Choose an application

• Reference Manager
• EndNote
• RefWorks (Direct export to RefWorks)

This book features a collection of recent findings in Applied Real and Complex Analysis that were presented at the 3rd International Conference “Boundary Value Problems, Functional Equations and Applications” (BAF-3), held in Rzeszow, Poland on 20-23 April 2016. The contributions presented here develop a technique related to the scope of the workshop and touching on the fields of differential and functional equations, complex and real analysis, with a special emphasis on topics related to boundary value problems. Further, the papers discuss various applications of the technique, mainly in solid mechanics (crack propagation, conductivity of composite materials), biomechanics (viscoelastic behavior of the periodontal ligament, modeling of swarms) and fluid dynamics (Stokes and Brinkman type flows, Hele-Shaw type flows). The book is addressed to all readers who are interested in the development and application of innovative research results that can help solve theoretical and real-world problems.

Functions of complex variables. --- Mathematics. --- Integral equations. --- Partial differential equations. --- Special functions. --- Partial Differential Equations. --- Special Functions. --- Functions of a Complex Variable. --- Integral Equations. --- Several Complex Variables and Analytic Spaces. --- Complex variables --- Elliptic functions --- Functions of real variables --- Special functions --- Mathematical analysis --- Partial differential equations --- Equations, Integral --- Functional equations --- Functional analysis --- Math --- Science --- Differential equations, partial. --- Functions, special.

Choose an application

• Reference Manager
• EndNote
• RefWorks (Direct export to RefWorks)

This volume presents research and expository papers highlighting the vibrant and fascinating study of irregularities in the distribution of primes. Written by an international group of experts, contributions present a self-contained yet unified exploration of a rapidly progressing area. Emphasis is given to the research inspired by Maier’s matrix method, which established a newfound understanding of the distribution of primes. Additionally, the book provides an historical overview of a large body of research in analytic number theory and approximation theory. The papers published within are intended as reference tools for graduate students and researchers in mathematics.

Mathematics. --- Functions of complex variables. --- Special functions. --- Number theory. --- Number Theory. --- Functions of a Complex Variable. --- Special Functions. --- Number study --- Numbers, Theory of --- Algebra --- Special functions --- Mathematical analysis --- Complex variables --- Elliptic functions --- Functions of real variables --- Math --- Science --- Numbers, Prime. --- Prime numbers --- Numbers, Natural --- Functions, special.

Choose an application

• Reference Manager
• EndNote
• RefWorks (Direct export to RefWorks)

This book highlights the remarkable importance of special functions, operational calculus, and variational methods. A considerable portion of the book is dedicated to second-order partial differential equations, as they offer mathematical models of various phenomena in physics and engineering. The book provides students and researchers with essential help on key mathematical topics, which are applied to a range of practical problems. These topics were chosen because, after teaching university courses for many years, the authors have found them to be essential, especially in the contexts of technology, engineering and economics. Given the diversity topics included in the book, the presentation of each is limited to the basic notions and results of the respective mathematical domain. Chapter 1 is devoted to complex functions. Here, much emphasis is placed on the theory of holomorphic functions, which facilitate the understanding of the role that the theory of functions of a complex variable plays in mathematical physics, especially in the modeling of plane problems. In addition, the book demonstrates the importance of the theories of special functions, operational calculus, and variational calculus. In the last chapter, the authors discuss the basic elements of one of the most modern areas of mathematics, namely the theory of optimal control.

Functions of several real variables. --- Functions, Special. --- Engineering. --- Mathematical physics. --- Calculus of variations. --- Engineering Mathematics. --- Calculus of Variations and Optimal Control; Optimization. --- Mathematical Applications in the Physical Sciences. --- Special functions --- Mathematical analysis --- Real variables --- Several real variables, Functions of --- Functions of real variables --- Engineering mathematics. --- Mathematical optimization. --- Optimization (Mathematics) --- Optimization techniques --- Optimization theory --- Systems optimization --- Maxima and minima --- Operations research --- Simulation methods --- System analysis --- Engineering --- Engineering analysis --- Mathematics --- Isoperimetrical problems --- Variations, Calculus of --- Physical mathematics --- Physics

Choose an application

• Reference Manager
• EndNote
• RefWorks (Direct export to RefWorks)

