Analysis I

Author: Terence Tao
Publisher: Springer
ISBN: 9789811017896
Release Date: 2016-08-29
Genre: Mathematics

This is part one of a two-volume book on real analysis and is intended for senior undergraduate students of mathematics who have already been exposed to calculus. The emphasis is on rigour and foundations of analysis. Beginning with the construction of the number systems and set theory, the book discusses the basics of analysis (limits, series, continuity, differentiation, Riemann integration), through to power series, several variable calculus and Fourier analysis, and then finally the Lebesgue integral. These are almost entirely set in the concrete setting of the real line and Euclidean spaces, although there is some material on abstract metric and topological spaces. The book also has appendices on mathematical logic and the decimal system. The entire text (omitting some less central topics) can be taught in two quarters of 25–30 lectures each. The course material is deeply intertwined with the exercises, as it is intended that the student actively learn the material (and practice thinking and writing rigorously) by proving several of the key results in the theory.

Mathematische Optimierungsverfahren des Operations Research

Author: Matthias Gerdts
Publisher: Walter de Gruyter
ISBN: 9783110249941
Release Date: 2011
Genre: Business & Economics

This book is an introduction into the optimization methods of operations research - and beyond. With its clear presentation, easy-to-read notation and exercises, it provides a solid foundation and serves as a reference work even after graduation from university.

Partial Differential Equations Modeling Analysis and Numerical Approximation

Author: Hervé Le Dret
Publisher: Birkhäuser
ISBN: 9783319270678
Release Date: 2016-02-11
Genre: Mathematics

This book is devoted to the study of partial differential equation problems both from the theoretical and numerical points of view. After presenting modeling aspects, it develops the theoretical analysis of partial differential equation problems for the three main classes of partial differential equations: elliptic, parabolic and hyperbolic. Several numerical approximation methods adapted to each of these examples are analyzed: finite difference, finite element and finite volumes methods, and they are illustrated using numerical simulation results. Although parts of the book are accessible to Bachelor students in mathematics or engineering, it is primarily aimed at Masters students in applied mathematics or computational engineering. The emphasis is on mathematical detail and rigor for the analysis of both continuous and discrete problems.

Applied Mathematics for the Analysis of Biomedical Data

Author: Peter J. Costa
Publisher: John Wiley & Sons
ISBN: 9781119269519
Release Date: 2017-02-21
Genre: Mathematics

Features a practical approach to the analysis of biomedical data via mathematical methods and provides a MATLAB® toolbox for the collection, visualization, and evaluation of experimental and real-life data Applied Mathematics for the Analysis of Biomedical Data: Models, Methods, and MATLAB® presents a practical approach to the task that biological scientists face when analyzing data. The primary focus is on the application of mathematical models and scientific computing methods to provide insight into the behavior of biological systems. The author draws upon his experience in academia, industry, and government–sponsored research as well as his expertise in MATLAB to produce a suite of computer programs with applications in epidemiology, machine learning, and biostatistics. These models are derived from real–world data and concerns. Among the topics included are the spread of infectious disease (HIV/AIDS) through a population, statistical pattern recognition methods to determine the presence of disease in a diagnostic sample, and the fundamentals of hypothesis testing. In addition, the author uses his professional experiences to present unique case studies whose analyses provide detailed insights into biological systems and the problems inherent in their examination. The book contains a well-developed and tested set of MATLAB functions that act as a general toolbox for practitioners of quantitative biology and biostatistics. This combination of MATLAB functions and practical tips amplifies the book’s technical merit and value to industry professionals. Through numerous examples and sample code blocks, the book provides readers with illustrations of MATLAB programming. Moreover, the associated toolbox permits readers to engage in the process of data analysis without needing to delve deeply into the mathematical theory. This gives an accessible view of the material for readers with varied backgrounds. As a result, the book provides a streamlined framework for the development of mathematical models, algorithms, and the corresponding computer code. In addition, the book features: Real–world computational procedures that can be readily applied to similar problems without the need for keen mathematical acumen Clear delineation of topics to accelerate access to data analysis Access to a book companion website containing the MATLAB toolbox created for this book, as well as a Solutions Manual with solutions to selected exercises Applied Mathematics for the Analysis of Biomedical Data: Models, Methods, and MATLAB® is an excellent textbook for students in mathematics, biostatistics, the life and social sciences, and quantitative, computational, and mathematical biology. This book is also an ideal reference for industrial scientists, biostatisticians, product development scientists, and practitioners who use mathematical models of biological systems in biomedical research, medical device development, and pharmaceutical submissions.

