Invitation To Classical Analysis
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Invitation To Classical Analysis
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Author : Peter L. Duren
language : en
Publisher: American Mathematical Soc.
Release Date : 2012
Invitation To Classical Analysis written by Peter L. Duren and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012 with Mathematics categories.
This book gives a rigorous treatment of selected topics in classical analysis, with many applications and examples. The exposition is at the undergraduate level, building on basic principles of advanced calculus without appeal to more sophisticated techniques of complex analysis and Lebesgue integration. Among the topics covered are Fourier series and integrals, approximation theory, Stirling's formula, the gamma function, Bernoulli numbers and polynomials, the Riemann zeta function, Tauberian theorems, elliptic integrals, ramifications of the Cantor set, and a theoretical discussion of differential equations including power series solutions at regular singular points, Bessel functions, hypergeometric functions, and Sturm comparison theory. Preliminary chapters offer rapid reviews of basic principles and further background material such as infinite products and commonly applied inequalities. This book is designed for individual study but can also serve as a text for second-semester courses in advanced calculus. Each chapter concludes with an abundance of exercises. Historical notes discuss the evolution of mathematical ideas and their relevance to physical applications. Special features are capsule scientific biographies of the major players and a gallery of portraits. Although this book is designed for undergraduate students, others may find it an accessible source of information on classical topics that underlie modern developments in pure and applied mathematics.
Complex Analysis An Invitation 2nd Edition
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Author : Murali Rao
language : en
Publisher: World Scientific Publishing Company
Release Date : 2015-01-28
Complex Analysis An Invitation 2nd Edition written by Murali Rao and has been published by World Scientific Publishing Company this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-01-28 with Mathematics categories.
This volume is an enlarged edition of a classic textbook on complex analysis. In addition to the classical material of the first edition it provides a concise and accessible treatment of Loewner theory, both in the disc and in the half-plane. Some of the new material has been described in research papers only or appears here for the first time. Each chapter ends with exercises.
An Invitation To Model Theory
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Author : Jonathan Kirby
language : en
Publisher: Cambridge University Press
Release Date : 2019-04-18
An Invitation To Model Theory written by Jonathan Kirby and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-04-18 with Mathematics categories.
An innovative and largely self-contained textbook bringing model theory to an undergraduate audience.
Invitation To Linear Programming And Game Theory
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Author : David C. Vella
language : en
Publisher: Cambridge University Press
Release Date : 2021-03-11
Invitation To Linear Programming And Game Theory written by David C. Vella and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-03-11 with Business & Economics categories.
Discover interplay between matrices, linear programming, and game theory at an introductory level, requiring only high school algebra and curiosity.
A Classical Invitation To Algebraic Numbers And Class Fields
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Author : Harvey Cohn
language : en
Publisher:
Release Date : 1978
A Classical Invitation To Algebraic Numbers And Class Fields written by Harvey Cohn and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1978 with Algebraic number theory categories.
Course In Analysis A Vol Iii Measure And Integration Theory Complex Valued Functions Of A Complex Variable
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Author : Niels Jacob
language : en
Publisher: World Scientific Publishing Company
Release Date : 2017-06-29
Course In Analysis A Vol Iii Measure And Integration Theory Complex Valued Functions Of A Complex Variable written by Niels Jacob and has been published by World Scientific Publishing Company this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-06-29 with Mathematics categories.
'It is a great book for a first year (US) graduate student. One of the nice features of the book is that the book contains full solutions for all of the problems which make it useful as reference for self-study or qualifying exam prep.' (See Full Review)MAA ReviewsIn this third volume of 'A Course in Analysis', two topics indispensible for every mathematician are treated: Measure and Integration Theory; and Complex Function Theory.In the first part measurable spaces and measure spaces are introduced and Caratheodory's extension theorem is proved. This is followed by the construction of the integral with respect to a measure, in particular with respect to the Lebesgue measure in the Euclidean space. The Radon-Nikodym theorem and the transformation theorem are discussed and much care is taken to handle convergence theorems with applications, as well as Lp-spaces.Integration on product spaces and Fubini's theorem is a further topic as is the discussion of the relation between the Lebesgue integral and the Riemann integral. In addition to these standard topics we deal with the Hausdorff measure, convolutions of functions and measures including the Friedrichs mollifier, absolutely continuous functions and functions of bounded variation. The fundamental theorem of calculus is revisited, and we also look at Sard's theorem or the Riesz-Kolmogorov theorem on pre-compact sets in Lp-spaces.The text can serve as a companion to lectures, but it can also be used for self-studying. This volume includes more than 275 problems solved completely in detail which should help the student further.
Understanding Analysis
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Author : Stephen Abbott
language : en
Publisher: Springer
Release Date : 2015-05-19
Understanding Analysis written by Stephen Abbott and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-05-19 with Mathematics categories.
