Basic Analysis Iii

Author : James K. Peterson
Publisher : CRC Press
ISBN 13 : 1351679309
Total Pages : 469 pages
Book Rating : 4.05/5 ( download)

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Download or read book Basic Analysis III written by James K. Peterson and published by CRC Press. This book was released on 2020-07-19 with total page 469 pages. Available in PDF, EPUB and Kindle. Book excerpt: Basic Analysis III: Mappings on Infinite Dimensional Spaces is intended as a first course in abstract linear analysis. This textbook cover metric spaces, normed linear spaces and inner product spaces, along with many other deeper abstract ideas such a completeness, operators and dual spaces. These topics act as an important tool in the development of a mathematically trained scientist. Feature: Can be used as a traditional textbook as well as for self-study Suitable for undergraduates in mathematics and associated disciplines Emphasizes learning how to understand the consequences of assumptions using a variety of tools to provide the proofs of propositions

Author : Jiri Lebl
Publisher : Createspace Independent Publishing Platform
ISBN 13 : 9781718862401
Total Pages : 282 pages
Book Rating : 4.07/5 ( download)

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Download or read book Basic Analysis I written by Jiri Lebl and published by Createspace Independent Publishing Platform. This book was released on 2018-05-08 with total page 282 pages. Available in PDF, EPUB and Kindle. Book excerpt: Version 5.0. A first course in rigorous mathematical analysis. Covers the real number system, sequences and series, continuous functions, the derivative, the Riemann integral, sequences of functions, and metric spaces. Originally developed to teach Math 444 at University of Illinois at Urbana-Champaign and later enhanced for Math 521 at University of Wisconsin-Madison and Math 4143 at Oklahoma State University. The first volume is either a stand-alone one-semester course or the first semester of a year-long course together with the second volume. It can be used anywhere from a semester early introduction to analysis for undergraduates (especially chapters 1-5) to a year-long course for advanced undergraduates and masters-level students. See http://www.jirka.org/ra/ Table of Contents (of this volume I): Introduction 1. Real Numbers 2. Sequences and Series 3. Continuous Functions 4. The Derivative 5. The Riemann Integral 6. Sequences of Functions 7. Metric Spaces This first volume contains what used to be the entire book "Basic Analysis" before edition 5, that is chapters 1-7. Second volume contains chapters on multidimensional differential and integral calculus and further topics on approximation of functions.

Author : Jiri Lebl
Publisher : Createspace Independent Publishing Platform
ISBN 13 : 9781718865488
Total Pages : 196 pages
Book Rating : 4.81/5 ( download)

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Download or read book Basic Analysis II written by Jiri Lebl and published by Createspace Independent Publishing Platform. This book was released on 2018-05-09 with total page 196 pages. Available in PDF, EPUB and Kindle. Book excerpt: Version 2.0. The second volume of Basic Analysis, a first course in mathematical analysis. This volume is the second semester material for a year-long sequence for advanced undergraduates or masters level students. This volume started with notes for Math 522 at University of Wisconsin-Madison, and then was heavily revised and modified for teaching Math 4153/5053 at Oklahoma State University. It covers differential calculus in several variables, line integrals, multivariable Riemann integral including a basic case of Green's Theorem, and topics on power series, Arzelà-Ascoli, Stone-Weierstrass, and Fourier Series. See http://www.jirka.org/ra/ Table of Contents (of this volume II): 8. Several Variables and Partial Derivatives 9. One Dimensional Integrals in Several Variables 10. Multivariable Integral 11. Functions as Limits

Author : James K. Peterson
Publisher : CRC Press
ISBN 13 : 1351679333
Total Pages : 530 pages
Book Rating : 4.36/5 ( download)

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Download or read book Basic Analysis II written by James K. Peterson and published by CRC Press. This book was released on 2020-07-19 with total page 530 pages. Available in PDF, EPUB and Kindle. Book excerpt: Basic Analysis II: A Modern Calculus in Many Variables focuses on differentiation in Rn and important concepts about mappings from Rn to Rm, such as the inverse and implicit function theorem and change of variable formulae for multidimensional integration. These topics converge nicely with many other important applied and theoretical areas which are no longer covered in mathematical science curricula. Although it follows on from the preceding volume, this is a self-contained book, accessible to undergraduates with a minimal grounding in analysis. Features Can be used as a traditional textbook as well as for self-study Suitable for undergraduates in mathematics and associated disciplines Emphasises learning how to understand the consequences of assumptions using a variety of tools to provide the proofs of propositions

