Integral and measure : from rather simple to rather complex /

• Κύριος συγγραφέας: Mackevičius, Vigirdas
• Μορφή: Ηλ. βιβλίο
• Γλώσσα: English
• Έκδοση: London : ISTE, Ltd ; 2014.; Hoboken : Wiley, 2014.
• Σειρά: Oregon State monographs. Mathematics and statistics series.
• Θέματα: Integrals, Generalized.; Lebesgue integral.; Mathematics.; Measurement.; MATHEMATICS > Calculus.; MATHEMATICS > Mathematical Analysis.; Electronic books.

 This book is devoted to integration, one of the two main operations in calculus. In Part 1, the definition of the integral of a one-variable function is different (not essentially, but rather methodically) from traditional definitions of Riemann or Lebesgue integrals. Such an approach allows us, on the one hand, to quickly develop the practical skills of integration as well as, on the other hand, in Part 2, to pass naturally to the more general Lebesgue integral. Based on the latter, in Part 2, the author develops a theory of integration for functions of several variables. In Part 3, within. 

 Cover page; Half-title page; Title page; Copyright page; Contents; Preface; Note for the Teacher or Who is better, Riemann or Lebesgue?; Notation; Part 1: Integration of One-Variable Functions; 1: Functions without Second-kind Discontinuities; P.1. Problems; 2: Indefinite Integral; P.2. Problems; 3: Definite Integral; 3.1. Introduction; P.3. Problems; 4: Applications of the Integral; 4.1. Area of a curvilinear trapezium; 4.2. A general scheme for applying the integrals; 4.3. Area of a surface of revolution; 4.4. Area of curvilinear sector; 4.5. Applications in mechanics; P.4. Problems.