First Course In Real Analysis
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| Author | : M.H. Protter |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 520 |
| Release | : 2012-12-06 |
| Genre | : Mathematics |
| ISBN | : 1461599903 |
The first course in analysis which follows elementary calculus is a critical one for students who are seriously interested in mathematics. Traditional advanced calculus was precisely what its name indicates-a course with topics in calculus emphasizing problem solving rather than theory. As a result students were often given a misleading impression of what mathematics is all about; on the other hand the current approach, with its emphasis on theory, gives the student insight in the fundamentals of analysis. In A First Course in Real Analysis we present a theoretical basis of analysis which is suitable for students who have just completed a course in elementary calculus. Since the sixteen chapters contain more than enough analysis for a one year course, the instructor teaching a one or two quarter or a one semester junior level course should easily find those topics which he or she thinks students should have. The first Chapter, on the real number system, serves two purposes. Because most students entering this course have had no experience in devising proofs of theorems, it provides an opportunity to develop facility in theorem proving. Although the elementary processes of numbers are familiar to most students, greater understanding of these processes is acquired by those who work the problems in Chapter 1. As a second purpose, we provide, for those instructors who wish to give a comprehen sive course in analysis, a fairly complete treatment of the real number system including a section on mathematical induction.
| Author | : Sterling K. Berberian |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 249 |
| Release | : 2012-09-10 |
| Genre | : Mathematics |
| ISBN | : 1441985484 |
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 | : Charles Chapman Pugh |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 445 |
| Release | : 2013-03-19 |
| Genre | : Mathematics |
| ISBN | : 0387216847 |
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.
| Author | : Malcolm W. Pownall |
| Publisher | : WCB/McGraw-Hill |
| Total Pages | : 467 |
| Release | : 1994 |
| Genre | : Mathematics |
| ISBN | : 9780697129086 |
This introductory textbook covers important mathematical concepts, including the language of mathematics sequences and series, limits and continuity, and a brief introduction to metric spaces.
| Author | : Christopher Heil |
| Publisher | : Springer |
| Total Pages | : 416 |
| Release | : 2019-07-20 |
| Genre | : Mathematics |
| ISBN | : 3030269035 |
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 | : Hugo D. Junghenn |
| Publisher | : CRC Press |
| Total Pages | : 613 |
| Release | : 2015-02-13 |
| Genre | : Mathematics |
| ISBN | : 148221928X |
A Course in Real Analysis provides a rigorous treatment of the foundations of differential and integral calculus at the advanced undergraduate level. The book's material has been extensively classroom tested in the author's two-semester undergraduate course on real analysis at The George Washington University.The first part of the text presents the
| Author | : William F. Trench |
| Publisher | : Prentice Hall |
| Total Pages | : 0 |
| Release | : 2003 |
| Genre | : Applied mathematics |
| ISBN | : 9780130457868 |
Using an extremely clear and informal approach, this book introduces readers to a rigorous understanding of mathematical analysis and presents challenging math concepts as clearly as possible. The real number system. Differential calculus of functions of one variable. Riemann integral functions of one variable. Integral calculus of real-valued functions. Metric Spaces. For those who want to gain an understanding of mathematical analysis and challenging mathematical concepts.
| Author | : John B. Conway |
| Publisher | : Cambridge University Press |
| Total Pages | : 357 |
| Release | : 2018 |
| Genre | : Mathematics |
| ISBN | : 1107173140 |
This concise text clearly presents the material needed for year-long analysis courses for advanced undergraduates or beginning graduates.
| Author | : George Pedrick |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 293 |
| Release | : 2012-09-10 |
| Genre | : Mathematics |
| ISBN | : 1441985549 |
This text on advanced calculus discusses such topics as number systems, the extreme value problem, continuous functions, differentiation, integration and infinite series. The reader will find the focus of attention shifted from the learning and applying of computational techniques to careful reasoning from hypothesis to conclusion. The book is intended both for a terminal course and as preparation for more advanced studies in mathematics, science, engineering and computation.
| Author | : Maxwell Rosenlicht |
| Publisher | : Courier Corporation |
| Total Pages | : 270 |
| Release | : 2012-05-04 |
| Genre | : Mathematics |
| ISBN | : 0486134687 |
Written for junior and senior undergraduates, this remarkably clear and accessible treatment covers set theory, the real number system, metric spaces, continuous functions, Riemann integration, multiple integrals, and more. 1968 edition.
