Real Mathematical Analysis PDF Download
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| Author | : Charles Chapman Pugh |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 445 |
| Release | : 2013-03-19 |
| Genre | : Mathematics |
| ISBN | : 0387216847 |
Download Real Mathematical Analysis Book in PDF, ePub and Kindle
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 | : Andrew Browder |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 348 |
| Release | : 2012-12-06 |
| Genre | : Mathematics |
| ISBN | : 1461207150 |
Download Mathematical Analysis Book in PDF, ePub and Kindle
Among the traditional purposes of such an introductory course is the training of a student in the conventions of pure mathematics: acquiring a feeling for what is considered a proof, and supplying literate written arguments to support mathematical propositions. To this extent, more than one proof is included for a theorem - where this is considered beneficial - so as to stimulate the students' reasoning for alternate approaches and ideas. The second half of this book, and consequently the second semester, covers differentiation and integration, as well as the connection between these concepts, as displayed in the general theorem of Stokes. Also included are some beautiful applications of this theory, such as Brouwer's fixed point theorem, and the Dirichlet principle for harmonic functions. Throughout, reference is made to earlier sections, so as to reinforce the main ideas by repetition. Unique in its applications to some topics not usually covered at this level.
| Author | : Charles H.C. Little |
| Publisher | : Springer |
| Total Pages | : 476 |
| 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 | : 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 | : Kenneth R. Davidson |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 523 |
| Release | : 2009-10-13 |
| Genre | : Mathematics |
| ISBN | : 0387980989 |
Download Real Analysis and Applications Book in PDF, ePub and Kindle
This new approach to real analysis stresses the use of the subject with respect to applications, i.e., how the principles and theory of real analysis can be applied in a variety of settings in subjects ranging from Fourier series and polynomial approximation to discrete dynamical systems and nonlinear optimization. Users will be prepared for more intensive work in each topic through these applications and their accompanying exercises. This book is appropriate for math enthusiasts with a prior knowledge of both calculus and linear algebra.
| Author | : Gerald B. Folland |
| Publisher | : John Wiley & Sons |
| Total Pages | : 368 |
| Release | : 2013-06-11 |
| Genre | : Mathematics |
| ISBN | : 1118626397 |
Download Real Analysis Book in PDF, ePub and Kindle
An in-depth look at real analysis and its applications-now expanded and revised. This new edition of the widely used analysis book continues to cover real analysis in greater detail and at a more advanced level than most books on the subject. Encompassing several subjects that underlie much of modern analysis, the book focuses on measure and integration theory, point set topology, and the basics of functional analysis. It illustrates the use of the general theories and introduces readers to other branches of analysis such as Fourier analysis, distribution theory, and probability theory. This edition is bolstered in content as well as in scope-extending its usefulness to students outside of pure analysis as well as those interested in dynamical systems. The numerous exercises, extensive bibliography, and review chapter on sets and metric spaces make Real Analysis: Modern Techniques and Their Applications, Second Edition invaluable for students in graduate-level analysis courses. New features include: * Revised material on the n-dimensional Lebesgue integral. * An improved proof of Tychonoff's theorem. * Expanded material on Fourier analysis. * A newly written chapter devoted to distributions and differential equations. * Updated material on Hausdorff dimension and fractal dimension.
| Author | : Vladimir A. Zorich |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 610 |
| Release | : 2004-01-22 |
| Genre | : Mathematics |
| ISBN | : 9783540403869 |
Download Mathematical Analysis I Book in PDF, ePub and Kindle
This work by Zorich on Mathematical Analysis constitutes a thorough first course in real analysis, leading from the most elementary facts about real numbers to such advanced topics as differential forms on manifolds, asymptotic methods, Fourier, Laplace, and Legendre transforms, and elliptic functions.
| Author | : Stephen Abbott |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 269 |
| Release | : 2012-12-06 |
| Genre | : Mathematics |
| ISBN | : 0387215069 |
Download Understanding Analysis Book in PDF, ePub and Kindle
This elementary presentation exposes readers to both the process of rigor and the rewards inherent in taking an axiomatic approach to the study of functions of a real variable. The aim is to challenge and improve mathematical intuition rather than to verify it. The philosophy of this book is to focus attention on questions which give analysis its inherent fascination. Each chapter begins with the discussion of some motivating examples and concludes with a series of questions.
| Author | : William F. Trench |
| Publisher | : Prentice Hall |
| Total Pages | : 0 |
| Release | : 2003 |
| Genre | : Applied mathematics |
| ISBN | : 9780130457868 |
Download Introduction to Real Analysis Book in PDF, ePub and Kindle
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 | : N. L. Carothers |
| Publisher | : Cambridge University Press |
| Total Pages | : 420 |
| Release | : 2000-08-15 |
| Genre | : Mathematics |
| ISBN | : 9780521497565 |
Download Real Analysis Book in PDF, ePub and Kindle
A text for a first graduate course in real analysis for students in pure and applied mathematics, statistics, education, engineering, and economics.
