This book has been written in a frankly partisian spirit-we believe that singularity theory offers an extremely useful approach to bifurcation prob- lems and we hope to convert the reader to this view
As long as a branch of knowledge offers an abundance of problems, it is full of vitality. David Hilbert Over the last 15 years I have given lectures on a variety of problems in nonlinear functional an
This volume contains the basics of what every scientist and engineer should know about complex analysis. A lively style combined with a simple, direct approach helps readers grasp the fundamentals, fr
First half of this highly-regarded book covers complex number plane; functions and limits; Riemann surfaces, the definite integral; power series; meromorphic functions, and much more. The second half
Since the characterization of generators of C0 semigroups was established in the 1940s, semigroups of linear operators and its neighboring areas have developed into an abstract theory that has become
This is a very successful textbook for undergraduate students of pure mathematics. Students often find the subject of complex analysis very difficult. Here the authors, who are experienced and well-known expositors, avoid many of such difficulties by using two principles: (1) generalising concepts familiar from real analysis; (2) adopting an approach which exhibits and makes use of the rich geometrical structure of the subject. An opening chapter provides a brief history of complex analysis which sets it in context and provides motivation.
The text covers enough material for an advanced undergraduate or first-year graduate course. Contents include calculus in the plane; harmonic functions in the plane; analytic functions and power serie
For the second edition of this very successful text, Professor Binmore has written two chapters on analysis in vector spaces. The discussion extends to the notion of the derivative of a vector function as a matrix and the use of second derivatives in classifying stationary points. Some necessary concepts from linear algebra are included where appropriate. The first edition contained numerous worked examples and an ample collection of exercises for all of which solutions were provided at the end of the book. The second edition retains this feature but in addition offers a set of problems for which no solutions are given. Teachers may find this a helpful innovation.
Outlines theory and techniques of calculus, emphasizing strong understanding of concepts, and the basic principles of analysis. Reviews elementary and intermediate calculus and features discussions of
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 ap
Measure and integration, metric spaces, the elements of functional analysis in Banach spaces, and spectral theory in Hilbert spaces — all in a single study. Only book of its kind. Unusual topic
This book offers an ideal introduction to the theory of partial differential equations. It focuses on elliptic equations and systematically develops the relevant existence schemes, always with a view
This book grew out of lectures on Riemann surfaces given by Otto Forster at the universities of Munich, Regensburg, and Munster. It provides a concise modern introduction to this rewarding subject, as