Reelle und Komplexe Analysis

Author: Walter Rudin
Publisher: Walter de Gruyter
ISBN: 348659186X
Release Date: 2009
Genre: Analysis - Lehrbuch

Besonderen Wert legt Rudin darauf, dem Leser die Zusammenhänge unterschiedlicher Bereiche der Analysis zu vermitteln und so die Grundlage für ein umfassenderes Verständnis zu schaffen. Das Werk zeichnet sich durch seine wissenschaftliche Prägnanz und Genauigkeit aus und hat damit die Entwicklung der modernen Analysis in nachhaltiger Art und Weise beeinflusst. Der "Baby-Rudin" gehört weltweit zu den beliebtesten Lehrbüchern der Analysis und ist in 13 Sprachen übersetzt. 1993 wurde es mit dem renommierten Steele Prize for Mathematical Exposition der American Mathematical Society ausgezeichnet. Übersetzt von Uwe Krieg.

Nonlinear Inclusions and Hemivariational Inequalities

Author: Stanisław Migórski
Publisher: Springer Science & Business Media
ISBN: 9781461442318
Release Date: 2012-09-18
Genre: Mathematics

This book introduces the reader the theory of nonlinear inclusions and hemivariational inequalities with emphasis on the study of contact mechanics. The work covers both abstract results in the area of nonlinear inclusions, hemivariational inequalities as well as the study of specific contact problems, including their modelling and their variational analysis. Provided results are based on original research on the existence, uniqueness, regularity and behavior of the solution for various classes of nonlinear stationary and evolutionary inclusions. In carrying out the variational analysis of various contact models, one systematically uses results of hemivariational inequalities and, in this way, illustrates the applications of nonlinear analysis in contact mechanics. New mathematical methods are introduced and applied in the study of nonlinear problems, which describe the contact between a deformable body and a foundation. Contact problems arise in industry, engineering and geophysics. Their variational analysis presented in this book lies the background for their numerical analysis. This volume will interest mathematicians, applied mathematicians, engineers, and scientists as well as advanced graduate students.

Automatic Text Summarization

Author: Juan-Manuel Torres-Moreno
Publisher: John Wiley & Sons
ISBN: 9781119044079
Release Date: 2014-09-25
Genre: Computers

Textual information in the form of digital documents quickly accumulates to create huge amounts of data. The majority of these documents are unstructured: it is unrestricted text and has not been organized into traditional databases. Processing documents is therefore a perfunctory task, mostly due to a lack of standards. It has thus become extremely difficult to implement automatic text analysis tasks. Automatic Text Summarization (ATS), by condensing the text while maintaining relevant information, can help to process this ever-increasing, difficult-to-handle, mass of information. This book examines the motivations and different algorithms for ATS. The author presents the recent state of the art before describing the main problems of ATS, as well as the difficulties and solutions provided by the community. The book provides recent advances in ATS, as well as current applications and trends. The approaches are statistical, linguistic and symbolic. Several examples are also included in order to clarify the theoretical concepts.

Additive Number Theory Inverse Problems and the Geometry of Sumsets

Author: Melvyn B. Nathanson
Publisher: Springer Science & Business Media
ISBN: 0387946551
Release Date: 1996-08-22
Genre: Mathematics

Many classical problems in additive number theory are direct problems, in which one starts with a set A of natural numbers and an integer H -> 2, and tries to describe the structure of the sumset hA consisting of all sums of h elements of A. By contrast, in an inverse problem, one starts with a sumset hA, and attempts to describe the structure of the underlying set A. In recent years there has been ramrkable progress in the study of inverse problems for finite sets of integers. In particular, there are important and beautiful inverse theorems due to Freiman, Kneser, Plünnecke, Vosper, and others. This volume includes their results, and culminates with an elegant proof by Ruzsa of the deep theorem of Freiman that a finite set of integers with a small sumset must be a large subset of an n-dimensional arithmetic progression.