Mathematical Analysis

Mathematics is playing an ever more important role in the physical and biological sciences, provoking a blurring of boundaries between scientific disciplines and a resurgence of interest in the modern as well as the classical techniques of applied...

This volume aims to bridge between elementary textbooks on calculus and established books on advanced analysis. It provides elucidation of the reversible process of differentiation and integration through two featured principles: the chain rule and its...

This second edition of a very popular two-volume work presents a thorough first course in analysis, leading from real numbers to such advanced topics as differential forms on manifolds; asymptotic methods; Fourier, Laplace, and Legendre transforms;...

The book provides a summary of the historical evolution of dimensional analysis, and frames the problem of dimensions, systems of units and similarity in a vision dominated by the conventions that formalise even the exact sciences.The first four chapters...

The ideas of Fourier have made their way into every branch of mathematics and mathematical physics, from the theory of numbers to quantum mechanics. Fourier Series and Integrals focuses on the extraordinary power and flexibility of Fourier's basic series...

Complex Analysis with Mathematica offers a way of learning and teaching a subject that lies at the heart of many areas of pure and applied mathematics, physics, engineering and even art. This book offers teachers and students an opportunity to learn...

'Radlin has done a nice job in producing a textbook which provides a learner friendly introduction to difference equations. It would suit as a core text for a first year course in the topic, aimed, as the title suggests, at physical science or...

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 nonstandard analysis not just...

* Presented from a geometric analytical viewpoint, this work addresses advanced topics in complex analysis that verge on modern areas of research * Methodically designed with individual chapters containing a rich collection of exercises, examples, and...

An entire generation of mathematicians has grown up during the time - tween the appearance of the ?rst edition of this textbook and the publication of the fourth edition, a translation of which is before you. The book is fam- iar to many people, who...

This important book provides a concise exposition of the basic ideas of the theory of distribution and Fourier transforms and its application to partial differential equations. The author clearly presents the ideas, precise statements of theorems, and...

From the author of The Pleasures of Counting and Naive Decision Making comes a calculus book perfect for self-study. It will open up the ideas of the calculus for any 16- to 18-year-old, about to begin studies in mathematics, and will be useful for...

This book presents a systematic and comprehensive account of the theory of differentiable manifolds and provides the necessary background for the use of fundamental differential topology tools. The text includes, in particular, the earlier works of...

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

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 book is designed to provide a path for the reader into an amalgamation oftwo venerable areas ofmathematics, Dynamical Systems and Number Theory. Many of the motivating theorems and conjectures in the new subject of Arithmetic Dynamics may be viewed...

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 difficulty, cover the...

This book is based on the lecture notes from a course we taught at Penn State University during the fall of 2002. The main goal of the course was to give a complete and detailed proof of the Morse Homology Theorem (Theo rem 7.4) at a level appropriate...

In the three and a half years since the first edition to these notes was written there has been progress on a number of relevant topics. D. Preiss answered in the affirmative the decades old question of whether a Banach space with an equivalent Gateaux...

This introduction to finite difference and finite element methods is aimed at graduate students who need to solve differential equations. The prerequisites are few (basic calculus, linear algebra, and ODEs) and so the book will be accessible and useful...

This is the first volume of the two-volume book on real and complex analysis. This volume is an introduction to measure theory and Lebesgue measure where the Riesz representation theorem is used to construct Lebesgue measure. Intended for undergraduate...

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...

The book provides an introduction to complex analysis for students with some familiarity with complex numbers from high school. It conists of sixteen chapters. The first eleven chapters are aimed at an Upper Division undergraduate audience. The remaining...

The Riemann hypothesis (RH) is perhaps the most important outstanding problem in mathematics. This two-volume text presents the main known equivalents to RH using analytic and computational methods. The book is gentle on the reader with definitions...

This book is devoted to the study of the acoustic wave equation and of the Maxwell system, the two most common wave equations encountered in physics or in engineering. The main goal is to present a detailed analysis of their mathematical and physical...

The purpose of the book is to discuss the latest advances in the theory of unitary representations and harmonic analysis for solvable Lie groups. The orbit method created by Kirillov is the most powerful tool to build the ground frame of these theories...

Lively prose and imaginative exercises draw the reader into this unique introductory real analysis textbook. Motivating the fundamental ideas and theorems that underpin real analysis with historical remarks and well-chosen quotes, the author shares his...

The book is devoted to the theory of gradient flows in the general framework of metric spaces, and in the more specific setting of the space of probability measures, which provide a surprising link between optimal transportation theory and many...

The subject of special functions is often presented as a collection of disparate results, rarely organized in a coherent way. This book emphasizes general principles that unify and demarcate the subjects of study. The authors' main goals are to provide...

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 properties of such...

Analysis underpins calculus, much as calculus underpins virtually all mathematical sciences. A sound understanding of analysis' results and techniques is therefore valuable for a wide range of disciplines both within mathematics itself and beyond its...

This book grew out of lectures on Riemann surfaces which the author gave at the universities of Munich, Regensburg and Munster. Its aim is to give an introduction to this rich and beautiful subject, while presenting methods from the theory of complex...

This second English edition of a very popular two-volume work presents a thorough first course in analysis, leading from real numbers to such advanced topics as differential forms on manifolds; asymptotic methods; Fourier, Laplace, and Legendre...

Analysis Volume IV introduces the reader to functional analysis (integration, Hilbert spaces, harmonic analysis in group theory) and to the methods of the theory of modular functions (theta and L series, elliptic functions, use of the Lie algebra of SL2)...

In this second edition of a Carus Monograph Classic, Steven G. Krantz, a leading worker in complex analysis and a winner of the Chauvenet Prize for outstanding mathematical exposition, develops material on classical non-Euclidean geometry. He shows how...

This book deals with the classical theory of Nevanlinna on the value distribution of meromorphic functions of one complex variable, based on minimum prerequisites for complex manifolds. The theory was extended to several variables by S. Kobayashi, T...

This book covers analysis on fractals, a developing area of mathematics which focuses on the dynamical aspects of fractals, such as heat diffusion on fractals and the vibration of a material with fractal structure. The book provides a self-contained...

A First Course on Numerical Methods is designed for students and researchers who seek practical knowledge of modern techniques in scientific computing. Avoiding encyclopaedic and heavily theoretical exposition, the book provides an in-depth treatment of...

Many practical applications require the reconstruction of a multivariate function from discrete, unstructured data. This book gives a self-contained, complete introduction into this subject. It concentrates on truly meshless methods such as radial basis...

This book contains the contributions resulting from the 6th Italian-Japanese workshop on Geometric Properties for Parabolic and Elliptic PDEs, which was held in Cortona (Italy) during the week of May 20-24, 2019. This book will be of great interest for...