This lively introductory text exposes the student to the rewards of a rigorous study of functions of a real variable. In each chapter, informal discussions of questions that give analysis its inherent fascination are followed by precise, but not overly formal, developments of the techniques needed to make sense of them. By focusing on the unifying themes of approximation and the resolution of paradoxes that arise in the transition from the finite to the infinite, the text turns what could be a daunting cascade of definitions and theorems into a coherent and engaging progression of ideas. Acutely aware of the need for rigor, the student is much better prepared to understand what constitutes a proper mathematical proof and how to write one. Fifteen years of classroom experience with the first edition of Understanding Analysis have solidified and refined the central narrative of the second edition. Roughly 150 new exercises join a selection of the best exercises from the first edition, and three more project-style sections have been added. Investigations of Euler’s computation of ζ(2), the Weierstrass Approximation Theorem, and the gamma function are now among the book’s cohort of seminal results serving as motivation and payoff for the beginning student to master the methods of analysis.
Introduction To Analysis In One Variable
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Author : Michael E. Taylor
language : en
Publisher: American Mathematical Soc.
Release Date : 2020-08-11
Introduction To Analysis In One Variable written by Michael E. Taylor and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-08-11 with Education categories.
This is a text for students who have had a three-course calculus sequence and who are ready to explore the logical structure of analysis as the backbone of calculus. It begins with a development of the real numbers, building this system from more basic objects (natural numbers, integers, rational numbers, Cauchy sequences), and it produces basic algebraic and metric properties of the real number line as propositions, rather than axioms. The text also makes use of the complex numbers and incorporates this into the development of differential and integral calculus. For example, it develops the theory of the exponential function for both real and complex arguments, and it makes a geometrical study of the curve (expit) (expit), for real t t, leading to a self-contained development of the trigonometric functions and to a derivation of the Euler identity that is very different from what one typically sees. Further topics include metric spaces, the Stone–Weierstrass theorem, and Fourier series.
Fundamentals Of Real And Complex Analysis
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Author : Asuman Güven Aksoy
language : en
Publisher: Springer Nature
Release Date : 2024-04-18
Fundamentals Of Real And Complex Analysis written by Asuman Güven Aksoy and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024-04-18 with Mathematics categories.
The primary aim of this text is to help transition undergraduates to study graduate level mathematics. It unites real and complex analysis after developing the basic techniques and aims at a larger readership than that of similar textbooks that have been published, as fewer mathematical requisites are required. The idea is to present analysis as a whole and emphasize the strong connections between various branches of the field. Ample examples and exercises reinforce concepts, and a helpful bibliography guides those wishing to delve deeper into particular topics. Graduate students who are studying for their qualifying exams in analysis will find use in this text, as well as those looking to advance their mathematical studies or who are moving on to explore another quantitative science. Chapter 1 contains many tools for higher mathematics; its content is easily accessible, though not elementary. Chapter 2 focuses on topics in real analysis such as p-adic completion, Banach Contraction Mapping Theorem and its applications, Fourier series, Lebesgue measure and integration. One of this chapter’s unique features is its treatment of functional equations. Chapter 3 covers the essential topics in complex analysis: it begins with a geometric introduction to the complex plane, then covers holomorphic functions, complex power series, conformal mappings, and the Riemann mapping theorem. In conjunction with the Bieberbach conjecture, the power and applications of Cauchy’s theorem through the integral formula and residue theorem are presented.
Course In Analysis A Vol Iv Fourier Analysis Ordinary Differential Equations Calculus Of Variations
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Author : Niels Jacob
language : en
Publisher: World Scientific
Release Date : 2018-07-19
Course In Analysis A Vol Iv Fourier Analysis Ordinary Differential Equations Calculus Of Variations written by Niels Jacob and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-07-19 with Mathematics categories.
In the part on Fourier analysis, we discuss pointwise convergence results, summability methods and, of course, convergence in the quadratic mean of Fourier series. More advanced topics include a first discussion of Hardy spaces. We also spend some time handling general orthogonal series expansions, in particular, related to orthogonal polynomials. Then we switch to the Fourier integral, i.e. the Fourier transform in Schwartz space, as well as in some Lebesgue spaces or of measures.Our treatment of ordinary differential equations starts with a discussion of some classical methods to obtain explicit integrals, followed by the existence theorems of Picard-Lindelöf and Peano which are proved by fixed point arguments. Linear systems are treated in great detail and we start a first discussion on boundary value problems. In particular, we look at Sturm-Liouville problems and orthogonal expansions. We also handle the hypergeometric differential equations (using complex methods) and their relations to special functions in mathematical physics. Some qualitative aspects are treated too, e.g. stability results (Ljapunov functions), phase diagrams, or flows.Our introduction to the calculus of variations includes a discussion of the Euler-Lagrange equations, the Legendre theory of necessary and sufficient conditions, and aspects of the Hamilton-Jacobi theory. Related first order partial differential equations are treated in more detail.The text serves as a companion to lecture courses, and it is also suitable for self-study. The text is complemented by ca. 260 problems with detailed solutions.