Calculus and mathematical analysis Books

Dieses Buch beruht auf 40 lahren intensiven Studiums der Differentialglei­ chungen, sowohl yom theoretischen als auch yom praktischen Gesichtspunkt aus, eines Studiums, das mit meiner Tatigkeit im Rechen-Institut M. Picones in...

The present book grew out of lecture notes prepared for a "Cours du troisieme cycle de la Suisse Romande", 1983 in Lausanne. The original notes are considerably extended and brought up to date. In fact the book offers at many...

Mathematics is vigorously and brilliantly pursued in our time on a very broad front; yet the authors of this text feel that not enough mathematical talent is devoted to furthering the interaction of mathematics with other sciences and disciplines. This...

The progress in protein and nucleic acid chemistry together with improvements of the previously employed tissue culture techniques have led to the solution of problems such as that of the generation of antibody diversity or of...

The past decade has seen a resurgence of interest in the study of the asymp­ totic behavior of sums formed from an independent sequence of random variables. In particular, recent attention has focused on the interaction of the...

This volume contains the Proceedings of the Workshop on Composite Media and Homogenization Theory held in Trieste, Italy, from January 15 to 26, 1990. The workshop was organized by the International Centre for Theo­ retical...

This volume contains a selection of papers by the participants of the 6. International Conference on Probability in Banach Spaces, Sand­ bjerg, Denmark, June 16-D1, 1986. The conference was attended by 45 participants from...

This volume contains five review articles, two in the Algebra part and three in the Geometry part, surveying the fields of cate­ gories and class field theory, in the Algebra part, and of Finsler spaces, structures on ...

The papers in these proceedings were presented at an Inter­ national Symposium on Stiff Differential Systems, which was held at the Hotel Quellenhof, Wildbad, Federal Republic of Germany, October 4-6, 1973. The sumposium was...

The aim of this book is to facilitate the use of Stokes' Theorem in applications. The text takes a differential geometric point of view and provides for the student a bridge between pure and applied mathematics by carefully building a formal rigorous...

This is a relatively fast paced graduate level introduction to complex algebraic geometry, from the basics to the frontier of the subject. It covers sheaf theory, cohomology, some Hodge theory, as well as some of the more...

-1. Opial-type inequalities for balanced fractional derivatives(Introduction, Background, Main Results, References). -2. Univariate right Caputo fractional Ostrowski inequalities (Introduction, Main Results, References). -3. Multivariate right Caputo...

Part 1. -Univariate Integral Inequalities based on Sobolev representations.- Introduction.- Background. -Main Results. -Applications.- References. Part 2.- Multivariate Integral Inequalities deriving from Sobolev representations.-Introduction...

Rigid (analytic) spaces were invented to describe degenerations, reductions, and moduli of algebraic curves and abelian varieties. This work, a revised and greatly expanded new English edition of an earlier French text by the...

-1. Uniform Approximation by General Multivariate Singular Integral Operators(Introduction, Main Results, Applications, References). -2. Approximation by General Multivariate Singular Integral Operators(Introduction, Main Results, Applications,...

This book is intended for students familiar with a beginner's version of differential and integral calculus stressing only manipulation offormulas and who are now looking for a closer study of basic concepts combined with a...

Two-fluid dynamics is a challenging subject rich in physics and prac­ tical applications. Many of the most interesting problems are tied to the loss of stability which is realized in preferential positioning and shaping of the...

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...

An introduction to analysis with the right mix of abstract theories and concrete problems. Starting with general measure theory, the book goes on to treat Borel and Radon measures and introduces the reader to Fourier analysis...

This is the third version of a book on differential manifolds. The first version appeared in 1962, and was written at the very beginning of a period of great expansion of the subject. At the time, I found no satisfactory book...

This substantially revised second edition teaches the bifurcation of asymptotic solutions to evolution problems governed by nonlinear differential equations. Written not just for mathematicians, it appeals to the widest...

A lively and vivid look at the material from function theory, including the residue calculus, supported by examples and practice exercises throughout. There is also ample discussion of the historical evolution of the theory,...

This book discusses a variety of problems which are usually treated in a second course on the theory of functions of one complex variable, the level being gauged for graduate students. It treats several topics in geometric...

