Mathematical Analysis

"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...

This book is a rigorous presentation of the method of matched asymptotic expansions, the primary tool for attacking singular perturbation problems. A knowledge of conventional asymptotic analysis is assumed. The first chapter introduces the theory and...

The expression of uncertainty in measurement poses a challenge since it involves physical, mathematical, and philosophical issues. This problem is intensified by the limitations of the probabilistic approach used by the current standard (the GUM...

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 a fundamental problem of...

Praise for the First Edition "...outstandingly appealing with regard to its style, contents, considerations of requirements of practice, choice of examples, and exercises." -Zentrablatt Math "...carefully structured with many detailed...

An accessible introduction to real analysis and its connection to elementary calculus Bridging the gap between the development and history of real analysis, Introduction to Real Analysis: An Educational Approach presents a comprehensive introduction...

This classic textbook has been used successfully by instructors and students for nearly three decades. This timely new edition offers minimal yet notable changes while retaining all the elements, presentation, and accessible exposition of previous...

This textbook is designed with the needs of today's student in mind. It is the ideal textbook for a first course in elementary differential equations for future engineers and scientists, including mathematicians. This book is accessible to anyone who has...

The purpose of this book is to present the classical analytic function theory of several variables as a standard subject in a course of mathematics after learning the elementary materials (sets, general topology, algebra, one complex variable). This...

Poisson structures appear in a large variety of contexts, ranging from string theory, classical/quantum mechanics and differential geometry to abstract algebra, algebraic geometry and representation theory. In each one of these contexts, it turns out...

This textbook introduces readers to real analysis in one and n dimensions. It is divided into two parts: Part I explores real analysis in one variable, starting with key concepts such as the construction of the real number system, metric spaces, and real...

Thorough introduction to an important area of mathematics Contains recent results Includes many exercisesBook InformationISBN 9783319783369Author Constantin P. NiculescuFormat HardbackPage Count 415Imprint Springer International Publishing...

This book is devoted to the study of certain integral representations for Neumann, Kapteyn, Schloemilch, Dini and Fourier series of Bessel and other special functions, such as Struve and von Lommel functions. The aim is also to find the coefficients of...

The focus of this book is on open conformal dynamical systems corresponding to the escape of a point through an open Euclidean ball. The ultimate goal is to understand the asymptotic behavior of the escape rate as the radius of the ball tends to zero. In...

This book presents, in a consistent and unified overview, results and developments in the field of todays spherical sampling, particularly arising in mathematical geosciences. Although the book often refers to original contributions, the authors made...

This book discusses the complex theory of differential equations or more precisely, the theory of differential equations on complex-analytic manifolds. Although the theory of differential equations on real manifolds is well known - it is described in...

This book provides an introduction to the ergodic theory and topological dynamics of actions of countable groups. It is organized around the theme of probabilistic and combinatorial independence, and highlights the complementary roles of the asymptotic...

This textbook is designed for a year-long course in real analysis taken by beginning graduate and advanced undergraduate students in mathematics and other areas such as statistics, engineering, and economics. Written by one of the leading scholars in the...

Special functions enable us to formulate a scientific problem by reduction such that a new, more concrete problem can be attacked within a well-structured framework, usually in the context of differential equations. A good understanding of special...

In Mathematical Analysis and Optimization for Economists, the author aims to introduce students of economics to the power and versatility of traditional as well as contemporary methodologies in mathematics and optimization theory; and, illustrates how...

• Extensively referenced to materials from earlier books• Presents the theory needed to support advanced applications• Supplements previous training in mathematics, with more detailed developments• Built from the author’s five decades of experience in...

Pragmatic and Adaptable Textbook Meets the Needs of Students and Instructors from Diverse Fields Numerical analysis is a core subject in data science and an essential tool for applied mathematicians, engineers, and physical and biological scientists...

Features a simplified presentation of numerical methods by introducing and implementing SAGE programs An Introduction to SAGE Programming: With Applications to SAGE Interacts for Numerical Methods emphasizes how to implement numerical methods using SAGE...

Introduces both the fundamentals of time dependent differential equations and their numerical solutions Introduction to Numerical Methods for Time Dependent Differential Equations delves into the underlying mathematical theory needed to solve time...

A solutions manual to accompany An Introduction to Numerical Methods and Analysis, Second Edition An Introduction to Numerical Methods and Analysis, Second Edition reflects the latest trends in the field, includes new material and revised exercises,...

One of the first books to provide in-depth and systematic application of finite element methods to the field of stochastic structural dynamics The parallel developments of the Finite Element Methods in the 1950 s and the engineering applications of...

Wigner's theorem is a fundamental part of the mathematical formulation of quantum mechanics. The theorem characterizes unitary and anti-unitary operators as symmetries of quantum mechanical systems, and is a key result when relating preserver problems to...

This book serves as a textbook for an undergraduate calculus course. It is written for readers with some previous exposure to the techniques of calculus who would like to see the subject in a conceptual framework. The book combines a review of methods of...

By the first year of graduate school, a young mathematician will have encountered at least three separate definitions of the integral. The associated integrals are typically studied in isolation, with little attention paid to the relationships between...

Tikhonov regularization is the most popular general-purpose method for regularization, a mathematical technique to suppress the effect of noise in data, and uses much of the machinery of Hilbert space theory. This book develops the theory of Tikhonov...

The description for this book, Lectures on Fourier Integrals. (AM-42), will be forthcoming.Book InformationISBN 9780691079943Author Salomon BochnerFormat PaperbackPage Count 333Imprint Princeton University PressPublisher Princeton University...

This book provides a modern introduction to harmonic analysis and synthesis on topological groups. It serves as a guide to the abstract theory of Fourier transformation. For the first time, it presents a detailed account of the theory of classical...

This is based on the course 'Calculus of Variations' taught at Peking University from 2006 to 2010 for advanced undergraduate to graduate students majoring in mathematics. The book contains 20 lectures covering both the theoretical background material as...

The 1947 paper by John von Neumann and Herman Goldstine, "Numerical Inverting of Matrices of High Order" (Bulletin of the AMS, Nov. 1947), is considered as the birth certificate of numerical analysis. Since its publication, the evolution of...

The wave maps system is one of the most beautiful and challenging nonlinear hyperbolic systems, which has captured the attention of mathematicians for more than thirty years now. In the study of its various issues, such as the well-posedness theory, the...

This monograph contains the author's work of the last four years in discrete and fractional analysis. It introduces the right delta and right nabla fractional calculus on time scales and continues with the right delta and right nabla discrete fractional...

This volume contains recent papers by several specialists in different fields of mathematical analysis. It offers a reasonably wide perspective of the current state of research, and new trends, in areas related to measure theory, harmonic analysis,...

This volume consists of a selection of research-type articles on dynamical systems, evolution equations, analytic number theory and closely related topics. A strong emphasis is on a fair balance between theoretical and more applied work, thus spanning...

This book gives a unified approach to the theory concerning a new matrix version of classical harmonic analysis. Most results in the book have their analogues as classical or newer results in harmonic analysis. It can be used as a source for further...

This book is an introductory text on real analysis for undergraduate students. The prerequisite for this book is a solid background in freshman calculus in one variable. The intended audience of this book includes undergraduate mathematics majors and...