Introduction to Mathematical Analysis PDF Download

Author: William R. Parzynski
Publisher: McGraw-Hill Companies
ISBN:
Category : Mathematics
Languages : en
Pages : 376

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Author: Christopher Heil
Publisher: Springer
ISBN: 3030269035
Category : Mathematics
Languages : en
Pages : 386

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Book Description
Developed over years of classroom use, this textbook provides a clear and accessible approach to real analysis. This modern interpretation is based on the author’s lecture notes and has been meticulously tailored to motivate students and inspire readers to explore the material, and to continue exploring even after they have finished the book. The definitions, theorems, and proofs contained within are presented with mathematical rigor, but conveyed in an accessible manner and with language and motivation meant for students who have not taken a previous course on this subject. The text covers all of the topics essential for an introductory course, including Lebesgue measure, measurable functions, Lebesgue integrals, differentiation, absolute continuity, Banach and Hilbert spaces, and more. Throughout each chapter, challenging exercises are presented, and the end of each section includes additional problems. Such an inclusive approach creates an abundance of opportunities for readers to develop their understanding, and aids instructors as they plan their coursework. Additional resources are available online, including expanded chapters, enrichment exercises, a detailed course outline, and much more. Introduction to Real Analysis is intended for first-year graduate students taking a first course in real analysis, as well as for instructors seeking detailed lecture material with structure and accessibility in mind. Additionally, its content is appropriate for Ph.D. students in any scientific or engineering discipline who have taken a standard upper-level undergraduate real analysis course.

Author: Charles Walmsley
Publisher:
ISBN:
Category : History
Languages : en
Pages : 316

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Originally published in 1926, this textbook aims to help physics and chemistry students become acquainted with the concepts and processes of differentiation and integration.

Author: Sterling K. Berberian
Publisher: Springer Science & Business Media
ISBN: 1441985484
Category : Mathematics
Languages : en
Pages : 249

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Book Description
Mathematics is the music of science, and real analysis is the Bach of mathematics. There are many other foolish things I could say about the subject of this book, but the foregoing will give the reader an idea of where my heart lies. The present book was written to support a first course in real analysis, normally taken after a year of elementary calculus. Real analysis is, roughly speaking, the modern setting for Calculus, "real" alluding to the field of real numbers that underlies it all. At center stage are functions, defined and taking values in sets of real numbers or in sets (the plane, 3-space, etc.) readily derived from the real numbers; a first course in real analysis traditionally places the emphasis on real-valued functions defined on sets of real numbers. The agenda for the course: (1) start with the axioms for the field ofreal numbers, (2) build, in one semester and with appropriate rigor, the foun dations of calculus (including the "Fundamental Theorem"), and, along the way, (3) develop those skills and attitudes that enable us to continue learning mathematics on our own. Three decades of experience with the exercise have not diminished my astonishment that it can be done.

Author: Thomas William Körner
Publisher: American Mathematical Soc.
ISBN: 0821834479
Category : Mathematics
Languages : en
Pages : 608

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Book Description
This book not only provides a lot of solid information about real analysis, it also answers those questions which students want to ask but cannot figure how to formulate. To read this book is to spend time with one of the modern masters in the subject. --Steven G. Krantz, Washington University, St. Louis One of the major assets of the book is Korner's very personal writing style. By keeping his own engagement with the material continually in view, he invites the reader to a similarly high level of involvement. And the witty and erudite asides that are sprinkled throughout the book are a real pleasure. --Gerald Folland, University of Washingtion, Seattle Many students acquire knowledge of a large number of theorems and methods of calculus without being able to say how they hang together. This book provides such students with the coherent account that they need. A Companion to Analysis explains the problems which must be resolved in order to obtain a rigorous development of the calculus and shows the student how those problems are dealt with. Starting with the real line, it moves on to finite dimensional spaces and then to metric spaces. Readers who work through this text will be ready for such courses as measure theory, functional analysis, complex analysis and differential geometry. Moreover, they will be well on the road which leads from mathematics student to mathematician. Able and hard working students can use this book for independent study, or it can be used as the basis for an advanced undergraduate or elementary graduate course. An appendix contains a large number of accessible but non-routine problems to improve knowledge and technique.

Author: Charles Walmsley
Publisher:
ISBN:
Category : Calculus
Languages : en
Pages : 293

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Author: Adam Bowers
Publisher: Springer
ISBN: 1493919458
Category : Mathematics
Languages : en
Pages : 242

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Book Description
Based on a graduate course by the celebrated analyst Nigel Kalton, this well-balanced introduction to functional analysis makes clear not only how, but why, the field developed. All major topics belonging to a first course in functional analysis are covered. However, unlike traditional introductions to the subject, Banach spaces are emphasized over Hilbert spaces, and many details are presented in a novel manner, such as the proof of the Hahn–Banach theorem based on an inf-convolution technique, the proof of Schauder's theorem, and the proof of the Milman–Pettis theorem. With the inclusion of many illustrative examples and exercises, An Introductory Course in Functional Analysis equips the reader to apply the theory and to master its subtleties. It is therefore well-suited as a textbook for a one- or two-semester introductory course in functional analysis or as a companion for independent study.

Author: Piotr Mikusinski
Publisher: World Scientific Publishing Company
ISBN: 9813202637
Category : Mathematics
Languages : en
Pages : 318

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Book Description
The book contains a rigorous exposition of calculus of a single real variable. It covers the standard topics of an introductory analysis course, namely, functions, continuity, differentiability, sequences and series of numbers, sequences and series of functions, and integration. A direct treatment of the Lebesgue integral, based solely on the concept of absolutely convergent series, is presented, which is a unique feature of a textbook at this level. The standard material is complemented by topics usually not found in comparable textbooks, for example, elementary functions are rigorously defined and their properties are carefully derived and an introduction to Fourier series is presented as an example of application of the Lebesgue integral.The text is for a post-calculus course for students majoring in mathematics or mathematics education. It will provide students with a solid background for further studies in analysis, deepen their understanding of calculus, and provide sound training in rigorous mathematical proof.

Author: Dorairaj Somasundaram
Publisher:
ISBN: 9788173190643
Category : Mathematics
Languages : en
Pages : 616

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Book Description
Intends to serve as a textbook in Real Analysis at the Advanced Calculus level. This book includes topics like Field of real numbers, Foundation of calculus, Compactness, Connectedness, Riemann integration, Fourier series, Calculus of several variables and Multiple integrals are presented systematically with diagrams and illustrations.

Author: Donald Yau
Publisher: World Scientific
ISBN: 9814417858
Category : Mathematics
Languages : en
Pages : 206

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Book Description
This book is an introductory text on real analysis for undergraduate students. The prerequisite for this book is a solid background in freshman calculus in one variable. The intended audience of this book includes undergraduate mathematics majors and students from other disciplines who use real analysis. Since this book is aimed at students who do not have much prior experience with proofs, the pace is slower in earlier chapters than in later chapters. There are hundreds of exercises, and hints for some of them are included.