Christian Constanda – författare

Based on proceedings of the International Conference on Integral Methods in Science and Engineering, this collection of papers addresses the solution of mathematical problems by integral methods in conjunction with approximation schemes from various physical domains. Topics and applications include: wavelet expansions, reaction-diffusion systems, variational methods , fracture theory, boundary value problems at resonance, micromechanics, fluid mechanics, combustion problems, nonlinear problems, elasticity theory, and plates and shells.

An enormous array of problems encountered by scientists and engineers are based on the design of mathematical models using many different types of ordinary differential, partial differential, integral, and integro-differential equations. Accordingly, the solutions of these equations are of great interest to practitioners and to science in general. Presenting a wealth of cutting-edge research by a diverse group of experts in the field, Integral Methods in Science and Engineering: Computational and Analytic Aspects gives a vivid picture of both the development of theoretical integral techniques and their use in specific science and engineering problems.

This book will be valuable for researchers in applied mathematics, physics, and mechanical and electrical engineering. It will likewise be a useful study guide for graduate students in these disciplines, and for various other professionals who use integration as an essential technique in their work.

Many problems in mathematical physics rely heavily on the use of elliptical partial differential equations, and boundary integral methods play a significant role in solving these equations. Stationary Oscillations of Elastic Plates studies the latter in the context of stationary vibrations of thin elastic plates. The techniques presented here reduce the complexity of classical  elasticity to a system of two independent variables, modeling problems of flexural-vibrational elastic body deformation with the aid of eigenfrequencies and simplifying them to manageable, uniquely solvable integral equations.

The book is intended for an audience with a knowledge of advanced calculus and some familiarity with functional analysis. It is a valuable resource for professionals in pure and applied mathematics, and for theoretical physicists and mechanical engineers whose work involves elastic plates. Graduate students in these fields can also benefit from the monograph as a supplementary text for courses relating to theories of elasticity or flexural vibrations.

"In my opinion, this is quite simply the best book of its kind that I have seen thus far."—Professor Peter Schiavone, University of Alberta, from the Foreword to the Fourth Edition

Praise for the previous editions

An ideal tool for students taking a first course in PDEs, as well as for the lecturers who teach such courses."—Marian Aron, Plymouth University, UK

"This is one of the best books on elementary PDEs this reviewer has read so far. Highly recommended."—CHOICE

Solution Techniques for Elementary Partial Differential Equations, Fourth Edition remains a top choice for a standard, undergraduate-level course on partial differential equations (PDEs). It provides a streamlined, direct approach to developing students’ competence in solving PDEs, and offers concise, easily understood explanations and worked examples that enable students to see the techniques in action.

New to the Fourth Edition

"In my opinion, this is quite simply the best book of its kind that I have seen thus far."—Professor Peter Schiavone, University of Alberta, from the Foreword to the Fourth Edition

Praise for the previous editions

An ideal tool for students taking a first course in PDEs, as well as for the lecturers who teach such courses."—Marian Aron, Plymouth University, UK

"This is one of the best books on elementary PDEs this reviewer has read so far. Highly recommended."—CHOICE

Solution Techniques for Elementary Partial Differential Equations, Fourth Edition remains a top choice for a standard, undergraduate-level course on partial differential equations (PDEs). It provides a streamlined, direct approach to developing students’ competence in solving PDEs, and offers concise, easily understood explanations and worked examples that enable students to see the techniques in action.

New to the Fourth Edition

Based on proceedings of the International Conference on Integral Methods in Science and Engineering, this collection of papers addresses the solution of mathematical problems by integral methods in conjunction with approximation schemes from various physical domains. Topics and applications include: wavelet expansions, reaction-diffusion systems, variational methods , fracture theory, boundary value problems at resonance, micromechanics, fluid mechanics, combustion problems, nonlinear problems, elasticity theory, and plates and shells.

Mathematical models of deformation of elastic plates are used by applied mathematicians and engineers in connection with a wide range of practical applications, from microchip production to the construction of skyscrapers and aircraft. This book employs two important analytic techniques to solve the fundamental boundary value problems for the theory of plates with transverse shear deformation, which offers a more complete picture of the physical process of bending than Kirchhoff’s classical one.

The first method transfers the ellipticity of the governing system to the boundary, leading to singular integral equations on the contour of the domain. These equations, established on the basis of the properties of suitable layer potentials, are then solved in spaces of smooth (Hölder continuous and Hölder continuously differentiable) functions.

The second technique rewrites the differential system in terms of complex variables and fully integrates it, expressing the solution as a combination of complex analytic potentials.

The last chapter develops a generalized Fourier series method closely connected with the structure of the system, which can be used to compute approximate solutions. The numerical results generated as an illustration for the interior Dirichlet problem are accompanied by remarks regarding the efficiency and accuracy of the procedure.

The presentation of the material is detailed and self-contained, making Mathematical Methods for Elastic Plates accessible to researchers and graduate students with a basic knowledge of advanced calculus.

Differential Equations for Scientists and Engineers is a book designed with students in mind. It attempts to take a concise, simple, and no-frills approach to differential equations. The approach used in this text is to give students extensive experience in main solution techniques with a lighter emphasis on the physical interpretation of the results. With a more manageable page count than comparable titles, and over 400 exercises that can be solved without a calculating device, this book emphasizes the understanding and practice of essential topics in a succinct fashion. At the end of each worked example, the author provides the Mathematica commands that can be used to check the results and where applicable, to generate graphical representations. It can be used independently by the average student, while those continuing with the subject will develop a fundamental framework with which to pursue more advanced material.  This book is designed for undergraduate students with some basic knowledge of precalculus algebra and a first course in calculus.

​​Advances in science and technology are driven by the development of rigorous mathematical foundations for the study of both theoretical and experimental models. With certain methodological variations, this type of study always comes down to the application of analytic or computational integration procedures, making such tools indispensible. With a wealth of cutting-edge research in the field, Integral Methods in Science and Engineering: Progress in Numerical and Analytic Techniques provides a detailed portrait of both the construction of theoretical integral techniques and their application to specific problems in science and engineering.

The chapters in this volume are based on talks given by well-known researchers at the Twelfth International Conference on Integral Methods in Science and Engineering, July 23–27, 2012, in Porto Alegre, Brazil. They address a broad range of topics, from problems of existence and uniqueness for singular integral equations on domain boundaries to numerical integration via finite and boundary elements, conservation laws, hybrid methods, and other quadrature-related approaches.  The contributing authors bring their expertise to bear on a number of topical problems that have to date resisted solution, thereby offering help and guidance to fellow professionals worldwide.

Integral Methods in Science and Engineering: Progress in Numerical and Analytic Techniques will be a valuable resource for researchers in applied mathematics, physics, and mechanicaland electrical engineering, for graduate students in these disciplines, and for various other professionals who use integration as an essential tool in their work.​

Imagine algebra class meets The Hitchhiker’s Guide to the Galaxy…

Meet JJ, an unusual character with a unique vantage position from which he can measure and monitor humanity’s progress. Armed with a device that compels all around it to tell the truth, JJ offers a satirical evaluation of our attitudes to numeracy and logic, touching upon several aspects of life on Earth along the way, from the criminal justice system and people’s use of language to highway driving and modern art.

A collection of mathematically-flavored stories and jokes, interlaced with puzzles, paradoxes and problems, fuse together in an entertaining, free-flowing narrative that will engage and amuse anyone with an interest in the issues confronting society today. JJ demonstrates how a lack of elementary mathematical knowledge can taint our work and general thinking and reflects upon the importance of what is arguably our most valuable weapon against ignorance: a sound mathematical education.