Primer of Modern Analysis

Primer of Modern Analysis

Author: K.T. Smith

Publisher: Springer Science & Business Media

Published: 2012-12-06

Total Pages: 457

ISBN-13: 1461211441

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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 students have unexpected enthusiasm and nerve. When hard work is put to them, they work harder and ask for more. The honors course (at the University of Wisconsin) which inspired this book was, I think, more fun than the book itself. And better. But then there is acting in teaching, and a typewriter is a poor substitute for an audience. The spontaneous, creative disorder that characterizes an exciting course becomes silly in a book. To write, one must cut and dry. Yet, I hope enough of the spontaneity, enough of the spirit of that course, is left to enable those using the book to create exciting courses of their own. Exercises in this book are not designed for drill. They are designed to clarify the meanings of the theorems, to force an understanding of the proofs, and to call attention to points in a proof that might otherwise be overlooked. The exercises, therefore, are a real part of the theory, not a collection of side issues, and as such nearly all of them are to be done. Some drill is, of course, necessary, particularly in the calculation of integrals.


Primer of Modern Analysis

Primer of Modern Analysis

Author: K.T. Smith

Publisher: Springer

Published: 1983-08-29

Total Pages: 446

ISBN-13: 0387907971

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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 students have unexpected enthusiasm and nerve. When hard work is put to them, they work harder and ask for more. The honors course (at the University of Wisconsin) which inspired this book was, I think, more fun than the book itself. And better. But then there is acting in teaching, and a typewriter is a poor substitute for an audience. The spontaneous, creative disorder that characterizes an exciting course becomes silly in a book. To write, one must cut and dry. Yet, I hope enough of the spontaneity, enough of the spirit of that course, is left to enable those using the book to create exciting courses of their own. Exercises in this book are not designed for drill. They are designed to clarify the meanings of the theorems, to force an understanding of the proofs, and to call attention to points in a proof that might otherwise be overlooked. The exercises, therefore, are a real part of the theory, not a collection of side issues, and as such nearly all of them are to be done. Some drill is, of course, necessary, particularly in the calculation of integrals.


A Basis Theory Primer

A Basis Theory Primer

Author: Christopher Heil

Publisher: Springer Science & Business Media

Published: 2011

Total Pages: 549

ISBN-13: 0817646868

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This textbook is a self-contained introduction to the abstract theory of bases and redundant frame expansions and their use in both applied and classical harmonic analysis. The four parts of the text take the reader from classical functional analysis and basis theory to modern time-frequency and wavelet theory. Extensive exercises complement the text and provide opportunities for learning-by-doing, making the text suitable for graduate-level courses. The self-contained presentation with clear proofs is accessible to graduate students, pure and applied mathematicians, and engineers interested in the mathematical underpinnings of applications.


A Primer of Infinitesimal Analysis

A Primer of Infinitesimal Analysis

Author: John L. Bell

Publisher: Cambridge University Press

Published: 2008-04-07

Total Pages: 7

ISBN-13: 0521887186

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A rigorous, axiomatically formulated presentation of the 'zero-square', or 'nilpotent' infinitesimal.


Modern Money Theory

Modern Money Theory

Author: L. Randall Wray

Publisher: Springer

Published: 2015-09-22

Total Pages: 322

ISBN-13: 1137539925

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This second edition explores how money 'works' in the modern economy and synthesises the key principles of Modern Money Theory, exploring macro accounting, currency regimes and exchange rates in both the USA and developing nations.


Longitudinal Data Analysis

Longitudinal Data Analysis

Author: Toon Taris

Publisher: SAGE

Published: 2000-11-13

Total Pages: 182

ISBN-13: 9780761960270

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This accessible introduction to the theory and practice of longitudinal research takes the reader through the strengths and weaknesses of this kind of research, making clear: how to design a longitudinal study; how to collect data most effectively; how to make the best use of statistical techniques; and how to interpret results. Although the book provides a broad overview of the field, the focus is always on the practical issues arising out of longitudinal research. This book supplies the student with all that they need to get started and acts as a manual for dealing with opportunities and pitfalls. It is the ideal primer for this growing area of social research.


A Primer of Real Analytic Functions

A Primer of Real Analytic Functions

Author: KRANTZ

Publisher: Birkhäuser

Published: 2013-03-09

Total Pages: 190

ISBN-13: 3034876440

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The subject of real analytic functions is one of the oldest in mathe matical analysis. Today it is encountered early in ones mathematical training: the first taste usually comes in calculus. While most work ing mathematicians use real analytic functions from time to time in their work, the vast lore of real analytic functions remains obscure and buried in the literature. It is remarkable that the most accessible treatment of Puiseux's theorem is in Lefschetz's quite old Algebraic Geometry, that the clearest discussion of resolution of singularities for real analytic manifolds is in a book review by Michael Atiyah, that there is no comprehensive discussion in print of the embedding prob lem for real analytic manifolds. We have had occasion in our collaborative research to become ac quainted with both the history and the scope of the theory of real analytic functions. It seems both appropriate and timely for us to gather together this information in a single volume. The material presented here is of three kinds. The elementary topics, covered in Chapter 1, are presented in great detail. Even results like a real ana lytic inverse function theorem are difficult to find in the literature, and we take pains here to present such topics carefully. Topics of middling difficulty, such as separate real analyticity, Puiseux series, the FBI transform, and related ideas (Chapters 2-4), are covered thoroughly but rather more briskly.


A Primer of Nonlinear Analysis

A Primer of Nonlinear Analysis

Author: Antonio Ambrosetti

Publisher: Cambridge University Press

Published: 1995-03-09

Total Pages: 184

ISBN-13: 9780521485739

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This is an elementary and self-contained introduction to nonlinear functional analysis and its applications, especially in bifurcation theory.