Calculus Books

This systematic exposition outlines the fundamentals of the theory of single sheeted domains of holomorphy. It further illustrates applications to quantum field theory, the theory of functions, and differential equations with constant coefficients...

This introductory text presents detailed accounts of the different forms of the theory developed by Stroock and Bismut, discussions of the relationship between these two approaches, and a variety of applications. 1987 edition.

Based on the popular "Workshop Approach", which has been hailed by the community for its hands on approach, these new versions of the popular Workshop Calculus allow the easy incorporation of a graphing calculator. Like the...

Abstract Calculus: A Categorical Approach provides an abstract approach to calculus. It is intended for graduate students pursuing PhDs in pure mathematics but junior and senior researchers in basically any field of mathematics and theoretical...

The concept of derivatives of non-integer order, known as fractional derivatives, first appeared in the letter between L'Hopital and Leibniz in which the question of a half-order derivative was posed. Since then, many formulations of fractional...

Aiming to "modernise" the course through the integration of Mathematica, this publication introduces students to its multivariable uses, instructs them on its use as a tool in simplifying calculations, and presents ...

This Student Guide is exceptional, maybe even unique, among such guides in that its author, Fred Soon, was actually a student user of the textbook during one of the years we were writing and debugging the book. (He was one of...

From the reviews "This is a reprint of the original edition of Lang's 'A First Course in Calculus', which was first published in 1964....The treatment is 'as rigorous as any mathematician would wish it'....[The exercises] are...

The trajectory of fractional calculus has undergone several periods of intensive development, both in pure and applied sciences. During the last few decades fractional calculus has also been associated with the power law effects and its various...

Applications of Fractional Calculus to Modeling in Dynamics and Chaos aims to present novel developments, trends, and applications of fractional-order derivatives with power law and Mittag-Leffler kernel in the areas of chemistry, mechanics, chaos,...

A complete course on metric, normed, and Hilbert spaces, including many results and exercises seldom found in texts on analysis at this level. The author covers an unusually wide range of material in a clear and concise format,...

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...

This book discusses some of the first principles of modern analysis. I t can be used for courses at several levels, depending upon the background and ability of the students. It was written on the premise that today's good...

This book grew out of lectures on Riemann surfaces given by Otto Forster at the universities of Munich, Regensburg, and Münster. It provides a concise modern introduction to this rewarding subject, as well as presenting methods...

This book is first of all designed as a text for the course usually called "theory of functions of a real variable". This course is at present cus­ tomarily offered as a first or second year graduate course in United States...

This book is intended as a textbook to be used in a first graduate level course, and covers the fundamental principals of optimization in finite dimensions. It develops the necessary background material in multivariable calculus using coordinates as well...

A discussion of certain advanced topics in operator theory, providing the necessary background while assuming only standard senior-first year graduate courses in general topology, measure theory, and algebra. Each chapter ends...

The present volume contains all the exercises and their solutions for Lang's second edition of Undergraduate Analysis. The wide variety of exercises, which range from computational to more conceptual and which are of vary­ ing...

Basic Multivariable Calculus fills the need for a student-oriented text devoted exclusively to the third-semester course in multivariable calculus. In this text, the basic algebraic, analytic, and geometric concepts of...

A book on the subject of normal families more than sixty years after the publication of Montel's treatise Ler;ons sur les familles normales de fonc­ tions analytiques et leurs applications is certainly long overdue. But, in a...

A discussion of the properties of conformal mappings in the complex plane, closely related to the study of fractals and chaos. Indeed, the book ends in a detailed study of the famous Mandelbrot set, which describes very general...

This book mainly discusses the representation theory of the special linear group 8L(2, 1R), and some applications of this theory. In fact the emphasis is on the applications; the working title of the book while it was being...

This book is an introductory text in functional analysis. Unlike many modern treatments, it begins with the particular and works its way to the more general. From the reviews: "This book is an excellent text for a first...

This new, revised edition covers all of the basic topics in calculus of several variables, including vectors, curves, functions of several variables, gradient, tangent plane, maxima and minima, potential functions, curve...

This fifth edition of Lang's book covers all the topics traditionally taught in the first-year calculus sequence. Divided into five parts, each section of A FIRST COURSE IN CALCULUS contains examples and applications relating...

This text places the basic ideas of real analysis and numerical analysis together in an applied setting that is both accessible and motivational to young students. The essentials of real analysis are presented in the context of...

The calculus has served for three centuries as the principal quantitative language of Western science. In the course of its genesis and evolution some of the most fundamental problems of mathematics were first con­ fronted and,...

The study of composition operators links some of the most basic questions you can ask about linear operators with beautiful classical results from analytic-function theory. The process invests old theorems with new mean­ ings,...

This monograph is an introduction to optimal control theory for systems governed by vector ordinary differential equations. It is not intended as a state-of-the-art handbook for researchers. We have tried to keep two types of...

From the reviews of the second edition: "The new methods of complex manifold theory are very useful tools for investigations in algebraic geometry, complex function theory, differential operators and so on. The differential...

This textbook is designed for the intermediate-level course on ordinary differential equations offered at many universities and colleges. It treats, as standard topics of such a course: existence and uniqueness theory, linear...

Developed for the professional Master's program in Computational Finance at Carnegie Mellon, the leading financial engineering program in the U.S. Has been tested in the classroom and revised over a period of several years...

A must-read for mathematicians, scientists and engineers who want to understand difference equations and discrete dynamics Contains the most complete and comprehenive analysis of the stability of one-dimensional maps...

Can be used as a graduate text Contains many exercises Contains new results

Introduction to the themes of mathematical analysis, geared toward advanced undergraduate and graduate students. Topics include operators, function spaces, Hilbert spaces, and elementary Fourier analysis. Numerous exercises and worked examples.1973...

Written by a prominent figure in the field of harmonic analysis, this classic monograph is geared toward advanced undergraduates and graduate students and focuses on methods related to Gelfand's theory of Banach algebra. 1953 edition.

This book covers applications of fractional calculus used for medical and health science.

This book is aimed at mathematics students, typically in the second year of a university course. The first chapter, however, is suitable for first-year students. Differentiable functions are treated initially from the ...

During the last decade the techniques of non-linear optim­ ization have emerged as an important subject for study and research. The increasingly widespread application of optim­ ization has been stimulated by the availability...

This book contains a rigorous coverage of those topics (and only those topics) that, in the author's judgement, are suitable for inclusion in a first course on Complex Functions. Roughly speaking, these can be summarized as...

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...

Fifteen years ago, most mathematicians who worked in the intersection of function theory and operator theory thought that progress on the Bergman spaces was unlikely, yet today the situation has completely changed. For several...

Providing the mathematical background required for the study of fractal topics, this book deals with integration in the modern sense, together with mathematical probability. The emphasis is on the particular results that aid...

The purpose of this book is to provide an integrated development of modern analysis and topology through the integrating vehicle of uniform spaces. It is intended that the material be accessible to a reader of modest background...

This book grew out of lectures on spectral theory which the author gave at the Scuola. Normale Superiore di Pisa in 1985 and at the Universite Laval in 1987. Its aim is to provide a rather quick introduction to the new...