Author : James K. Peterson
Publisher : CRC Press
ISBN 13 : 1351679457
Total Pages : 595 pages
Book Rating : 4.59/5 ( download)

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Download or read book Basic Analysis I written by James K. Peterson and published by CRC Press. This book was released on 2020-05-13 with total page 595 pages. Available in PDF, EPUB and Kindle. Book excerpt: Basic Analysis I: Functions of a Real Variable is designed for students who have completed the usual calculus and ordinary differential equation sequence and a basic course in linear algebra. This is a critical course in the use of abstraction, but is just first volume in a sequence of courses which prepare students to become practicing scientists. This book is written with the aim of balancing the theory and abstraction with clear explanations and arguments, so that students who are from a variety of different areas can follow this text and use it profitably for self-study. It can also be used as a supplementary text for anyone whose work requires that they begin to assimilate more abstract mathematical concepts as part of their professional growth. Features Can be used as a traditional textbook as well as for self-study Suitable for undergraduate mathematics students, or for those in other disciplines requiring a solid grounding in abstraction Emphasises learning how to understand the consequences of assumptions using a variety of tools to provide the proofs of propositions

Author : JAMES K. PETERSON
Publisher : CRC Press
ISBN 13 : 9781138055148
Total Pages : 2688 pages
Book Rating : 4.4X/5 ( download)

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Download or read book Basic Analysis written by JAMES K. PETERSON and published by CRC Press. This book was released on 2021-05-25 with total page 2688 pages. Available in PDF, EPUB and Kindle. Book excerpt: Basic Analysis: Volumes I-V is written with the aim of balancing theory and abstraction with clear explanations and arguments, so that students and researchers alike who are from a variety of different areas can follow this text and use it profitably for self-study. The first volume is designed for students who have completed the usual calculus and ordinary differential equation sequence and a basic course in linear algebra. This is a critical course in the use of abstraction, but is just first volume in a sequence of courses which prepare students to become practicing scientists. The second volume focuses on differentiation in n-dimensions and important concepts about mappings between finite dimensional Euclidean spaces, such as the inverse and implicit function theorem and change of variable formulae for multidimensional integration. These important topics provide background in important applied and theoretical areas which are no longer covered in mathematical science curricula. Although it follows on from the preceding volume, this is a self-contained book, accessible to undergraduates with a standard course in undergraduate analysis. The third volume is intended as a first course in abstract linear analysis. This textbook covers metric spaces, normed linear spaces and inner product spaces, along with many other deeper abstract ideas such a completeness, operators and dual spaces. These topics act as an important tool in the development of a mathematically trained scientist. The fourth volume introduces students to concepts from measure theory and continues their training in the abstract way of looking at the world. This is a most important skill to have when your life's work will involve quantitative modeling to gain insight into the real world. This text generalizes the notion of integration to a very abstract setting in a variety of ways. We generalize the notion of the length of an interval to the measure of a set and learn how to construct the usual ideas from integration using measures. We discuss carefully the many notions of convergence that measure theory provides. The final volume introduces graduate students in science with concepts from topology and functional analysis, both linear and nonlinear. It is the fifth book in a series designed to train interested readers how to think properly using mathematical abstractions, and how to use the tools of mathematical analysis in applications. It is important to realize that the most difficult part of applying mathematical reasoning to a new problem domain is choosing the underlying mathematical framework to use on the problem. Once that choice is made, we have many tools we can use to solve the problem. However, a different choice would open up avenues of analysis from a different, perhaps more productive perspective. In this volume, the nature of these critical choices is discussed using applications involving the immune system and cognition. Features: Can be used as a supplementary text for anyone whose work requires that they begin to assimilate more abstract mathematical concepts as part of their professional growth Function as a traditional textbook as well as a resource for self-study Suitable for mathematics students and for those in other disciplines such as biology, physics, and economics and others requiring a careful and solid grounding in the use of abstraction in problem solving Emphasizes learning how to understand the consequences of the underlying assumptions used in building a model Regularly uses computation tools to help understand abstract concepts.

Author : Anthony W. Knapp
Publisher : Springer Science & Business Media
ISBN 13 : 0817644415
Total Pages : 671 pages
Book Rating : 4.13/5 ( download)

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Download or read book Basic Real Analysis written by Anthony W. Knapp and published by Springer Science & Business Media. This book was released on 2007-10-04 with total page 671 pages. Available in PDF, EPUB and Kindle. Book excerpt: Systematically develop the concepts and tools that are vital to every mathematician, whether pure or applied, aspiring or established A comprehensive treatment with a global view of the subject, emphasizing the connections between real analysis and other branches of mathematics Included throughout are many examples and hundreds of problems, and a separate 55-page section gives hints or complete solutions for most.

