Mathematical Analysis

This book covers an interdisciplinary approach for understanding mathematical modeling by offering a collection of models, solved problems related to the models, the methodologies employed, and the results using projects and case studies with insight...

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'Et moi, ..., si favait su comment eo reveoir. je One service mathematics has rendered the n'y serais point all6.' human race. It has put common sense back Jules Verne where it belongs, on the topmost shelf next to the dusty canister labelled 'discarded...

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This accessible text covers key results in functional analysis that are essential for further study in the calculus of variations, analysis, dynamical systems, and the theory of partial differential equations. The treatment of Hilbert spaces covers the...

Like differentiability, convexity is a natural and powerful property of functions that plays a significant role in many areas of mathematics, both pure and applied. It ties together notions from topology, algebra, geometry and analysis, and is an...

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Even the simplest singularities of planar curves, e.g. where the curve crosses itself, or where it forms a cusp, are best understood in terms of complex numbers. The full treatment uses techniques from algebra, algebraic geometry, complex analysis and...

The Mandelbrot set is a fractal shape that classifies the dynamics of quadratic polynomials. It has a remarkably rich geometric and combinatorial structure. This volume provides a systematic exposition of current knowledge about the Mandelbrot set and...

The subject of analysis on Lie groups comprises an eclectic group of topics which can be treated from many different perspectives. This self-contained text concentrates on the perspective of analysis, to the topics and methods of non-commutative harmonic...

The study of geodesic flows on homogenous spaces is an area of research that has yielded some fascinating developments. This book, first published in 2000, focuses on many of these, and one of its highlights is an elementary and complete proof (due to...

Subfactors have been a subject of considerable research activity for about fifteen years and are known to have significant relations with other fields such as low dimensional topology and algebraic quantum field theory. These notes give an introduction...

This substantial revision of the text Numerical Solution of Partial Differential Equations by the Finite Element Method by C. Johnson is a two volume introduction to the computational solution of differential equations using a unified approach organised...

This book treats the very special and fundamental mathematical properties that hold for a family of Gaussian (or normal) random variables. Such random variables have many applications in probability theory, other parts of mathematics, statistics and...

The theory of prehomogeneous vector spaces is a relatively new subject although its origin can be traced back through the works of Siegel to Gauss. The study of the zeta functions related to prehomogeneous vector spaces can yield interesting information...

This is a one-stop introduction to the methods of ergodic theory applied to holomorphic iteration. The authors begin with introductory chapters presenting the necessary tools from ergodic theory thermodynamical formalism, and then focus on recent...

These notes treat in full detail the theory of representations of the group of automorphisms of a homogeneous tree. The unitary irreducible representations are classified in three types: a continuous series of spherical representations; two special...

This 1996 book unites the study of dynamical systems and numerical solution of differential equations. The first three chapters contain the elements of the theory of dynamical systems and the numerical solution of initial-value problems. In the remaining...

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This book is concerned with the well-established mathematical technique known as Fourier analysis (or alternatively as harmonic or spectral analysis). It is a handbook comprising a collection of the most important theorems in Fourier analysis, presented...

Throughout the academic year 1986-7, the University of Illinois was host to a symposium on mathematical analysis which was attended by some of the leading figures in the field. This book arises out of this special year and lays emphasis on the synthesis...

An interval is a natural way of specifying a number that is specified only within certain tolerances. Interval analysis consists of the tools and methods needed to solve linear and nonlinear systems of equations in the presence of data uncertainties...

Acta Numerica is an annual publication containing invited survey papers by leading researchers in numerical mathematics and scientific computing. The papers present overviews of recent developments in their area and provide 'state of the art' techniques...

This book is concerned with the well-established mathematical technique known as Fourier analysis (or alternatively as harmonic or spectral analysis). It is a handbook comprising a collection of the most important theorems in Fourier analysis, presented...

Numerical Ranges II is a sequel to Numerical Ranges of Operators on Normed Spaces and of Elements of Normed Algebras written by the same authors and published in this series in 1971. The present volume reflects the progress made in the subject, expanding...

Originally published in 1987, this book is devoted to the approximation of real functions by real rational functions. These are, in many ways, a more convenient tool than polynomials, and interest in them was growing, especially since D. Newman's work in...

This reference book provides the main definitions, theorems and techniques in the theory of Birkhoff interpolation by polynomials. The book begins with an article by G. G. Lorentz that discusses some of the important developments in approximation and...

Numerical analysis is the subject of applied mathematics concerned mainly with using computers in evaluating or approximating mathematical models. As such, it is crucial to all applications of mathematics in science and engineering, as well as being an...

Acta Numerica is an annual volume presenting substantive survey articles in numerical analysis and scientific computing. The subjects and authors are chosen by a distinguished international editorial board so as to report the most important developments...

Numerical analysis is the subject of applied mathematics concerned mainly with using computers in evaluating or approximating mathematical models. As such, it is crucial to all applications of mathematics in science and engineering, as well as being an...

Continuing the tradition established with the 1992 volume, 1993's Acta Numerica presents six invited papers on a broad range of topics from numerical analysis. Papers treat each topic at a level intelligible by any numerical analyst from graduate student...

This reference book provides the main definitions, theorems and techniques in the theory of Birkhoff interpolation by polynomials. The book begins with an article by G. G. Lorentz that discusses some of the important developments in approximation and...

Incompressible computational fluid dynamics is an emerging and important discipline, with numerous applications in industry and science. Its methods employ rigourous mathematical analysis far beyond what is presently possible for compressible flows...

The class of multivalent functions is an important one in complex analysis. They occur for example in the proof of De Branges' theorem which, in 1985, settled the long-standing Bieberbach conjecture. The second edition of Professor Hayman's celebrated...

This book is concerned with the theory of unbounded derivations in C*-algebras, a subject whose study was motivated by questions in quantum physics and statistical mechanics, and to which the author has made a considerable contribution. This is an active...

The geometry and analysis that is discussed in this book extends to classical results for general discrete or Lie groups, and the methods used are analytical but have little to do with what is described these days as real analysis. Most of the results...

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This book presents the basic tools of modern analysis within the context of the fundamental problem of operator theory: to calculate spectra of specific operators on infinite dimensional spaces, especially operators on Hilbert spaces. The tools are...

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The Hilbert transform has many uses, including solving problems in aerodynamics, condensed matter physics, optics, fluids, and engineering. Written in a style that will suit a wide audience (including the physical sciences), this book will become the...