Intermediate Mathematical Analysis


Book Description

Geared toward those who have studied elementary calculus, this book stresses concepts rather than techniques. It prepares students for a first demanding course in analysis, dealing primarily with real-valued functions of a real variable. Complex numbers appear only in supplements and the last two chapters. 1968 edition.




Intermediate Real Analysis


Book Description

There are a great deal of books on introductory analysis in print today, many written by mathematicians of the first rank. The publication of another such book therefore warrants a defense. I have taught analysis for many years and have used a variety of texts during this time. These books were of excellent quality mathematically but did not satisfy the needs of the students I was teaching. They were written for mathematicians but not for those who were first aspiring to attain that status. The desire to fill this gap gave rise to the writing of this book. This book is intended to serve as a text for an introductory course in analysis. Its readers will most likely be mathematics, science, or engineering majors undertaking the last quarter of their undergraduate education. The aim of a first course in analysis is to provide the student with a sound foundation for analysis, to familiarize him with the kind of careful thinking used in advanced mathematics, and to provide him with tools for further work in it. The typical student we are dealing with has completed a three-semester calculus course and possibly an introductory course in differential equations. He may even have been exposed to a semester or two of modern algebra. All this time his training has most likely been intuitive with heuristics taking the place of proof. This may have been appropriate for that stage of his development.




Intermediate Mathematical Analysis


Book Description

This textbook provides a readable, though rigorous, introduction to the differentiation and integration of functions of several complex variables. In addition to presenting the classical theory of the subject, the author includes informal explanations of many proofs along with numerous exercises and problems that will help readers gain an in-depth understanding of the subject. Students are not assumed to have more background than a standard first course in calculus of one variable. Key concepts that are introduced include the composition of functions of several variables, compactness, uniform continuity, and connectivity. The author goes on to develop the theories of differentiation and integration, including Taylor's theorem, Lagrange's multipliers, the implicit function theory, inverse function theorem, iterated integration, improper integrals, and the change of variable theorem for integrals. As a special feature, the author offers a logically sound treatment of partial differentiation in Euler's notation. The book concludes with an indication of how the subject may be further developed. With its clear style and fresh approach, this text provides a useful bridge between the elementary calculus of one variable and the theory of functions in abstract spaces.




Intermediate Mathematical Analysis


Book Description

Presents advanced topics such as continuity, uniform continuity, tests of convergence of series, uniform convergence of series, power series, polynomial approximations and Fourier series in a more general setting. Metric and Normed Linear Spaces are introduced at an early stage and are used wherever found advantageous.




Intermediate Mathematical Analysis


Book Description

"Intermediate Mathematical Analysis aims at presenting advanced topics such as continuity, uniform continuity, tests of convergence of series, uniform convergence of series, power series, polynomial approximations and Fourier series in a more general setting. Metric and normed linear spaces are introduced at an early stage and are used wherever found advantageous. The book places a consistent emphasis on showing the power of the classical analysis by applying it to the study of real valued functions and their applications." -- Publisher's description.







Advanced Real Analysis


Book Description

* Presents a comprehensive treatment with a global view of the subject * Rich in examples, problems with hints, and solutions, the book makes a welcome addition to the library of every mathematician




Real Analysis (Classic Version)


Book Description

This text is designed for graduate-level courses in real analysis. Real Analysis, 4th Edition, covers the basic material that every graduate student should know in the classical theory of functions of a real variable, measure and integration theory, and some of the more important and elementary topics in general topology and normed linear space theory. This text assumes a general background in undergraduate mathematics and familiarity with the material covered in an undergraduate course on the fundamental concepts of analysis.




Mathematical Analysis of Physical Problems


Book Description

This mathematical reference for theoretical physics employs common techniques and concepts to link classical and modern physics. It provides the necessary mathematics to solve most of the problems. Topics include the vibrating string, linear vector spaces, the potential equation, problems of diffusion and attenuation, probability and stochastic processes, and much more. 1972 edition.




Intermediate Analysis


Book Description