Fundamental Mathematical Analysis
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Fundamental Mathematical Analysis
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Author : Robert Magnus
language : en
Publisher: Springer Nature
Release Date : 2020-07-14
Fundamental Mathematical Analysis written by Robert Magnus and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-07-14 with Mathematics categories.
This textbook offers a comprehensive undergraduate course in real analysis in one variable. Taking the view that analysis can only be properly appreciated as a rigorous theory, the book recognises the difficulties that students experience when encountering this theory for the first time, carefully addressing them throughout. Historically, it was the precise description of real numbers and the correct definition of limit that placed analysis on a solid foundation. The book therefore begins with these crucial ideas and the fundamental notion of sequence. Infinite series are then introduced, followed by the key concept of continuity. These lay the groundwork for differential and integral calculus, which are carefully covered in the following chapters. Pointers for further study are included throughout the book, and for the more adventurous there is a selection of "nuggets", exciting topics not commonly discussed at this level. Examples of nuggets include Newton's method, the irrationality of π, Bernoulli numbers, and the Gamma function. Based on decades of teaching experience, this book is written with the undergraduate student in mind. A large number of exercises, many with hints, provide the practice necessary for learning, while the included "nuggets" provide opportunities to deepen understanding and broaden horizons.
The Fundamentals Of Mathematical Analysis
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Author : G. M. Fikhtengol'ts
language : en
Publisher: Elsevier
Release Date : 1965-01-01
The Fundamentals Of Mathematical Analysis written by G. M. Fikhtengol'ts and has been published by Elsevier this book supported file pdf, txt, epub, kindle and other format this book has been release on 1965-01-01 with Mathematics categories.
The Fundamentals of Mathematical Analysis, Volume 2 focuses on the fundamental concepts of mathematical analysis. This book discusses the theorems on the comparison of series, condition for uniform convergence, and application of the fundamental formula of integral calculus. The differentiation under the integral sign, Lagrange's method of undetermined multipliers, and definition of curvilinear integrals of the second kind are also elaborated. This text likewise covers the transformation of plane domains, case of a piece-wise smooth surface, and problem of calculating the mass of a solid. Other topics include the flow of a vector through a surface, determination of coefficients by the Euler-Fourier method, and generalized equation of closure. This volume is a good reference for students and researchers conducting work on mathematical analysis.
Mathematical Analysis Fundamentals
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Author : Agamirza Bashirov
language : en
Publisher: Academic Press
Release Date : 2014-03-27
Mathematical Analysis Fundamentals written by Agamirza Bashirov and has been published by Academic Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-03-27 with Mathematics categories.
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
Foundations Of Mathematical Analysis
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Author : Saminathan Ponnusamy
language : en
Publisher: Springer Science & Business Media
Release Date : 2011-12-16
Foundations Of Mathematical Analysis written by Saminathan Ponnusamy and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-12-16 with Mathematics categories.
Mathematical analysis is fundamental to the undergraduate curriculum not only because it is the stepping stone for the study of advanced analysis, but also because of its applications to other branches of mathematics, physics, and engineering at both the undergraduate and graduate levels. This self-contained textbook consists of eleven chapters, which are further divided into sections and subsections. Each section includes a careful selection of special topics covered that will serve to illustrate the scope and power of various methods in real analysis. The exposition is developed with thorough explanations, motivating examples, exercises, and illustrations conveying geometric intuition in a pleasant and informal style to help readers grasp difficult concepts. Foundations of Mathematical Analysis is intended for undergraduate students and beginning graduate students interested in a fundamental introduction to the subject. It may be used in the classroom or as a self-study guide without any required prerequisites.
Fundamentals Of Mathematical Analysis
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Author : Adel N. Boules
language : en
Publisher:
Release Date : 2021
Fundamentals Of Mathematical Analysis written by Adel N. Boules and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021 with Mathematics categories.
"A beginning graduate textbook on 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. Instructors can choose material from this part as their students' background warrants. Chapter 4 is the spine of the book and is essential for an effective reading of the rest of the book. It is an extensive study of metric spaces, including the core topics of completeness, compactness, and function spaces, with a good number of applications. The remaining 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. The entire book is suitable for a two-semester course on analysis, and material can be chosen to design one-semester courses on topology, real analysis, or functional analysis. The book is designed as an accessible classical introduction to the subject, 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."--Provided by publisher.
Mathematical Analysis I
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Author : Vladimir A. Zorich
language : en
Publisher: Springer Science & Business Media
Release Date : 2004-01-22
Mathematical Analysis I written by Vladimir A. Zorich and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2004-01-22 with Mathematics categories.
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.
