Fundamentals Of Real Analysis PDF Download
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| Author | : Sterling K. Berberian |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 504 |
| Release | : 2013-03-15 |
| Genre | : Mathematics |
| ISBN | : 9780387984803 |
Download Fundamentals of Real Analysis Book in PDF, ePub and Kindle
"This book is very well organized and clearly written and contains an adequate supply of exercises. If one is comfortable with the choice of topics in the book, it would be a good candidate for a text in a graduate real analysis course." -- MATHEMATICAL REVIEWS
| Author | : Michael C. Reed |
| Publisher | : John Wiley & Sons |
| Total Pages | : 440 |
| Release | : 1998 |
| Genre | : Mathematics |
| ISBN | : |
Download Fundamental Ideas of Analysis Book in PDF, ePub and Kindle
The ideas and methods of mathematics, long central to the physical sciences, now play an increasingly important role in a wide variety of disciplines. Analysis provides theorems that prove that results are true and provides techniques to estimate the errors in approximate calculations. The ideas and methods of analysis play a fundamental role in ordinary differential equations, probability theory, differential geometry, numerical analysis, complex analysis, partial differential equations, as well as in most areas of applied mathematics.
| Author | : Richard Johnsonbaugh |
| Publisher | : Courier Corporation |
| Total Pages | : 450 |
| Release | : 2012-09-11 |
| Genre | : Mathematics |
| ISBN | : 0486134776 |
Download Foundations of Mathematical Analysis Book in PDF, ePub and Kindle
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.
| Author | : Charles H.C. Little |
| Publisher | : Springer |
| Total Pages | : 483 |
| Release | : 2015-05-28 |
| Genre | : Mathematics |
| ISBN | : 1493926519 |
Download Real Analysis via Sequences and Series Book in PDF, ePub and Kindle
This text gives a rigorous treatment of the foundations of calculus. In contrast to more traditional approaches, infinite sequences and series are placed at the forefront. The approach taken has not only the merit of simplicity, but students are well placed to understand and appreciate more sophisticated concepts in advanced mathematics. The authors mitigate potential difficulties in mastering the material by motivating definitions, results and proofs. Simple examples are provided to illustrate new material and exercises are included at the end of most sections. Noteworthy topics include: an extensive discussion of convergence tests for infinite series, Wallis’s formula and Stirling’s formula, proofs of the irrationality of π and e and a treatment of Newton’s method as a special instance of finding fixed points of iterated functions.
| Author | : Steven G. Krantz |
| Publisher | : CRC Press |
| Total Pages | : 306 |
| Release | : 2016-12-12 |
| Genre | : Mathematics |
| ISBN | : 1498777708 |
Download Real Analysis and Foundations, Fourth Edition Book in PDF, ePub and Kindle
A Readable yet Rigorous Approach to an Essential Part of Mathematical Thinking Back by popular demand, Real Analysis and Foundations, Third Edition bridges the gap between classic theoretical texts and less rigorous ones, providing a smooth transition from logic and proofs to real analysis. Along with the basic material, the text covers Riemann-Stieltjes integrals, Fourier analysis, metric spaces and applications, and differential equations. New to the Third Edition Offering a more streamlined presentation, this edition moves elementary number systems and set theory and logic to appendices and removes the material on wavelet theory, measure theory, differential forms, and the method of characteristics. It also adds a chapter on normed linear spaces and includes more examples and varying levels of exercises. Extensive Examples and Thorough Explanations Cultivate an In-Depth Understanding This best-selling book continues to give students a solid foundation in mathematical analysis and its applications. It prepares them for further exploration of measure theory, functional analysis, harmonic analysis, and beyond.
| Author | : Michael Field |
| Publisher | : Springer |
| Total Pages | : 462 |
| Release | : 2017-11-06 |
| Genre | : Mathematics |
| ISBN | : 331967546X |
Download Essential Real Analysis Book in PDF, ePub and Kindle
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.
