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New Methods for Solving Elliptic Equations
This influential monograph, translated from the Russian by D. E. Brown, presents original methods for the theory and solution of elliptic partial differential equations. Vekua utilizes the theory of functions of a complex variable to develop integral representations for solutions of general elliptic equations in two dimensions. The text covers a wide range of boundary-value problems and is wide…
- Edition
- 1st
- ISBN/ISSN
- 0720423538
- Collation
- -
- Series Title
- -
- Call Number
- 517.36 V394
Locally Convex Spaces and Linear Partial Differential Equations
This monograph investigates the deep, structural relationship between locally convex spaces and the theory of linear partial differential equations (PDEs). Trèves demonstrates how abstract functional analysis—specifically the duality theory of topological vector spaces—provides the necessary framework to solve fundamental problems in PDEs, such as existence, approximation, and regularity o…
- Edition
- 1st
- ISBN/ISSN
- 0387039031
- Collation
- -
- Series Title
- -
- Call Number
- 517.6 J812
Topological Vector Spaces, Distributions and Kernels
This foundational monograph provides a rigorous and systematic exposition of the three subjects mentioned in its title, which are central to modern functional analysis and partial differential equations. Trèves develops the theory of topological vector spaces with a focus on their applications to the study of distributions (generalized functions). A major highlight is the treatment of the kern…
- Edition
- 1st
- ISBN/ISSN
- 0126994501
- Collation
- -
- Series Title
- -
- Call Number
- 517.5 T812
Introduction to Measure and Integration
This classic textbook provides a self-contained introduction to the theory of finite measures and integration in general spaces, intended for advanced undergraduate or postgraduate mathematics students. The book establishes measure as the primary concept, deriving the integral by extending its definition from simple functions using monotone limits. While covering general measure spaces, it plac…
- Edition
- 1st
- ISBN/ISSN
- 0521098041
- Collation
- -
- Series Title
- -
- Call Number
- 517 T246
Fundamental Concepts of Analysis
This textbook provides a rigorous introduction to the foundational principles of real analysis. It is designed to bridge the gap between elementary calculus and advanced mathematics by focusing on the logical structure of the real number system, set theory, and the concepts of limits, continuity, and convergence. The authors emphasize clear definitions and formal proofs, helping students develo…
- Edition
- 1st
- ISBN/ISSN
- 0133355055
- Collation
- -
- Series Title
- -
- Call Number
- 517 S642
Generalized Hypergeometric Functions
This textbook provides a foundational and comprehensive guide to understanding generalized hypergeometric functions, which are central to mathematical physics because common analytical functions like Bessel and Legendre functions are special cases of them. Planned as an extended revision of W. N. Bailey's 1935 work, the book covers topics including the Gauss function, hypergeometric integrals, …
- Edition
- 1st
- ISBN/ISSN
- 052106483X
- Collation
- -
- Series Title
- -
- Call Number
- 517.88 S631
Mathematical Analysis: An Introduction
This foundational textbook serves as a rigorous introduction to basic classical analysis, following a traditional pedagogical path. Designed for advanced secondary students and first-year university undergraduates, the text provides a detailed treatment of fundamental topics including limits, infinite series, continuity, and differentiability (referred to by the authors as "derivability"). By e…
- Edition
- 1st
- ISBN/ISSN
- -
- Collation
- -
- Series Title
- -
- Call Number
- 517 S425
Principal Functions
This research monograph systematically develops the theory and applications of principal functions on Riemann surfaces and Riemannian spaces. The central problem addressed is the construction of a harmonic function that "imitates" a given singularity or boundary behavior within a specific neighborhood. These functions serve as essential, versatile tools across various branches of modern mathema…
- Edition
- 1st
- ISBN/ISSN
- 0442069987
- Collation
- -
- Series Title
- -
- Call Number
- 517.5 R692
Functions, Limits, and Continuity
This textbook provides a rigorous and systematic introduction to the fundamental concepts of mathematical analysis, specifically targeting the theory of limits and the continuity of real-valued functions. Ribenboim adopts a precise axiomatic approach to develop the properties of the real number system, utilizing sequences, Cauchy convergence, and accumulation points to build a solid foundation …
- Edition
- 1st
- ISBN/ISSN
- 0471718009
- Collation
- -
- Series Title
- -
- Call Number
- 517.5 R484
Elements of Complex Variables
This textbook provides a rigorous and comprehensive introduction to the theory of functions of a complex variable. Specifically designed for students transitioning from calculus to higher-level mathematical analysis, the author emphasizes conceptual clarity and logical precision to minimize the vagueness often encountered by beginners. The text covers foundational topics—including analytic fu…
- Edition
- 2nd
- ISBN/ISSN
- 0030144264
- Collation
- -
- Series Title
- -
- Call Number
- 517.8 P414
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