Introduction To Analysis In One Variable
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Introduction To Analysis In One Variable
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Author : Michael E. Taylor
language : en
Publisher: American Mathematical Soc.
Release Date : 2020-08-11
Introduction To Analysis In One Variable written by Michael E. Taylor and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-08-11 with Education categories.
This is a text for students who have had a three-course calculus sequence and who are ready to explore the logical structure of analysis as the backbone of calculus. It begins with a development of the real numbers, building this system from more basic objects (natural numbers, integers, rational numbers, Cauchy sequences), and it produces basic algebraic and metric properties of the real number line as propositions, rather than axioms. The text also makes use of the complex numbers and incorporates this into the development of differential and integral calculus. For example, it develops the theory of the exponential function for both real and complex arguments, and it makes a geometrical study of the curve (expit) (expit), for real t t, leading to a self-contained development of the trigonometric functions and to a derivation of the Euler identity that is very different from what one typically sees. Further topics include metric spaces, the Stone–Weierstrass theorem, and Fourier series.
Introduction To Analysis In Several Variables Advanced Calculus
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Author : Michael E. Taylor
language : en
Publisher: American Mathematical Soc.
Release Date : 2020-07-27
Introduction To Analysis In Several Variables Advanced Calculus written by Michael E. Taylor and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-07-27 with Education categories.
This text was produced for the second part of a two-part sequence on advanced calculus, whose aim is to provide a firm logical foundation for analysis. The first part treats analysis in one variable, and the text at hand treats analysis in several variables. After a review of topics from one-variable analysis and linear algebra, the text treats in succession multivariable differential calculus, including systems of differential equations, and multivariable integral calculus. It builds on this to develop calculus on surfaces in Euclidean space and also on manifolds. It introduces differential forms and establishes a general Stokes formula. It describes various applications of Stokes formula, from harmonic functions to degree theory. The text then studies the differential geometry of surfaces, including geodesics and curvature, and makes contact with degree theory, via the Gauss–Bonnet theorem. The text also takes up Fourier analysis, and bridges this with results on surfaces, via Fourier analysis on spheres and on compact matrix groups.
Complex Analysis In One Variable
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Author : Raghavan Narasimhan
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Complex Analysis In One Variable written by Raghavan Narasimhan and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.
The original edition of this book has been out of print for some years. The appear ance of the present second edition owes much to the initiative of Yves Nievergelt at Eastern Washington University, and the support of Ann Kostant, Mathematics Editor at Birkhauser. Since the book was first published, several people have remarked on the absence of exercises and expressed the opinion that the book would have been more useful had exercises been included. In 1997, Yves Nievergelt informed me that, for a decade, he had regularly taught a course at Eastern Washington based on the book, and that he had systematically compiled exercises for his course. He kindly put his work at my disposal. Thus, the present edition appears in two parts. The first is essentially just a reprint of the original edition. I have corrected the misprints of which I have become aware (including those pointed out to me by others), and have made a small number of other minor changes.
Real Analysis
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Author : Miklós Laczkovich
language : en
Publisher: Springer
Release Date : 2015-10-08
Real Analysis written by Miklós Laczkovich and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-10-08 with Mathematics categories.
Based on courses given at Eötvös Loránd University (Hungary) over the past 30 years, this introductory textbook develops the central concepts of the analysis of functions of one variable — systematically, with many examples and illustrations, and in a manner that builds upon, and sharpens, the student’s mathematical intuition. The book provides a solid grounding in the basics of logic and proofs, sets, and real numbers, in preparation for a study of the main topics: limits, continuity, rational functions and transcendental functions, differentiation, and integration. Numerous applications to other areas of mathematics, and to physics, are given, thereby demonstrating the practical scope and power of the theoretical concepts treated. In the spirit of learning-by-doing, Real Analysis includes more than 500 engaging exercises for the student keen on mastering the basics of analysis. The wealth of material, and modular organization, of the book make it adaptable as a textbook for courses of various levels; the hints and solutions provided for the more challenging exercises make it ideal for independent study.
A Concise Introduction To Analysis
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Author : Daniel W. Stroock
language : en
Publisher: Springer
Release Date : 2015-10-31
A Concise Introduction To Analysis written by Daniel W. Stroock and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-10-31 with Mathematics categories.
This book provides an introduction to the basic ideas and tools used in mathematical analysis. It is a hybrid cross between an advanced calculus and a more advanced analysis text and covers topics in both real and complex variables. Considerable space is given to developing Riemann integration theory in higher dimensions, including a rigorous treatment of Fubini's theorem, polar coordinates and the divergence theorem. These are used in the final chapter to derive Cauchy's formula, which is then applied to prove some of the basic properties of analytic functions. Among the unusual features of this book is the treatment of analytic function theory as an application of ideas and results in real analysis. For instance, Cauchy's integral formula for analytic functions is derived as an application of the divergence theorem. The last section of each chapter is devoted to exercises that should be viewed as an integral part of the text. A Concise Introduction to Analysis should appeal to upper level undergraduate mathematics students, graduate students in fields where mathematics is used, as well as to those wishing to supplement their mathematical education on their own. Wherever possible, an attempt has been made to give interesting examples that demonstrate how the ideas are used and why it is important to have a rigorous grasp of them.