In the spring of 1976, George Andrews of Pennsylvania State University visited the library at Trinity College, Cambridge, to examine the papers of the late G.N. Watson. Among these papers, Andrews discovered a sheaf of 138 pages in the handwriting of Srinivasa Ramanujan. This manuscript was soon designated, "Ramanujan's lost notebook." Its discovery has frequently been deemed the mathematical equivalent of finding Beethoven's tenth symphony. This fifth and final installment of the authors’ examination of Ramanujan’s lost notebook focuses on the mock theta functions first introduced in Ramanujan’s famous Last Letter. This volume proves all of the assertions about mock theta functions in the lost notebook and in the Last Letter, particularly the celebrated mock theta conjectures. Other topics feature Ramanujan’s many elegant Euler products and the remaining entries on continued fractions not discussed in the preceding volumes. Review from the second volume: "Fans of Ramanujan's mathematics are sure to be delighted by this book. While some of the content is taken directly from published papers, most chapters contain new material and some previously published proofs have been improved. Many entries are just begging for further study and will undoubtedly be inspiring research for decades to come. The next installment in this series is eagerly awaited." - MathSciNet Review from the first volume: "Andrews and Berndt are to be congratulated on the job they are doing. This is the first step...on the way to an understanding of the work of the genius Ramanujan. It should act as an inspiration to future generations of mathematicians to tackle a job that will never be complete." - Gazette of the Australian Mathematical Society.

Mathematical analysis. --- Mathematicians --- 517.1 Mathematical analysis --- Mathematical analysis --- Ramanujan Aiyangar, Srinivasa, --- Ṣrīnivāsa-Rāmānuja Aiyaṅgār, --- Ramanujan, Srinivasa, --- Aiyangar, Srinivasa Ramanujan, --- Iyengar, Srinivasa Iyengar Ramanuja, --- Ramanuja Iyengar, Srinivasa Iyengar, --- Ramanudzhan Aĭengar, --- Ramanujan, S. --- Ramanujam, S. --- Functions, special. --- Functions of complex variables. --- Number theory. --- Special Functions. --- Functions of a Complex Variable. --- Number Theory. --- Number study --- Numbers, Theory of --- Algebra --- Complex variables --- Elliptic functions --- Functions of real variables --- Special functions --- Special functions.

Choose an application

• Reference Manager
• EndNote
• RefWorks (Direct export to RefWorks)

This book develops the foundations of "summability calculus", which is a comprehensive theory of fractional finite sums. It fills an important gap in the literature by unifying and extending disparate historical results. It also presents new material that has not been published before. Importantly, it shows how the study of fractional finite sums benefits from and contributes to many areas of mathematics, such as divergent series, numerical integration, approximation theory, asymptotic methods, special functions, series acceleration, Fourier analysis, the calculus of finite differences, and information theory. As such, it appeals to a wide audience of mathematicians whose interests include the study of special functions, summability theory, analytic number theory, series and sequences, approximation theory, asymptotic expansions, or numerical methods. Richly illustrated, it features chapter summaries, and includes numerous examples and exercises. The content is mostly developed from scratch using only undergraduate mathematics, such as calculus and linear algebra.   .

Mathematical analysis. --- Fractional calculus. --- Finite differences. --- Mathematics. --- Approximation theory. --- Differential equations. --- Functions of real variables. --- Sequences (Mathematics). --- Special functions. --- Number theory. --- Number Theory. --- Real Functions. --- Special Functions. --- Ordinary Differential Equations. --- Sequences, Series, Summability. --- Approximations and Expansions. --- Differences, Finite --- Finite difference method --- Numerical analysis --- Derivatives and integrals, Fractional --- Differentiation of arbitrary order, Integration and --- Differintegration, Generalized --- Fractional derivatives and integrals --- Generalized calculus --- Generalized differintegration --- Integrals, Fractional derivatives and --- Integration and differentiation of arbitrary order --- Calculus --- 517.1 Mathematical analysis --- Mathematical analysis --- Functions, special. --- Differential Equations. --- Special functions --- Mathematical sequences --- Numerical sequences --- Algebra --- Mathematics --- Math --- Science --- 517.91 Differential equations --- Differential equations --- Number study --- Numbers, Theory of --- 517.1 --- Fractional calculus --- Finite differences --- 517.2 --- 517.2 Differential calculus. Differentiation --- Differential calculus. Differentiation --- Theory of approximation --- Functional analysis --- Functions --- Polynomials --- Chebyshev systems --- Real variables --- Functions of complex variables