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| Author | : Charles Walmsley |
| Publisher | : |
| Total Pages | : 316 |
| Release | : 1926 |
| Genre | : History |
| ISBN | : |
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 | : William R. Parzynski |
| Publisher | : McGraw-Hill Companies |
| Total Pages | : 376 |
| Release | : 1982 |
| Genre | : Mathematics |
| ISBN | : |
| Author | : Christopher Heil |
| Publisher | : Springer |
| Total Pages | : 386 |
| 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 | : 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 Walmsley |
| Publisher | : |
| Total Pages | : 293 |
| Release | : 1926 |
| Genre | : Calculus |
| ISBN | : |
| Author | : Donald Yau |
| Publisher | : World Scientific |
| Total Pages | : 206 |
| Release | : 2013 |
| Genre | : Mathematics |
| ISBN | : 9814417858 |
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.
| Author | : Piotr Mikusinski |
| Publisher | : World Scientific Publishing Company |
| Total Pages | : 318 |
| Release | : 2017-02-17 |
| Genre | : Mathematics |
| ISBN | : 9813202637 |
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 | : |
| Total Pages | : 616 |
| Release | : 1996-01-30 |
| Genre | : Mathematics |
| ISBN | : 9788173190643 |
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 | : 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 | : J. C. Burkill |
| Publisher | : Cambridge University Press |
| Total Pages | : 536 |
| Release | : 2002-10-24 |
| Genre | : Mathematics |
| ISBN | : 9780521523431 |
A classic calculus text reissued in the Cambridge Mathematical Library. Clear and logical, with many examples.
