Mathematical Analysis Fundamentals Books

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Mathematical Analysis Fundamentals


Mathematical Analysis Fundamentals
  • Author : Agamirza Bashirov
  • Publisher : Academic Press
  • Release : 2014-03-27
  • ISBN : 9780128010501
  • Language : En, Es, Fr & De
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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


Fundamental Mathematical Analysis
  • Author : Robert Magnus
  • Publisher : Springer Nature
  • Release : 2020-07-14
  • ISBN : 9783030463212
  • Language : En, Es, Fr & De
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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


Fundamentals of Mathematical Analysis
  • Author : Adel N. Boules
  • Publisher : Oxford University Press, USA
  • Release : 2021-03-09
  • ISBN : 9780198868781
  • Language : En, Es, Fr & De
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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


Fundamentals of Mathematical Analysis
  • Author : Rod Haggarty
  • Publisher : Addison-Wesley Longman
  • Release : 1993-01-01
  • ISBN : 0201631970
  • Language : En, Es, Fr & De
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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


Fundamentals of Real Analysis
  • Author : Sterling K. Berberian
  • Publisher : Springer Science & Business Media
  • Release : 2013-03-15
  • ISBN : 0387984801
  • Language : En, Es, Fr & De
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"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