Mathematical Analysis Fundamentals Book

Mathematical Analysis Fundamentals


  • Author : Agamirza Bashirov
  • Publisher : Academic Press
  • Release Date : 2014-03-27
  • Genre: Mathematics
  • Pages : 362
  • ISBN 10 : 9780128010501

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Mathematical Analysis Fundamentals Excerpt :

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.

Fundamental Mathematical Analysis Book

Fundamental Mathematical Analysis


  • Author : Robert Magnus
  • Publisher : Springer Nature
  • Release Date : 2020-07-14
  • Genre: Mathematics
  • Pages : 433
  • ISBN 10 : 9783030463212

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Fundamental Mathematical Analysis Excerpt :

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.

Fundamentals of Mathematical Analysis Book

Fundamentals of Mathematical Analysis


  • Author : Adel N. Boules
  • Publisher : Oxford University Press, USA
  • Release Date : 2021-03-09
  • Genre: Mathematics
  • Pages : 481
  • ISBN 10 : 9780198868781

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Fundamentals of Mathematical Analysis Excerpt :

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.

Fundamentals of Mathematical Analysis Book

Fundamentals of Mathematical Analysis


  • Author : Paul J. Sally (Jr.)
  • Publisher : American Mathematical Soc.
  • Release Date : 2013
  • Genre: Mathematics
  • Pages : 379
  • ISBN 10 : 9780821891414

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Fundamentals of Mathematical Analysis Excerpt :

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.

Fundamentals of Mathematical Analysis Book

Fundamentals of Mathematical Analysis


  • Author : Rod Haggarty
  • Publisher : Addison-Wesley Longman
  • Release Date : 1993-01-01
  • Genre: Calculus
  • Pages : 332
  • ISBN 10 : 0201631970

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Fundamentals of Mathematical Analysis Excerpt :

Providing students with an introduction to the fundamentals of analysis, this book continues to present the fundamental concepts of analysis in as painless a manner as possible. To achieve this aim, the second edition has made many improvements in exposition.

Fundamentals of Real Analysis Book
Score: 3.5
From 3 Ratings

Fundamentals of Real Analysis


  • Author : Sterling K. Berberian
  • Publisher : Springer Science & Business Media
  • Release Date : 2013-03-15
  • Genre: Mathematics
  • Pages : 504
  • ISBN 10 : 0387984801

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Fundamentals of Real Analysis Excerpt :

"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

Mathematical Analysis Fundamentals Book

Mathematical Analysis Fundamentals


  • Author : Agamirza Bashirov
  • Publisher : Elsevier
  • Release Date : 2016-07-14
  • Genre: Mathematics
  • Pages : 364
  • ISBN 10 : 0128102691

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Mathematical Analysis Fundamentals Excerpt :

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."

Fundamentals of Functional Analysis Book

Fundamentals of Functional Analysis


  • Author : Semën Samsonovich Kutateladze
  • Publisher : Springer Science & Business Media
  • Release Date : 2013-03-09
  • Genre: Mathematics
  • Pages : 289
  • ISBN 10 : 9789401587556

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Fundamentals of Functional Analysis Excerpt :

to the English Translation This is a concise guide to basic sections of modern functional analysis. Included are such topics as the principles of Banach and Hilbert spaces, the theory of multinormed and uniform spaces, the Riesz-Dunford holomorphic functional calculus, the Fredholm index theory, convex analysis and duality theory for locally convex spaces. With standard provisos the presentation is self-contained, exposing about a h- dred famous "named" theorems furnished with complete proofs and culminating in the Gelfand-Nalmark-Segal construction for C*-algebras. The first Russian edition was printed by the Siberian Division of "Nauka" P- lishers in 1983. Since then the monograph has served as the standard textbook on functional analysis at the University of Novosibirsk. This volume is translated from the second Russian edition printed by the Sobolev Institute of Mathematics of the Siberian Division of the Russian Academy of Sciences· in 1995. It incorporates new sections on Radon measures, the Schwartz spaces of distributions, and a supplementary list of theoretical exercises and problems. This edition was typeset using AMS-'lEX, the American Mathematical Society's 'lEX system. To clear my conscience completely, I also confess that := stands for the definor, the assignment operator, signifies the end of the proof.

