Mathematical Analysis

An ideal text for an advanced course in the theory of complex functions, this book leads readers to experience function theory personally and to participate in the work of the creative mathematician. The author includes numerous glimpses of the function...

"This book collects in one volume the author's considerable results in the area of the summation of series and their representation in closed form, and details the techniques by which they have been obtained... the calculations are given in plenty...

While mathematics students generally meet the Riemann integral early in their undergraduate studies, those whose interests lie more in the direction of applied mathematics will probably find themselves needing to use the Lebesgue or Lebesgue-Stieltjes...

For more than two thousand years some familiarity with mathematics has been regarded as an indispensable part of the intellectual equipment of every cultured person. Today the traditional place of mathematics in education is in grave danger...

The Levy Laplacian is an infinite-dimensional generalization of the well-known classical Laplacian. The theory has become well developed in recent years and this book was the first systematic treatment of the Levy-Laplace operator. The book describes the...

Spaces of holomorphic functions have been a prominent theme in analysis since early in the twentieth century. Of interest to complex analysts, functional analysts, operator theorists and systems theorists, their study is now flourishing. This volume, an...

Even the simplest mathematical abstraction of the phenomena of reality the real line-can be regarded from different points of view by different mathematical disciplines. For example, the algebraic approach to the study of the real line involves...

Aimed at mathematicians, physicists, engineers, and grad students, this monograph will be useful for the nonlinear analysis of problems arising in geometry or mathematical physics. The material presented covers recent and original results by the authors,...

An up-to-date and unified treatment of bifurcation theory for variational inequalities in reflexive spaces and the use of the theory in a variety of applications, such as: obstacle problems from elasticity theory, unilateral problems; torsion problems;...

A state-of-the-art edited survey covering all aspects of sampling theory. Theory, methods and applications are discussed in authoritative expositions ranging from multi-dimensional signal analysis to wavelet transforms. The book is an essential...

The approach here relies on two beliefs. The first is that almost nobody fully understands calculus the first time around. The second is that graphing calculators can be used to simplify the theory of limits for students. This book presents the...

This book is an outgrowth of lectures given on several occasions at Chalmers University of Technology and Goteborg University during the last ten years. As opposed to most introductory books on complex analysis, this one as sumes that the reader has...

The main idea of this book is to present a good portion of the standard material on functions of a complex variable, as well as some new material, from the point of view of functional analysis. The main object of study is the algebra H(G) of all...

This text is unique in accepting probability theory as an essential part of measure theory. Therefore, many examples are taken from probability, and probabilistic concepts such as independence and Markov processes are integrated into the text. Also, more...

This monograph represents a summary of our work in the last two years in applying the method of simulated annealing to the solution of problems that arise in the physical design of VLSI circuits. Our study is experimental in nature, in that we are con...

In the modern theory of boundary value problems the following ap proach to investigation is agreed upon (we call it the functional approach): some functional spaces are chosen; the statements of boundary value prob the basis of these spaces; and the...

Written by internationally renowned mathematicians, this state-of-the-art textbook examines four research directions in harmonic analysis and features some of the latest applications in the field. The work is the first one that combines spline theory,...

The first edition of Stochastic Partial Differential Equations: A Modeling, White Noise Functional Approach, gave a comprehensive introduction to SPDEs. In this, the second edition, the authors build on the theory of SPDEs driven by space-time Brownian...

The analysis of Euclidean space is well-developed. The classical Lie groups that act naturally on Euclidean space-the rotations, dilations, and trans lations-have both shaped and guided this development. In particular, the Fourier transform and the...

The International Conference on Differential Equations and Nonlinear Mechanics was hosted by the University of Central Florida in Orlando from March 17-19, 1999. One of the conference days was dedicated to Professor V. Lakshmikantham in th honor of his...

Abstract semilinear functional differential equations arise from many biological, chemical, and physical systems which are characterized by both spatial and temporal variables and exhibit various spatio-temporal patterns. The aim of this book is to...

The first part of a self-contained, elementary textbook, combining linear functional analysis, nonlinear functional analysis, numerical functional analysis, and their substantial applications with each other. As such, the book addresses undergraduate...

In addition to coverage of univariate interpolation and approximation, the text includes material on multivariate interpolation and multivariate numerical integration, a generalization of the Bernstein polynomials that has not previously appeared in book...

After an introduction to the geometry of polynomials and a discussion of refinements of the Fundamental Theorem of Algebra, the book turns to a consideration of various special polynomials. Chebyshev and Descartes systems are then introduced, and Muntz...

This well-written book contains the analytical tools, concepts, and viewpoints needed for modern applied mathematics. It treats various practical methods for solving problems such as differential equations, boundary value problems, and integral equations...

A summary of the most important results in the existence and stability of periodic solutions for ordinary differential equations achieved in the twentieth century, along with relevant applications. It differs from standard classical texts on non-linear...

This work is based on the lecture notes of the course M742: Topics in Partial Dif- ferential Equations, which I taught in the Spring semester of 1997 at Indiana Univer- sity. My main intention in this course was to give a concise introduction to solving...

This self-contained title demonstrates an important interplay between abstract and concrete operator theory. Key ideas are developed in a step-by-step approach, beginning with required background and historical material, and culminating in the final...

A complex torus is a connected compact complex Lie group. Any complex 9 9 torus is of the form X =Book InformationISBN 9780817641030Author Herbert LangeFormat HardbackPage Count 255Imprint Birkhauser Boston IncPublisher Birkhauser Boston IncWeight(grams)...

The analysis, processing, evolution, optimization and/or regulation, and control of shapes and images appear naturally in engineering (shape optimization, image processing, visual control), numerical analysis (interval analysis), physics (front...

This book considers methods of approximate analysis of mechanical, elec tromechanical, and other systems described by ordinary differential equa tions. Modern mathematical modeling of sophisticated mechanical systems consists of several stages: first,...

A self-contained and systematic development of an aspect of analysis which deals with the theory of fundamental solutions for differential operators, and their applications to boundary value problems of mathematical physics, applied mathematics, and...

The Norbert Wiener Center for Harmonic Analysis and Applications provides a state-of-the-art research venue for the broad emerging area of mathematical engineering in the context of harmonic analysis. This two-volume set consists of contributions from...

All modem introductions to complex analysis follow, more or less explicitly, the pattern laid down in Whittaker and Watson [75]. In "part I'' we find the foundational material, the basic definitions and theorems. In "part II" we find the...

This book examines in detail the nonlinear Ginzburg-Landau functional, the model most commonly used in the study of superconductivity. Specifically covered are cases in the presence of a strong magnetic field and with a sufficiently large Ginzburg-Landau...

This comprehensive monograph details polynomially convex sets. It presents the general properties of polynomially convex sets with particular attention to the theory of the hulls of one-dimensional sets. Coverage examines in considerable detail questions...

This self-contained work illustrates the application of integral methods to diverse problems in mathematics, physics, biology, and engineering. The chapters contain state-of-the-art information on current research in a variety of important practical...

This self-contained text provides an introduction to modern harmonic analysis in the context in which it is actually applied, in particular, through complex function theory and partial differential equations. It takes the novice mathematical reader from...

Analysis of nonlinear models and problems is crucial in the application of mathematics to real-world problems. This book approaches this important topic by focusing on collocation methods for solving nonlinear evolution equations and applying them to a...

This superb and self-contained work is an introductory presentation of basic ideas, structures, and results of differential and integral calculus for functions of several variables. The wide range of topics covered include the differential calculus of...