Intermediate Analysis
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Author : John Meigs Hubbell Olmsted
language : en
Publisher:
Release Date : 1956
Intermediate Analysis written by John Meigs Hubbell Olmsted and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1956 with Mathematics categories.
Introduction To Complex Analysis In Several Variables
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Author : Volker Scheidemann
language : en
Publisher: Springer Nature
Release Date : 2023-04-26
Introduction To Complex Analysis In Several Variables written by Volker Scheidemann and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-04-26 with Mathematics categories.
This book gives a comprehensive introduction to complex analysis in several variables. While it focusses on a number of topics in complex analysis rather than trying to cover as much material as possible, references to other parts of mathematics such as functional analysis or algebras are made to help broaden the view and the understanding of the chosen topics. A major focus are extension phenomena alien to the one-dimensional theory, which are expressed in the famous Hartog's Kugelsatz, the theorem of Cartan-Thullen, and Bochner's theorem. The book aims primarily at students starting to work in the field of complex analysis in several variables and instructors preparing a course. To that end, a lot of examples and supporting exercises are provided throughout the text. This second edition includes hints and suggestions for the solution of the provided exercises, with various degrees of support.
Basic Analysis I
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Author : James K. Peterson
language : en
Publisher: CRC Press
Release Date : 2020-05-13
Basic Analysis I written by James K. Peterson and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-05-13 with Mathematics categories.
Basic Analysis I: Functions of a Real Variable is designed for students who have completed the usual calculus and ordinary differential equation sequence and a basic course in linear algebra. This is a critical course in the use of abstraction, but is just first volume in a sequence of courses which prepare students to become practicing scientists. This book is written with the aim of balancing the theory and abstraction with clear explanations and arguments, so that students who are from a variety of different areas can follow this text and use it profitably for self-study. It can also be used as a supplementary text for anyone whose work requires that they begin to assimilate more abstract mathematical concepts as part of their professional growth. Features Can be used as a traditional textbook as well as for self-study Suitable for undergraduate mathematics students, or for those in other disciplines requiring a solid grounding in abstraction Emphasises learning how to understand the consequences of assumptions using a variety of tools to provide the proofs of propositions
Practical Analysis In One Variable
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Author : Donald Estep
language : en
Publisher: Springer Science & Business Media
Release Date : 2006-04-06
Practical Analysis In One Variable written by Donald Estep and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-04-06 with Mathematics categories.
Background I was an eighteen-year-old freshman when I began studying analysis. I had arrived at Columbia University ready to major in physics or perhaps engineering. But my seduction into mathematics began immediately with Lipman Bers’ calculus course, which stood supreme in a year of exciting classes. Then after the course was over, Professor Bers called me into his o?ce and handed me a small blue book called Principles of Mathematical Analysis by W. Rudin. He told me that if I could read this book over the summer,understandmostofit,andproveitbydoingmostoftheproblems, then I might have a career as a mathematician. So began twenty years of struggle to master the ideas in “Little Rudin. ” I began because of a challenge to my ego but this shallow reason was quickly forgotten as I learned about the beauty and the power of analysis that summer. Anyone who recalls taking a “serious” mathematics course for the ?rst time will empathize with my feelings about this new world into which I fell. In school, I restlessly wandered through complex analysis, analyticnumbertheory,andpartialdi?erentialequations,beforeeventually settling in numerical analysis. But underlying all of this indecision was an ever-present and ever-growing appreciation of analysis. An appreciation thatstillsustainsmyintellectevenintheoftencynicalworldofthemodern academic professional. But developing this appreciation did not come easy to me, and the p- sentation in this book is motivated by my struggles to understand the viii Preface most basic concepts of analysis. To paraphrase J.
Introduction To Mathematical Analysis
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Author : Igor Kriz
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-07-25
Introduction To Mathematical Analysis written by Igor Kriz and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-07-25 with Mathematics categories.
The book begins at the level of an undergraduate student assuming only basic knowledge of calculus in one variable. It rigorously treats topics such as multivariable differential calculus, Lebesgue integral, vector calculus and differential equations. After having built on a solid foundation of topology and linear algebra, the text later expands into more advanced topics such as complex analysis, differential forms, calculus of variations, differential geometry and even functional analysis. Overall, this text provides a unique and well-rounded introduction to the highly developed and multi-faceted subject of mathematical analysis, as understood by a mathematician today.