Proofs and Fundamentals Book

Proofs and Fundamentals


  • Author : Ethan D. Bloch
  • Publisher : Springer Science & Business Media
  • Release Date : 2013-12-01
  • Genre: Mathematics
  • Pages : 424
  • ISBN 10 : 9781461221302

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Proofs and Fundamentals Excerpt :

The aim of this book is to help students write mathematics better. Throughout it are large exercise sets well-integrated with the text and varying appropriately from easy to hard. Basic issues are treated, and attention is given to small issues like not placing a mathematical symbol directly after a punctuation mark. And it provides many examples of what students should think and what they should write and how these two are often not the same.

Fundamentals of Algebraic Microlocal Analysis Book

Fundamentals of Algebraic Microlocal Analysis


  • Author : Goro Kato
  • Publisher : CRC Press
  • Release Date : 2020-08-11
  • Genre: Mathematics
  • Pages : 230
  • ISBN 10 : 9781000148398

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Fundamentals of Algebraic Microlocal Analysis Excerpt :

"Provides a thorough introduction to the algebraic theory of systems of differential equations, as developed by the Japanese school of M. Sato and his colleagues. Features a complete review of hyperfunction-microfunction theory and the theory of D-modules. Strikes the perfect balance between analytic and algebraic aspects."

Fundamentals of Abstract Analysis Book

Fundamentals of Abstract Analysis


  • Author : Andrew Gleason
  • Publisher : A K PETERS
  • Release Date : 2019-12-17
  • Genre: Uncategoriezed
  • Pages : 416
  • ISBN 10 : 0367450178

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Fundamentals of Abstract Analysis Excerpt :

This classic is an ideal introduction for students into the methodology and thinking of higher mathematics. It covers material not usually taught in the more technically-oriented introductory classes and will give students a well-rounded foundation for future studies.

Advanced Calculus  Fundamentals of Mathematics Book

Advanced Calculus Fundamentals of Mathematics


  • Author : Carlos Polanco
  • Publisher : Bentham Science Publishers
  • Release Date : 2019-07-31
  • Genre: Mathematics
  • Pages : 212
  • ISBN 10 : 9789811415074

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Advanced Calculus Fundamentals of Mathematics Excerpt :

Vector calculus is an essential mathematical tool for performing mathematical analysis of physical and natural phenomena. It is employed in advanced applications in the field of engineering and computer simulations. This textbook covers the fundamental requirements of vector calculus in curricula for college students in mathematics and engineering programs. Chapters start from the basics of vector algebra, real valued functions, different forms of integrals, geometric algebra and the various theorems relevant to vector calculus and differential forms. Readers will find a concise and clear study of vector calculus, along with several examples, exercises, and a case study in each chapter. The solutions to the exercises are also included at the end of the book. This is an ideal book for students with a basic background in mathematics who wish to learn about advanced calculus as part of their college curriculum and equip themselves with the knowledge to apply theoretical concepts in practical situations.

Tools of the Trade Book

Tools of the Trade


  • Author : Paul Sally
  • Publisher : American Mathematical Soc.
  • Release Date : 2008
  • Genre: Mathematics
  • Pages : 193
  • ISBN 10 : 9780821846346

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Tools of the Trade Excerpt :

This book provides a transition from the formula-full aspects of the beginning study of college level mathematics to the rich and creative world of more advanced topics. It is designed to assist the student in mastering the techniques of analysis and proof that are required to do mathematics. Along with the standard material such as linear algebra, construction of the real numbers via Cauchy sequences, metric spaces and complete metric spaces, there are three projects at the end of each chapter that form an integral part of the text. These projects include a detailed discussion of topics such as group theory, convergence of infinite series, decimal expansions of real numbers, point set topology and topological groups. They are carefully designed to guide the student through the subject matter. Together with numerous exercises included in the book, these projects may be used as part of the regular classroom presentation, as self-study projects for students, or for Inquiry Based Learning activities presented by the students.