Bolzano And The Foundations Of Mathematical Analysis
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Bolzano And The Foundations Of Mathematical Analysis
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Author : Jarnik Vojtech
language : en
Publisher:
Release Date : 1991
Bolzano And The Foundations Of Mathematical Analysis written by Jarnik Vojtech and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1991 with categories.
Bolzano And The Foundations Of Mathematical Analysis
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Author : Vojtěch Jarník
language : en
Publisher:
Release Date : 1981
Bolzano And The Foundations Of Mathematical Analysis written by Vojtěch Jarník and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1981 with Logic, Symbolic and mathematical categories.
Bolzano And The Foundations Of Mathematical Analysis
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Author : Vojtěch Jarník
language : en
Publisher:
Release Date : 1981
Bolzano And The Foundations Of Mathematical Analysis written by Vojtěch Jarník and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1981 with categories.
Bolzano And The Foundation Of Mathematical Analysis
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Author : Vojtěch Jarník
language : en
Publisher:
Release Date : 1981
Bolzano And The Foundation Of Mathematical Analysis written by Vojtěch Jarník and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1981 with categories.
Foundations Of Mathematical Real Analysis Computer Science Mathematical Analysis
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Author : Chidume O. C
language : en
Publisher: Ibadan University Press
Release Date : 2019-08-29
Foundations Of Mathematical Real Analysis Computer Science Mathematical Analysis written by Chidume O. C and has been published by Ibadan University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-08-29 with Education categories.
This book is intended as a serious introduction to the studyof mathematical analysis. In contrast to calculus, mathematical analysis does not involve formula manipulation, memorizing integrals or applications to other fields of science. No.It involves geometric intuition and proofs of theorems. It ispure mathematics! Given the mathematical preparation andinterest of our intended audience which, apart from mathematics majors, includes students of statistics, computer science, physics, students of mathematics education and students of engineering, we have not given the axiomatic development of the real number system. However, we assumethat the reader is familiar with sets and functions. This bookis divided into two parts. Part I covers elements of mathematical analysis which include: the real number system, bounded subsets of real numbers, sequences of real numbers, monotone sequences, Bolzano-Weierstrass theorem, Cauchysequences and completeness of R, continuity, intermediatevalue theorem, continuous maps on [a, b], uniform continuity, closed sets, compact sets, differentiability, series of nonnegative real numbers, alternating series, absolute and conditional convergence; and re-arrangement of series. The contents of Part I are adequate for a semester course in mathematical analysis at the 200 level. Part II covers Riemannintegrals. In particular, the Riemann integral, basic properties of Riemann integral, pointwise convergence of sequencesof functions, uniform convergence of sequences of functions, series of real-valued functions: term by term differentiationand integration; power series: uniform convergence of powerseries; uniform convergence at end points; and equi-continuity are covered. Part II covers the standard syllabus for asemester mathematical analysis course at the 300 level. Thetopics covered in this book provide a reasonable preparationfor any serious study of higher mathematics. But for one toreally benefit from the book, one must spend a great deal ofixtime on it, studying the contents very carefully and attempting all the exercises, especially the miscellaneous exercises atthe end of the book. These exercises constitute an importantintegral part of the book.Each chapter begins with clear statements of the most important theorems of the chapter. The proofs of these theoremsgenerally contain fundamental ideas of mathematical analysis. Students are therefore encouraged to study them verycarefully and to discover these id
A Course In Mathematical Analysis Volume 1 Foundations And Elementary Real Analysis
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Author : D. J. H. Garling
language : en
Publisher: Cambridge University Press
Release Date : 2013-04-25
A Course In Mathematical Analysis Volume 1 Foundations And Elementary Real Analysis written by D. J. H. Garling and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-04-25 with Mathematics categories.
The three volumes of A Course in Mathematical Analysis provide a full and detailed account of all those elements of real and complex analysis that an undergraduate mathematics student can expect to encounter in their first two or three years of study. Containing hundreds of exercises, examples and applications, these books will become an invaluable resource for both students and instructors. This first volume focuses on the analysis of real-valued functions of a real variable. Besides developing the basic theory it describes many applications, including a chapter on Fourier series. It also includes a Prologue in which the author introduces the axioms of set theory and uses them to construct the real number system. Volume 2 goes on to consider metric and topological spaces and functions of several variables. Volume 3 covers complex analysis and the theory of measure and integration.
The Development Of The Foundations Of Mathematical Analysis From Euler To Riemann
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Author : I. Grattan-Guinness
language : en
Publisher:
Release Date : 1970
The Development Of The Foundations Of Mathematical Analysis From Euler To Riemann written by I. Grattan-Guinness and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1970 with Mathematics categories.
Essential Real Analysis
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Author : Michael Field
language : en
Publisher: Springer
Release Date : 2017-11-06
Essential Real Analysis written by Michael Field and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-11-06 with Mathematics categories.
This book provides a rigorous introduction to the techniques and results of real analysis, metric spaces and multivariate differentiation, suitable for undergraduate courses. Starting from the very foundations of analysis, it offers a complete first course in real analysis, including topics rarely found in such detail in an undergraduate textbook such as the construction of non-analytic smooth functions, applications of the Euler-Maclaurin formula to estimates, and fractal geometry. Drawing on the author’s extensive teaching and research experience, the exposition is guided by carefully chosen examples and counter-examples, with the emphasis placed on the key ideas underlying the theory. Much of the content is informed by its applicability: Fourier analysis is developed to the point where it can be rigorously applied to partial differential equations or computation, and the theory of metric spaces includes applications to ordinary differential equations and fractals. Essential Real Analysis will appeal to students in pure and applied mathematics, as well as scientists looking to acquire a firm footing in mathematical analysis. Numerous exercises of varying difficulty, including some suitable for group work or class discussion, make this book suitable for self-study as well as lecture courses.
Foundations Of Mathematical Analysis
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Author : Richard Johnsonbaugh
language : en
Publisher: Courier Corporation
Release Date : 2012-09-11
Foundations Of Mathematical Analysis written by Richard Johnsonbaugh and has been published by Courier Corporation this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-09-11 with Mathematics categories.
Definitive look at modern analysis, with views of applications to statistics, numerical analysis, Fourier series, differential equations, mathematical analysis, and functional analysis. More than 750 exercises; some hints and solutions. 1981 edition.
Foundations Of Analysis
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Author : Joseph L. Taylor
language : en
Publisher: American Mathematical Soc.
Release Date : 2012
Foundations Of Analysis written by Joseph L. 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 2012 with Mathematics categories.
Foundations of Analysis has two main goals. The first is to develop in students the mathematical maturity and sophistication they will need as they move through the upper division curriculum. The second is to present a rigorous development of both single and several variable calculus, beginning with a study of the properties of the real number system. The presentation is both thorough and concise, with simple, straightforward explanations. The exercises differ widely in level of abstraction and level of difficulty. They vary from the simple to the quite difficult and from the computational to the theoretical. Each section contains a number of examples designed to illustrate the material in the section and to teach students how to approach the exercises for that section. --Book cover.