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Multiple Integrals in Calculus: Improper Integrals, Line Integrals, Surface Integrals
Paperback
Series: de Gruyter Textbook
Publisher Price: $105.99
ISBN13: 9783119143455
Publisher: de Gruyter
Published: Nov 6 2025
Pages: 384
Weight: 1.34
Height: 0.79 Width: 6.69 Depth: 9.61
Language: English
The book consists of eight chapters, each focusing on different aspects of multiple integrals and related topics in mathematical analysis.
In Chapter 1, multiple integrals are defined and developed. The Jordan measure in n-dimensional unit balls is introduced, along with the definition and criteria for multiple integrals, as well as their properties.
In Chapter 3, we focus on improper multiple integrals and their properties. The chapter deduces criteria for the integrability of functions of several variables and develops concepts such as improper integrals of nonnegative functions, comparison criteria, and absolute convergence.
Chapter 4 investigates the Stieltjes integral and its properties. Topics covered include the differentiation of monotone functions of finite variation and the Helly principle of choice, as well as continuous functions of finite variation.
Chapter 5 addresses curvilinear integrals, defining line integrals of both the first and second kinds. It also discusses the independence of line integrals from the path of integration.
In Chapter 6, surface integrals of the first and second kinds are introduced. The chapter presents the Gauss-Ostrogradsky theorem and Stokes' formulas, along with advanced practical problems to practice these concepts.
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