Calculus and mathematical analysis Books

A comprehensive exposition on analytic methods for solving science and engineering problems, written from the unifying viewpoint of distribution theory and enriched with many modern topics which are important to practioners and...

The book contains the methods and bases of functional analysis that are directly adjacent to the problems of numerical mathematics and its applications; they are what one needs for the understand­ ing from a general viewpoint...

Modern software tools like Maple have the potential to alter radically the way mathematics is taught, learned, and done. Bringing such tools into the classroom during lectures, assignments, and examinations means that new ways...

This self-contained monograph traces the evolution of the limit-point/limit-circle problem from its 1910 inception, in a paper by Hermann Weyl, to its modern-day extensions to the asymptotic analysis of nonlinear differential...

Concern with the class of problems investigated in this monograph began for me as a graduate student at MIT (1958-62) when serving as research assistant to Professor Eric Reissner who initiated me into the subject and whose...

This book developed from a series of lectures I gave at the Symposium on Nonlinear Microlocal Analysis held at Nanjing University in October. 1988. Its purpose is to give an overview of the use of microlocal analysis and...

Explores relationship between Fourier Analysis, convex geometry, and related areas; in the past, study of this relationship has led to important mathematical advances Presents new results and applications to diverse fields such...

This book on the theory of three-dimensional spinors and their applications fills an important gap in the literature. It gives an introductory treatment of spinors. From the reviews: "Gathers much of what can be done with 3-D...

This self-contained work on Hilbert space operators takes a problem-solving approach to the subject, combining theoretical results with a wide variety of exercises that range from the straightforward to the...

This book gives an introductory exposition of the theory of hyperfunctions and regular singularities. This first English introduction to hyperfunctions brings readers to the forefront of research in the theory of harmonic...

The theory of General Relativity, after its invention by Albert Einstein, remained for many years a monument of mathemati­ cal speculation, striking in its ambition and its formal beauty, but quite separated from the main...

In many scientific or engineering applications, where ordinary differen­ tial equation (OOE),partial differential equation (POE), or integral equation (IE) models are involved, numerical simulation is in common use for...

INTRODUCTION . . . . . . xiii § 1. LINEAR EQUATIONS. BASIC NOTIONS . 3 § 2. EQUATIONS WITH A CLOSED OPERATOR 6 § 3. THE ADJOINT EQUATION . . . . . . 10 § 4. THE EQUATION ADJOINT TO THE FACTORED EQUATION. 17 § 5. AN EQUATION...

The lectures in this volume were given as part of a NATO Advanced Study Institute From finite to infinite dimensional dynamical systems held at the Isaac Newton Institute for Mathematical Sciences, Cambridge, U. K. , between 21...

In the last few years the use of geometrie methods has permeated many more branehes of mathematies and the seiences. Briefly its role may be eharaeterized as folIows. Whereas methods of mathematieal analysis deseribe phenomena...

This volume contains a collection of papers in Analytic and Elementary Number Theory in memory of Professor Paul Erdös, one of the greatest mathematicians of this century. Written by many leading researchers, the papers deal...

Common Waveform Analysis, which will be of interest to both electrical engineers and mathematicians, applies the classic Fourier analysis to common waveforms. The following questions are answered: Can a signal be considered...

This useful book addresses electrothermal problems in modern VLSI systems. It discusses electrothermal phenomena and the fundamental building blocks that electrothermal simulation requires. The authors present three important...

Wavelet theory is on the boundary between mathematics and engineering, making it ideal for demonstrating to students that mathematics research is thriving in the modern day. Students can see non-trivial mathematics ideas...

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,...

Second Year Calculus: From Celestial Mechanics to Special Relativity covers multi-variable and vector calculus, emphasizing the historical physical problems which gave rise to the concepts of calculus. The book guides us from...

The first edition of this work has become the standard introduction to the theory of p-adic numbers at both the advanced undergraduate and beginning graduate level. This second edition includes a deeper treatment of p-adic...

The unifying approach of functional analysis is to view functions as points in abstract vector space and the differential and integral operators as linear transformations on these spaces. The author's goal is to present the...

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...

Given the ease with which computers can do iteration it is now possible for almost anyone to generate beautiful images whose roots lie in discrete dynamical systems. Images of Mandelbrot and Julia sets abound in publications...

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...

Science students have to spend much of their time learning how to do laboratory work, even if they intend to become theoretical, rather than experimental, scientists. It is important that they understand how experiments are...

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...

Topics in Hyperplane Arrangements, Polytopes and Box-Splines brings together many areas of research that focus on methods to compute the number of integral points in suitable families or variable polytopes. The topics introduced expand upon differential...

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...

All the exercises plus their solutions for Serge Lang's fourth edition of "Complex Analysis," ISBN 0-387-98592-1. The problems in the first 8 chapters are suitable for an introductory course at undergraduate level and cover...

"This book is very well organized and clearly written and contains an adequate supply of exercises. If one is comfortable with the choice of topics in the book, it would be a good candidate for a text in a graduate real...

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...

This new approach to real analysis stresses the use of the subject with respect to applications, i.e., how the principles and theory of real analysis can be applied in a variety of settings in subjects ranging from Fourier series and polynomial...

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...

Used in undergraduate classrooms across the USA, this is a clearly written, rigorous introduction to differential equations and their applications. Fully understandable to students who have had one year of calculus, this book...