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Books in Analysis

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    • Measure and Integration

      Concepts, Examples, and Applications
      • 1st Edition
      • Rudi Weikard + 2 more
      • English
      Measure and Integration: Examples, Concepts, and Applications offers a comprehensive introduction to the fundamental principles and methods of real analysis, providing readers with a solid foundation through clear explanations, rigorous proofs, and an abundance of thoughtfully constructed exercises. From the very first chapter, students are encouraged to engage actively with concepts, applying them to a range of practical examples that reinforce both understanding and analytical skills. The book’s structured approach ensures that readers not only grasp key theorems and core techniques, but also develop the problem-solving abilities essential for higher-level mathematics and related applications.The text also delves into advanced areas such as integration on product spaces, Radon functionals, functions of bounded variation, Lebesgue-Stieltjes measures, convolutions, probability, and differential equations. Each chapter concludes with advanced exercises, clearly marked for difficulty, allowing both students and instructors to tailor their study or coursework. An appendix with complete solutions supports independent learning, making the book a valuable resource for both classroom use and self-study.

    • Generalized Quantum Calculus with Applications

      • 1st Edition
      • Svetlin G. Georgiev + 1 more
      • English
      Generalized Quantum Calculus with Applications is devoted to the qualitative theory of general quantum calculus and its applications to general quantum differential equations and inequalities. The book is aimed at upper-level undergraduate students and beginning graduate students in a range of interdisciplinary courses including physical sciences and engineering, from quantum mechanics to differential equations, with pedagogically organized chapters that each concludes with a section of practical problems. Generalized quantum calculus includes a generalization of the q-quantum calculus and the time scale calculus. There are many open problems and difficulties in q-quantum calculus and time-scale calculus, and this book explores how to use the generalized quantum operators to solve difficulties arising in q-quantum calculus and time-scale calculus, including but not limited to generalized quantum integration, generalized quantum chain rules, and generalized quantum Taylor formula.Since generalized quantum calculus includes the q-quantum and time-scale calculus, this book can be utilized by a wide audience of researchers and students. This text is one of few foundational books on generalized quantum calculus and can be used for future discoveries in the area of integral transforms, variational calculus, integral equations, and inequalities in the language of generalized quantum calculus. This book also offers detailed proofs, exercises, and examples to aid instructors, researchers, and users in their studies.

    • Fuzzy Mathematics, Graphs, and Similarity Measures

      Analysis and Application Across Global Challenges
      • 1st Edition
      • John Mordeson + 1 more
      • English
      Fuzzy Mathematics, Graphs, and Similarity Measures provides a solid foundation in core analytical tracks of mathematics of uncertainty, from fuzzy mathematics to graphs and similarity measures with applications in a range of timely cases studies and world challenges. Following a full grounding in fuzzy graph indices, connectivity in fuzzy graph structures, lattice isomorphisms, and similarity measures, the book applies these models in analyzing world challenges, from human trafficking to modern slavery, global poverty, global hunger, homelessness, biodiversity, extinction, terrorism and bioterrorism, pandemics, and climate change.Connections and constructive steps forward are tied throughout to UN Sustainable Development Goals (SDGs). The authors demonstrate and instruct readers in applying techniques from mathematics of uncertainty in examining issues where accurate data is impossible to obtain. In addition to a diverse range of cases studies, exercises reinforce key concepts in each chapter, and an online instructor’s manual supports teaching across a range of course contexts.

    • Advanced Mathematics for Engineering Students

      The Essential Toolbox
      • 1st Edition
      • Brent J. Lewis + 2 more
      • English
      Advanced Mathematics for Engineering Students: The Essential Toolbox provides a concise treatment for applied mathematics. Derived from two semester advanced mathematics courses at the author’s university, the book delivers the mathematical foundation needed in an engineering program of study. Other treatments typically provide a thorough but somewhat complicated presentation where students do not appreciate the application. This book focuses on the development of tools to solve most types of mathematical problems that arise in engineering – a “toolbox” for the engineer. It provides an important foundation but goes one step further and demonstrates the practical use of new technology for applied analysis with commercial software packages (e.g., algebraic, numerical and statistical).

