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A Primer of Real Functions
Author: Ralph P. Boas
Publisher: Cambridge University Press
Published: 1996
Total Pages: 330
ISBN-13: 9780883850299
DOWNLOAD EBOOK →This is a revised, updated, and significantly augmented edition of a classic Carus Monograph (a bestseller for over 25 years) on the theory of functions of a real variable. Earlier editions of this classic Carus Monograph covered sets, metric spaces, continuous functions, and differentiable functions. The fourth edition adds sections on measurable sets and functions, the Lebesgue and Stieltjes integrals, and applications. The book retains the informal chatty style of the previous editions, remaining accessible to readers with some mathematical sophistication and a background in calculus. The book is, thus, suitable either for self-study or for supplemental reading in a course on advanced calculus or real analysis. Not intended as a systematic treatise, this book has more the character of a sequence of lectures on a variety of interesting topics connected with real functions. Many of these topics are not commonly encountered in undergraduate textbooks: e.g., the existence of continuous everywhere-oscillating functions (via the Baire category theorem); the universal chord theorem; two functions having equal derivatives, yet not differing by a constant; and application of Stieltjes integration to the speed of convergence of infinite series. This book recaptures the sense of wonder that was associated with the subject in its early days. It is a must for mathematics libraries.
A Primer of Real Analytic Functions
Author: KRANTZ
Publisher: Birkhäuser
Published: 2013-03-09
Total Pages: 190
ISBN-13: 3034876440
DOWNLOAD EBOOK →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 Real Analytic Functions
Author: Steven G. Krantz
Publisher: Springer Science & Business Media
Published: 2012-09-08
Total Pages: 215
ISBN-13: 0817681345
DOWNLOAD EBOOK →Key topics in the theory of real analytic functions are covered in this text,and are rather difficult to pry out of the mathematics literature.; This expanded and updated 2nd ed. will be published out of Boston in Birkhäuser Adavaned Texts series.; Many historical remarks, examples, references and an excellent index should encourage the reader study this valuable and exciting theory.; Superior advanced textbook or monograph for a graduate course or seminars on real analytic functions.; New to the second edition a revised and comprehensive treatment of the Faá de Bruno formula, topologies on the space of real analytic functions,; alternative characterizations of real analytic functions, surjectivity of partial differential operators, And the Weierstrass preparation theorem.
Real Mathematical Analysis
Author: Charles C. Pugh
Publisher: Springer Science & Business Media
Published: 2003-11-14
Total Pages: 456
ISBN-13: 9780387952970
DOWNLOAD EBOOK →Was plane geometry your favourite math course in high school? Did you like proving theorems? Are you sick of memorising integrals? If so, real analysis could be your cup of tea. In contrast to calculus and elementary algebra, it involves neither formula manipulation nor applications to other fields of science. None. It is Pure Mathematics, and it is sure to appeal to the budding pure mathematician. In this new introduction to undergraduate real analysis the author takes a different approach from past studies of the subject, by stressing the importance of pictures in mathematics and hard problems. The exposition is informal and relaxed, with many helpful asides, examples and occasional comments from mathematicians like Dieudonne, Littlewood and Osserman. The author has taught the subject many times over the last 35 years at Berkeley and this book is based on the honours version of this course. The book contains an excellent selection of more than 500 exercises.
A Primer of Real Functions
A Primer of Real Analytic Functions
Author: Steven George Krantz
Publisher: Birkhauser
Published: 2002
Total Pages: 205
ISBN-13: 9783764342647
DOWNLOAD EBOOK →It is a pleasure and a privilege to write this new edition of A Primer 0/ Real Ana lytic Functions. The theory of real analytic functions is the wellspring of mathe matical analysis. It is remarkable that this is the first book on the subject, and we want to keep it up to date and as correct as possible. With these thoughts in mind, we have utilized helpful remarks and criticisms from many readers and have thereby made numerous emendations. We have also added material. There is a now a treatment of the Weierstrass preparation theorem, a new argument to establish Hensel's lemma and Puiseux's theorem, a new treat ment of Faa di Bruno's forrnula, a thorough discussion of topologies on spaces of real analytic functions, and a second independent argument for the implicit func tion theorem. We trust that these new topics will make the book more complete, and hence a more useful reference. It is a pleasure to thank our editor, Ann Kostant of Birkhäuser Boston, for mak ing the publishing process as smooth and trouble-free as possible. We are grateful for useful communications from the readers of our first edition, and we look for ward to further constructive feedback.
Primer of Real Functions
A Primer of Real Analytic Functions
Author: Steven George Krantz
Publisher: Birkhauser
Published: 1992-01-01
Total Pages: 184
ISBN-13: 9783764327682
DOWNLOAD EBOOK →Treats the subject of analytic functions of one or more real variables, using almost solely the techniques of real analysis, an approach that alters the usual progression of ideas and raises previously neglected questions. The beginning requires only a background in calculus, but the increasingly complex topics require increasing sophistication. Annotation copyright by Book News, Inc., Portland, OR
Basic Real Analysis
Author: Houshang H. Sohrab
Publisher: Springer Science & Business Media
Published: 2003-06-03
Total Pages: 584
ISBN-13: 9780817642112
DOWNLOAD EBOOK →Basic Real Analysis demonstrates the richness of real analysis, giving students an introduction both to mathematical rigor and to the deep theorems and counter examples that arise from such rigor. In this modern and systematic text, all the touchstone results and fundamentals are carefully presented in a style that requires little prior familiarity with proofs or mathematical language. With its many examples, exercises and broad view of analysis, this work is ideal for senior undergraduates and beginning graduate students, either in the classroom or for self-study.