The term "weakly differentiable functions" in the title refers to those inte­ n grable functions defined on an open subset of R whose partial derivatives in the sense of distributions are either LP functions or (signed)...

An introduction to nonstandard analysis based on a course given by the author. It is suitable for beginning graduates or upper undergraduates, or for self-study by anyone familiar with elementary real analysis. It presents...

This book provides an introduction to the basic concepts in differential topology, differential geometry, and differential equations, and some of the main basic theorems in all three areas. This new edition includes new...

In this text which gradually develops the tools for formulating and manipulating the field equations of Continuum Mechanics, the mathematics of tensor analysis is introduced in four, well-separated stages, and the physical...

This book is a slightly expanded reproduction of the first two chapters (plus Introduction) of my book Perturbation Theory tor Linear Operators, Grundlehren der mathematischen Wissenschaften 132, Springer 1980. Ever since, or...

Historically, nonclassical physics developed in three stages. First came a collection of ad hoc assumptions and then a cookbook of equations known as "quantum mechanics". The equations and their philosophical underpinnings were...

This monograph grew out of the notes relating to the lecture courses that I gave at the University of Helsinki from 1977 to 1979, at the Eidgenossische Technische Hochschule Zurich in 1980, and at the University of Minnesota in...

This is the first volume of a three-volume introduction to modern geometry which emphasizes applications to other areas of mathematics and theoretical physics. Topics covered include tensors and their differential calculus, the...

This book provides a rigorous yet elementary introduction to the theory of analytic functions of a single complex variable. While presupposing in its readership a degree of mathematical maturity, it insists on no formal...

Preparing students for further study of both the classical works and current research, this is an accessible text for students who have had a course in real and complex analysis and understand the basic properties of L p spaces...

Providing an introduction to functional analysis, this text treats in detail its application to boundary-value problems and finite elements, and is distinguished by the fact that abstract concepts are motivated and illustrated...

Presenting basic results of topology, calculus of several variables, and approximation theory which are rarely treated in a single volume, this textbook includes several beautiful, but almost forgotten, classical theorems of Descartes, Erdős, Fejér,...

Modern algorithmic techniques for summation, most of which were introduced in the 1990s, are developed here and carefully implemented in the computer algebra system Maple™.The algorithms of Fasenmyer, Gosper, Zeilberger, Petkovšek and van Hoeij for...

Functional analysis owes much of its early impetus to problems that arise in the calculus of variations. In turn, the methods developed there have been applied to optimal control, an area that also requires new tools, such as...

This text provides an accessible, self-contained and rigorous introduction to complex analysis and differential equations. Topics covered include holomorphic functions, Fourier series, ordinary and partial differential equations. The text is divided into...

This two-volume textbook provides comprehensive coverage of partial differential equations, spanning elliptic, parabolic, and hyperbolic types in two and several variables. In this second volume, special emphasis is placed on functional analytic methods...

This two-volume textbook provides comprehensive coverage of partial differential equations, spanning elliptic, parabolic, and hyperbolic types in two and several variables.In this first volume, special emphasis is placed on geometric and complex variable...

The theory of elliptic boundary problems is fundamental in analysis and the role of spaces of weakly differentiable functions (also called Sobolev spaces) is essential in this theory as a tool for analysing the regularity of the solutions.This book...

This textbook is a self-contained and easy-to-read introduction to ergodic theory and the theory of dynamical systems, with a particular emphasis on chaotic dynamics.This book contains a broad selection of topics and explores the fundamental ideas of the...

This textbook, based on three series of lectures held by the author at the University of Strasbourg, presents functional analysis in a non-traditional way by generalizing elementary theorems of plane geometry to spaces of arbitrary dimension. This...

In this book, there is a strong emphasis on application with the necessary mathematical grounding. There are plenty of worked examples with all solutions provided. This enlarged new edition includes generalised Fourier series and a completely new chapter...

Mathematical models can be used to meet many of the challenges and opportunities offered by modern biology. The description of biological phenomena requires a range of mathematical theories. This is the case particularly for...

"Hypernumbers and Extrafunctions" presents a rigorous mathematical approach to operate with infinite values. First, concepts of real and complex numbers are expanded to include a new universe of numbers called hypernumbers which includes infinite...