    • Nonlinear Differential Problems with Smooth and Nonsmooth Constraints

      • 1st Edition
      • Dumitru Motreanu
      • English
      Nonlinear Differential Problems with Smooth and Nonsmooth Constraints systematically evaluates how to solve boundary value problems with smooth and nonsmooth constraints. Primarily covering nonlinear elliptic eigenvalue problems and quasilinear elliptic problems using techniques amalgamated from a range of sophisticated nonlinear analysis domains, the work is suitable for PhD and other early career researchers seeking solutions to nonlinear differential equations. Although an advanced work, the book is self-contained, requiring only graduate-level knowledge of functional analysis and topology. Whenever suitable, open problems are stated and partial solutions proposed. The work is accompanied by end-of-chapter problems and carefully curated references.

    • Beyond Pseudo-Rotations in Pseudo-Euclidean Spaces

      • 1st Edition
      • Abraham Ungar
      • English
      Beyond Pseudo-Rotations in Pseudo-Euclidean Spaces presents for the first time a unified study of the Lorentz transformation group SO(m, n) of signature (m, n), m, n ∈ N, which is fully analogous to the Lorentz group SO(1, 3) of Einstein’s special theory of relativity. It is based on a novel parametric realization of pseudo-rotations by a vector-like parameter with two orientation parameters. The book is of interest to specialized researchers in the areas of algebra, geometry and mathematical physics, containing new results that suggest further exploration in these areas.

    • Means in Mathematical Analysis

      Bivariate Means
      • 1st Edition
      • Gheorghe Toader + 1 more
      • English
      Means in Mathematical Analysis addresses developments in global analysis, non-linear analysis, and the many problems of associated fields, including dynamical systems, ergodic theory, combinatorics, differential equations, approximation theory, analytic inequalities, functional equations and probability theory. The series comprises highly specialized research monographs written by eminent scientists, handbooks and selected multi-contributor reference works (edited volumes), bringing together an extensive body of information. It deals with the fundamental interplay of nonlinear analysis with other headline domains, particularly geometry and analytic number theory, within the mathematical sciences.

    • Computational Analysis of Structured Media

      • 1st Edition
      • Simon Gluzman + 2 more
      • English
      Computational Analysis of Structured Media presents a systematical approach to analytical formulae for the effective properties of deterministic and random composites. Schwarz’s method and functional equations yield for use in symbolic-numeric computations relevant to the effective properties. The work is primarily concerned with constructive topics of boundary value problems, complex analysis, and their applications to composites. Symbolic-numerical computations are widely used to deduce new formulae interesting for applied mathematicians and engineers. The main line of presentation is the investigation of two-phase 2D composites with non-overlapping inclusions randomly embedded in matrices.

    • Finite Elements for Analysis and Design

      Computational Mathematics and Applications Series
      • 1st Edition
      • J. E. Akin
      • English
      The finite element method (FEM) is an analysis tool for problem-solving used throughout applied mathematics, engineering, and scientific computing. Finite Elements for Analysis and Design provides a thoroughlyrevised and up-to-date account of this important tool and its numerous applications, with added emphasis on basic theory. Numerous worked examples are included to illustrate the material.

    • Handbook of Mathematical Formulas and Integrals

      • 1st Edition
      • Alan Jeffrey
      • English
      If there is a formula to solve a given problem in mathematics, you will find it in Alan Jeffrey's Handbook of Mathematical Formulas and Integrals. Thanks to its unique thumb-tab indexing feature, answers are easy to find based upon the type of problem they solve. The Handbook covers important formulas, functions, relations, and methods from algebra, trigonometric and exponential functions, combinatorics, probability, matrix theory, calculus and vector calculus, both ordinary and partial differential equations, Fourier series, orthogonal polynomials, and Laplace transforms. Based on Gradshteyn and Ryzhik's Table of Integrals, Series, and Products, Fifth Edition (edited by Jeffrey), but far more accessible and written with particular attention to the needs of students and practicing scientists and engineers, this book is an essential resource. Affordable and authoritative, it is the first place to look for help and a rewarding place to browse.