of calculating the mass of a solid. Other topics include the flow of a vector through a surface, determination of coefficients by the Euler-Fourier method, and generalized equation of closure. This volume is a good reference for students and researchers conducting work on mathematical analysis.