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Author: Ajit Kumar Publisher: CRC Press ISBN: 1482216388 Category : Mathematics Languages : en Pages : 322
Book Description
Based on the authors’ combined 35 years of experience in teaching, A Basic Course in Real Analysis introduces students to the aspects of real analysis in a friendly way. The authors offer insights into the way a typical mathematician works observing patterns, conducting experiments by means of looking at or creating examples, trying to understand the underlying principles, and coming up with guesses or conjectures and then proving them rigorously based on his or her explorations. With more than 100 pictures, the book creates interest in real analysis by encouraging students to think geometrically. Each difficult proof is prefaced by a strategy and explanation of how the strategy is translated into rigorous and precise proofs. The authors then explain the mystery and role of inequalities in analysis to train students to arrive at estimates that will be useful for proofs. They highlight the role of the least upper bound property of real numbers, which underlies all crucial results in real analysis. In addition, the book demonstrates analysis as a qualitative as well as quantitative study of functions, exposing students to arguments that fall under hard analysis. Although there are many books available on this subject, students often find it difficult to learn the essence of analysis on their own or after going through a course on real analysis. Written in a conversational tone, this book explains the hows and whys of real analysis and provides guidance that makes readers think at every stage.
Author: Ajit Kumar Publisher: CRC Press ISBN: 1482216388 Category : Mathematics Languages : en Pages : 322
Book Description
Based on the authors’ combined 35 years of experience in teaching, A Basic Course in Real Analysis introduces students to the aspects of real analysis in a friendly way. The authors offer insights into the way a typical mathematician works observing patterns, conducting experiments by means of looking at or creating examples, trying to understand the underlying principles, and coming up with guesses or conjectures and then proving them rigorously based on his or her explorations. With more than 100 pictures, the book creates interest in real analysis by encouraging students to think geometrically. Each difficult proof is prefaced by a strategy and explanation of how the strategy is translated into rigorous and precise proofs. The authors then explain the mystery and role of inequalities in analysis to train students to arrive at estimates that will be useful for proofs. They highlight the role of the least upper bound property of real numbers, which underlies all crucial results in real analysis. In addition, the book demonstrates analysis as a qualitative as well as quantitative study of functions, exposing students to arguments that fall under hard analysis. Although there are many books available on this subject, students often find it difficult to learn the essence of analysis on their own or after going through a course on real analysis. Written in a conversational tone, this book explains the hows and whys of real analysis and provides guidance that makes readers think at every stage.
Author: Houshang H. Sohrab Publisher: Springer Science & Business Media ISBN: 9780817642112 Category : Mathematics Languages : en Pages : 584
Book Description
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.
Author: D. J. H. Garling Publisher: Cambridge University Press ISBN: 1107311381 Category : Mathematics Languages : en Pages :
Book Description
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.
Author: James Howland Publisher: Jones & Bartlett Learning ISBN: 0763773182 Category : Mathematics Languages : en Pages : 233
Book Description
Ideal for the one-semester undergraduate course, Basic Real Analysis is intended for students who have recently completed a traditional calculus course and proves the basic theorems of Single Variable Calculus in a simple and accessible manner. It gradually builds upon key material as to not overwhelm students beginning the course and becomes more rigorous as they progresses. Optional appendices on sets and functions, countable and uncountable sets, and point set topology are included for those instructors who wish include these topics in their course. The author includes hints throughout the text to help students solve challenging problems. An online instructor's solutions manual is also available.
Author: Murray H. Protter Publisher: Springer Science & Business Media ISBN: 0387227490 Category : Mathematics Languages : en Pages : 284
Book Description
From the author of the highly-acclaimed "A First Course in Real Analysis" comes a volume designed specifically for a short one-semester course in real analysis. Many students of mathematics and the physical and computer sciences need a text that presents the most important material in a brief and elementary fashion. The author meets this need with such elementary topics as the real number system, the theory at the basis of elementary calculus, the topology of metric spaces and infinite series. There are proofs of the basic theorems on limits at a pace that is deliberate and detailed, backed by illustrative examples throughout and no less than 45 figures.
Author: A. D. R. Choudary Publisher: Springer ISBN: 8132221486 Category : Mathematics Languages : en Pages : 525
Book Description
The book targets undergraduate and postgraduate mathematics students and helps them develop a deep understanding of mathematical analysis. Designed as a first course in real analysis, it helps students learn how abstract mathematical analysis solves mathematical problems that relate to the real world. As well as providing a valuable source of inspiration for contemporary research in mathematics, the book helps students read, understand and construct mathematical proofs, develop their problem-solving abilities and comprehend the importance and frontiers of computer facilities and much more. It offers comprehensive material for both seminars and independent study for readers with a basic knowledge of calculus and linear algebra. The first nine chapters followed by the appendix on the Stieltjes integral are recommended for graduate students studying probability and statistics, while the first eight chapters followed by the appendix on dynamical systems will be of use to students of biology and environmental sciences. Chapter 10 and the appendixes are of interest to those pursuing further studies at specialized advanced levels. Exercises at the end of each section, as well as commentaries at the end of each chapter, further aid readers’ understanding. The ultimate goal of the book is to raise awareness of the fine architecture of analysis and its relationship with the other fields of mathematics.
Author: Jiri Lebl Publisher: Createspace Independent Pub ISBN: 9781505695915 Category : Mathematics Languages : en Pages : 244
Book Description
A first course in mathematical analysis. Covers the real number system, sequences and series, continuous functions, the derivative, the Riemann integral, sequences of functions, and metric spaces. Originally developed to teach Math 444 at University of Illinois at Urbana-Champaign and later enhanced for Math 521 at University of Wisconsin-Madison. See http: //www.jirka.org/ra
Author: Jiri Lebl Publisher: Createspace Independent Publishing Platform ISBN: 9781718865488 Category : Languages : en Pages : 196
Book Description
Version 2.0. The second volume of Basic Analysis, a first course in mathematical analysis. This volume is the second semester material for a year-long sequence for advanced undergraduates or masters level students. This volume started with notes for Math 522 at University of Wisconsin-Madison, and then was heavily revised and modified for teaching Math 4153/5053 at Oklahoma State University. It covers differential calculus in several variables, line integrals, multivariable Riemann integral including a basic case of Green's Theorem, and topics on power series, Arzelà-Ascoli, Stone-Weierstrass, and Fourier Series. See http://www.jirka.org/ra/ Table of Contents (of this volume II): 8. Several Variables and Partial Derivatives 9. One Dimensional Integrals in Several Variables 10. Multivariable Integral 11. Functions as Limits
Author: Anthony W. Knapp Publisher: Springer Science & Business Media ISBN: 0817644423 Category : Mathematics Languages : en Pages : 466
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
Author: V. K. Bhat Publisher: Alpha Science International, Limited ISBN: 9781842657058 Category : Mathematics Languages : en Pages : 0
Book Description
Covers basic results pertaining to the set of real numbers. This book includes chapters like real number system, sequences, limit and continuity of functions, differentiability and integration. It is a foundational course for beginners.
Author: Ajit Kumar
Author: Ajit Kumar
Author: Houshang H. Sohrab
Author: D. J. H. Garling
Author: James Howland
Author: Murray H. Protter
Author: A. D. R. Choudary
Author: Jiri Lebl
Author: Jiri Lebl
Author: Anthony W. Knapp
Author: V. K. Bhat