Fundamental Concepts In Modern Analysis
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Author : Vagn Lundsgaard Hansen
language : en
Publisher: World Scientific
Release Date : 1999
Fundamental Concepts In Modern Analysis written by Vagn Lundsgaard Hansen and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 1999 with Science categories.
Many advanced mathematical disciplines, such as dynamical systems, calculus of variations, differential geometry and the theory of Lie groups, have a common foundation in general topology and calculus in normed vector spaces. In this book, mathematically inclined engineering students are offered an opportunity to go into some depth with fundamental notions from mathematical analysis that are not only important from a mathematical point of view but also occur frequently in the more theoretical parts of the engineering sciences. The book should also appeal to university students in mathematics and in the physical sciences.
Basic Real Analysis
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Author : Houshang H. Sohrab
language : en
Publisher: Springer Science & Business Media
Release Date : 2011-06-27
Basic Real Analysis written by Houshang H. Sohrab and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-06-27 with Mathematics categories.
One of the bedrocks of any mathematics education, the study of real analysis introduces students both to mathematical rigor and to the deep theorems and counterexamples that arise from such rigor: for instance, the construction of number systems, the Cantor Set, the Weierstrass nowhere differentiable function, and the Weierstrass approximation theorem. Basic Real Analysis is a modern, systematic text that presents the fundamentals and touchstone results of the subject in full rigor, but in a style that requires little prior familiarity with proofs or mathematical language. Key features include: * A broad view of mathematics throughout the book * Treatment of all concepts for real numbers first, with extensions to metric spaces later, in a separate chapter * Elegant proofs * Excellent choice of topics * Numerous examples and exercises to enforce methodology; exercises integrated into the main text, as well as at the end of each chapter * Emphasis on monotone functions throughout * Good development of integration theory * Special topics on Banach and Hilbert spaces and Fourier series, often not included in many courses on real analysis * Solid preparation for deeper study of functional analysis * Chapter on elementary probability * Comprehensive bibliography and index * Solutions manual available to instructors upon request By covering all the basics and developing rigor simultaneously, this introduction to real analysis is ideal for senior undergraduates and beginning graduate students, both as a classroom text or for self-study. With its wide range of topics and its view of real analysis in a larger context, the book will be appropriate for more advanced readers as well.
Mathematical Analysis
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Author : Bernd S. W. Schröder
language : en
Publisher: John Wiley & Sons
Release Date : 2008-01-28
Mathematical Analysis written by Bernd S. W. Schröder and has been published by John Wiley & Sons this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008-01-28 with Mathematics categories.
A self-contained introduction to the fundamentals of mathematical analysis Mathematical Analysis: A Concise Introduction presents the foundations of analysis and illustrates its role in mathematics. By focusing on the essentials, reinforcing learning through exercises, and featuring a unique "learn by doing" approach, the book develops the reader's proof writing skills and establishes fundamental comprehension of analysis that is essential for further exploration of pure and applied mathematics. This book is directly applicable to areas such as differential equations, probability theory, numerical analysis, differential geometry, and functional analysis. Mathematical Analysis is composed of three parts: ?Part One presents the analysis of functions of one variable, including sequences, continuity, differentiation, Riemann integration, series, and the Lebesgue integral. A detailed explanation of proof writing is provided with specific attention devoted to standard proof techniques. To facilitate an efficient transition to more abstract settings, the results for single variable functions are proved using methods that translate to metric spaces. ?Part Two explores the more abstract counterparts of the concepts outlined earlier in the text. The reader is introduced to the fundamental spaces of analysis, including Lp spaces, and the book successfully details how appropriate definitions of integration, continuity, and differentiation lead to a powerful and widely applicable foundation for further study of applied mathematics. The interrelation between measure theory, topology, and differentiation is then examined in the proof of the Multidimensional Substitution Formula. Further areas of coverage in this section include manifolds, Stokes' Theorem, Hilbert spaces, the convergence of Fourier series, and Riesz' Representation Theorem. ?Part Three provides an overview of the motivations for analysis as well as its applications in various subjects. A special focus on ordinary and partial differential equations presents some theoretical and practical challenges that exist in these areas. Topical coverage includes Navier-Stokes equations and the finite element method. Mathematical Analysis: A Concise Introduction includes an extensive index and over 900 exercises ranging in level of difficulty, from conceptual questions and adaptations of proofs to proofs with and without hints. These opportunities for reinforcement, along with the overall concise and well-organized treatment of analysis, make this book essential for readers in upper-undergraduate or beginning graduate mathematics courses who would like to build a solid foundation in analysis for further work in all analysis-based branches of mathematics.
Fundamentals Of Real Analysis
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Author : Sterling K. Berberian
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-03-15
Fundamentals Of Real Analysis written by Sterling K. Berberian and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-03-15 with Mathematics categories.
"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