Fundamental Ideas Of Analysis
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| Author | : Michael C. Reed |
| Publisher | : John Wiley & Sons |
| Total Pages | : 440 |
| Release | : 1998 |
| Genre | : Mathematics |
| ISBN | : |
The ideas and methods of mathematics, long central to the physical sciences, now play an increasingly important role in a wide variety of disciplines. Analysis provides theorems that prove that results are true and provides techniques to estimate the errors in approximate calculations. The ideas and methods of analysis play a fundamental role in ordinary differential equations, probability theory, differential geometry, numerical analysis, complex analysis, partial differential equations, as well as in most areas of applied mathematics.
| Author | : Mohammed J. Zaki |
| Publisher | : Cambridge University Press |
| Total Pages | : 607 |
| Release | : 2014-05-12 |
| Genre | : Computers |
| ISBN | : 0521766338 |
A comprehensive overview of data mining from an algorithmic perspective, integrating related concepts from machine learning and statistics.
| Author | : Robert Magnus |
| Publisher | : Springer Nature |
| Total Pages | : 445 |
| Release | : 2020-07-14 |
| Genre | : Mathematics |
| ISBN | : 3030463214 |
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.
| Author | : Bernd S. W. Schröder |
| Publisher | : John Wiley & Sons |
| Total Pages | : 584 |
| Release | : 2008-01-28 |
| Genre | : Mathematics |
| ISBN | : 9780470226766 |
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.
| Author | : Robert J. Zimmer |
| Publisher | : University of Chicago Press |
| Total Pages | : 169 |
| Release | : 1990-01-15 |
| Genre | : Mathematics |
| ISBN | : 0226983382 |
Functional analysis is a broad mathematical area with strong connections to many domains within mathematics and physics. This book, based on a first-year graduate course taught by Robert J. Zimmer at the University of Chicago, is a complete, concise presentation of fundamental ideas and theorems of functional analysis. It introduces essential notions and results from many areas of mathematics to which functional analysis makes important contributions, and it demonstrates the unity of perspective and technique made possible by the functional analytic approach. Zimmer provides an introductory chapter summarizing measure theory and the elementary theory of Banach and Hilbert spaces, followed by a discussion of various examples of topological vector spaces, seminorms defining them, and natural classes of linear operators. He then presents basic results for a wide range of topics: convexity and fixed point theorems, compact operators, compact groups and their representations, spectral theory of bounded operators, ergodic theory, commutative C*-algebras, Fourier transforms, Sobolev embedding theorems, distributions, and elliptic differential operators. In treating all of these topics, Zimmer's emphasis is not on the development of all related machinery or on encyclopedic coverage but rather on the direct, complete presentation of central theorems and the structural framework and examples needed to understand them. Sets of exercises are included at the end of each chapter. For graduate students and researchers in mathematics who have mastered elementary analysis, this book is an entrée and reference to the full range of theory and applications in which functional analysis plays a part. For physics students and researchers interested in these topics, the lectures supply a thorough mathematical grounding.
| Author | : Vagn Lundsgaard Hansen |
| Publisher | : World Scientific |
| Total Pages | : 250 |
| Release | : 1999 |
| Genre | : Science |
| ISBN | : 9789810238940 |
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.
| Author | : Sebastian Rezat |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 417 |
| Release | : 2013-12-13 |
| Genre | : Education |
| ISBN | : 1461434890 |
The diversity of research domains and theories in the field of mathematics education has been a permanent subject of discussions from the origins of the discipline up to the present. On the one hand the diversity is regarded as a resource for rich scientific development on the other hand it gives rise to the often repeated criticism of the discipline’s lack of focus and identity. As one way of focusing on core issues of the discipline the book seeks to open up a discussion about fundamental ideas in the field of mathematics education that permeate different research domains and perspectives. The book addresses transformation as one fundamental idea in mathematics education and examines it from different perspectives. Transformations are related to knowledge, related to signs and representations of mathematics, related to concepts and ideas, and related to instruments for the learning of mathematics. The book seeks to answer the following questions: What do we know about transformations in the different domains? What kinds of transformations are crucial? How is transformation in each case conceptualized?
| Author | : R. Tyrrell Rockafellar |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 747 |
| Release | : 2009-06-26 |
| Genre | : Mathematics |
| ISBN | : 3642024319 |
From its origins in the minimization of integral functionals, the notion of variations has evolved greatly in connection with applications in optimization, equilibrium, and control. This book develops a unified framework and provides a detailed exposition of variational geometry and subdifferential calculus in their current forms beyond classical and convex analysis. Also covered are set-convergence, set-valued mappings, epi-convergence, duality, and normal integrands.
| Author | : Joseph L. Taylor |
| Publisher | : American Mathematical Soc. |
| Total Pages | : 411 |
| Release | : 2012 |
| Genre | : Mathematics |
| ISBN | : 0821889842 |
Foundations of Analysis has two main goals. The first is to develop in students the mathematical maturity and sophistication they will need as they move through the upper division curriculum. The second is to present a rigorous development of both single and several variable calculus, beginning with a study of the properties of the real number system. The presentation is both thorough and concise, with simple, straightforward explanations. The exercises differ widely in level of abstraction and level of difficulty. They vary from the simple to the quite difficult and from the computational to the theoretical. Each section contains a number of examples designed to illustrate the material in the section and to teach students how to approach the exercises for that section. --Book cover.
| Author | : Thomas N. Bulkowski |
| Publisher | : John Wiley & Sons |
| Total Pages | : 325 |
| Release | : 2012-12-10 |
| Genre | : Business & Economics |
| ISBN | : 1118508750 |
Comprehensive coverage of the four major trading styles Evolution of a Trader explores the four trading styles that people use when learning to trade or invest in the stock market. Often, beginners enter the stock market by: Buying and holding onto a stock (value investing). That works well until the trend ends or a bear market begins. Then they try Position trading. This is the same as buy-and-hold, except the technique sells positions before a significant trend change occurs. Swing trading follows when traders increase their frequency of trading, trying to catch the short-term up and down swings. Finally, people try Day trading by completing their trades in a single day. This series provides comprehensive coverage of the four trading styles by offering numerous tips, sharing discoveries, and discussing specific trading setups to help you become a successful trader or investor as you journey through each style. Trading Basics takes an in-depth look at money management, stops, support and resistance, and offers dozens of tips every trader should know. Fundamental Analysis and Position Trading discusses when to sell a buy-and-hold position, uncovers which fundamentals work best, and uses them to find stocks that become 10-baggers—stocks that climb by 10 times their original value. Swing and Day Trading reveals methods to time the market swings, including specific trading setups, but it covers the basics as well, such as setting up a home trading office and how much money you can make day trading.