Author : Barry Simon
Publisher : American Mathematical Soc.
ISBN 13 : 1470410990
Total Pages : 789 pages
Book Rating : 4.95/5 ( download)

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Download or read book Real Analysis: A Comprehensive Course in Analysis, Part 1 written by Barry Simon and published by American Mathematical Soc.. This book was released on 2015-11-02 with total page 789 pages. Available in PDF, EPUB and Kindle. Book excerpt: A Comprehensive Course in Analysis by Poincaré Prize winner Barry Simon is a five-volume set that can serve as a graduate-level analysis textbook with a lot of additional bonus information, including hundreds of problems and numerous notes that extend the text and provide important historical background. Depth and breadth of exposition make this set a valuable reference source for almost all areas of classical analysis. Part 1 is devoted to real analysis. From one point of view, it presents the infinitesimal calculus of the twentieth century with the ultimate integral calculus (measure theory) and the ultimate differential calculus (distribution theory). From another, it shows the triumph of abstract spaces: topological spaces, Banach and Hilbert spaces, measure spaces, Riesz spaces, Polish spaces, locally convex spaces, Fréchet spaces, Schwartz space, and spaces. Finally it is the study of big techniques, including the Fourier series and transform, dual spaces, the Baire category, fixed point theorems, probability ideas, and Hausdorff dimension. Applications include the constructions of nowhere differentiable functions, Brownian motion, space-filling curves, solutions of the moment problem, Haar measure, and equilibrium measures in potential theory.

Author : James K. Peterson
Publisher : CRC Press
ISBN 13 : 1351679155
Total Pages : 586 pages
Book Rating : 4.52/5 ( download)

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Download or read book Basic Analysis V written by James K. Peterson and published by CRC Press. This book was released on 2021-08-20 with total page 586 pages. Available in PDF, EPUB and Kindle. Book excerpt: Basic Analysis V: Functional Analysis and Topology introduces graduate students in science to concepts from topology and functional analysis, both linear and nonlinear. It is the fifth book in a series designed to train interested readers how to think properly using mathematical abstractions, and how to use the tools of mathematical analysis in applications. It is important to realize that the most difficult part of applying mathematical reasoning to a new problem domain is choosing the underlying mathematical framework to use on the problem. Once that choice is made, we have many tools we can use to solve the problem. However, a different choice would open up avenues of analysis from a different, perhaps more productive, perspective. In this volume, the nature of these critical choices is discussed using applications involving the immune system and cognition. Features Develops a proof of the Jordan Canonical form to show some basic ideas in algebraic topology Provides a thorough treatment of topological spaces, finishing with the Krein–Milman theorem Discusses topological degree theory (Brouwer, Leray–Schauder, and Coincidence) Carefully develops manifolds and functions on manifolds ending with Riemannian metrics Suitable for advanced students in mathematics and associated disciplines Can be used as a traditional textbook as well as for self-study Author James K. Peterson is an Emeritus Professor at the School of Mathematical and Statistical Sciences, Clemson University. He tries hard to build interesting models of complex phenomena using a blend of mathematics, computation, and science. To this end, he has written four books on how to teach such things to biologists and cognitive scientists. These books grew out of his Calculus for Biologists courses offered to the biology majors from 2007 to 2015. He has taught the analysis courses since he started teaching both at Clemson and at his previous post at Michigan Technological University. In between, he spent time as a senior engineer in various aerospace firms and even did a short stint in a software development company. The problems he was exposed to were very hard, and not amenable to solution using just one approach. Using tools from many branches of mathematics, from many types of computational languages, and from first-principles analysis of natural phenomena was absolutely essential to make progress. In both mathematical and applied areas, students often need to use advanced mathematics tools they have not learned properly. So, he has recently written a series of five books on mathematical analysis to help researchers with the problem of learning new things after they have earned their degrees and are practicing scientists. Along the way, he has also written papers in immunology, cognitive science, and neural network technology, in addition to having grants from the NSF, NASA, and the US Army. He also likes to paint, build furniture, and write stories.

Author : Vladimir A. Zorich
Publisher : Springer Science & Business Media
ISBN 13 : 9783540403869
Total Pages : 610 pages
Book Rating : 4.68/5 ( download)

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Download or read book Mathematical Analysis I written by Vladimir A. Zorich and published by Springer Science & Business Media. This book was released on 2004-01-22 with total page 610 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.