| Author | : James Foran |
| Publisher | : CRC Press |
| Total Pages | : 504 |
| Release | : 1991-01-07 |
| Genre | : Mathematics |
| ISBN | : 9780824784539 |
Download Fundamentals of Real Analysis Book in PDF, ePub and Kindle
Guides students from simple aspects of set theory to more complex structures. Based on a two-semester course in real analysis, this textbook explains fundamentals of the theory of functions of a real variable, including subsets of the line, the theory of measure, the Lebesgue integral and its relati
| Author | : Adel N. Boules |
| Publisher | : Oxford University Press, USA |
| Total Pages | : 481 |
| Release | : 2021-03-09 |
| Genre | : Mathematics |
| ISBN | : 0198868782 |
Download Fundamentals of Mathematical Analysis Book in PDF, ePub and Kindle
Fundamentals of Mathematical Analysis explores real and functional analysis with a substantial component on topology. The three leading chapters furnish background information on the real and complex number fields, a concise introduction to set theory, and a rigorous treatment of vector spaces. Fundamentals of Mathematical Analysis is an extensive study of metric spaces, including the core topics of completeness, compactness and function spaces, with a good number of applications. The later chapters consist of an introduction to general topology, a classical treatment of Banach and Hilbert spaces, the elements of operator theory, and a deep account of measure and integration theories. Several courses can be based on the book. This book is suitable for a two-semester course on analysis, and material can be chosen to design one-semester courses on topology or real analysis. It is designed as an accessible classical introduction to the subject and aims to achieve excellent breadth and depth and contains an abundance of examples and exercises. The topics are carefully sequenced, the proofs are detailed, and the writing style is clear and concise. The only prerequisites assumed are a thorough understanding of undergraduate real analysis and linear algebra, and a degree of mathematical maturity.
| Author | : Agamirza Bashirov |
| Publisher | : Academic Press |
| Total Pages | : 363 |
| Release | : 2014-03-27 |
| Genre | : Mathematics |
| ISBN | : 0128010509 |
Download Mathematical Analysis Fundamentals Book in PDF, ePub and Kindle
The author’s goal is a rigorous presentation of the fundamentals of analysis, starting from elementary level and moving to the advanced coursework. The curriculum of all mathematics (pure or applied) and physics programs include a compulsory course in mathematical analysis. This book will serve as can serve a main textbook of such (one semester) courses. The book can also serve as additional reading for such courses as real analysis, functional analysis, harmonic analysis etc. For non-math major students requiring math beyond calculus, this is a more friendly approach than many math-centric options. Friendly and well-rounded presentation of pre-analysis topics such as sets, proof techniques and systems of numbers Deeper discussion of the basic concept of convergence for the system of real numbers, pointing out its specific features, and for metric spaces Presentation of Riemann integration and its place in the whole integration theory for single variable, including the Kurzweil-Henstock integration Elements of multiplicative calculus aiming to demonstrate the non-absoluteness of Newtonian calculus
| Author | : Paul J. Sally (Jr.) |
| Publisher | : American Mathematical Soc. |
| Total Pages | : 379 |
| Release | : 2013 |
| Genre | : Mathematics |
| ISBN | : 0821891413 |
Download Fundamentals of Mathematical Analysis Book in PDF, ePub and Kindle
This is a textbook for a course in Honors Analysis (for freshman/sophomore undergraduates) or Real Analysis (for junior/senior undergraduates) or Analysis-I (beginning graduates). It is intended for students who completed a course in ``AP Calculus'', possibly followed by a routine course in multivariable calculus and a computational course in linear algebra. There are three features that distinguish this book from many other books of a similar nature and which are important for the use of this book as a text. The first, and most important, feature is the collection of exercises. These are spread throughout the chapters and should be regarded as an essential component of the student's learning. Some of these exercises comprise a routine follow-up to the material, while others challenge the student's understanding more deeply. The second feature is the set of independent projects presented at the end of each chapter. These projects supplement the content studied in their respective chapters. They can be used to expand the student's knowledge and understanding or as an opportunity to conduct a seminar in Inquiry Based Learning in which the students present the material to their class. The third really important feature is a series of challenge problems that increase in impossibility as the chapters progress.
