A Concrete Approach To Classical Analysis

Author : Marian Muresan
Publisher : Springer Science & Business Media
Page : 433 pages
File Size : 55,9 Mb
Release : 2015-09-16
Category : Mathematics
ISBN : 9780387789330

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A Concrete Approach to Classical Analysis by Marian Muresan Pdf

Mathematical analysis offers a solid basis for many achievements in applied mathematics and discrete mathematics. This new textbook is focused on differential and integral calculus, and includes a wealth of useful and relevant examples, exercises, and results enlightening the reader to the power of mathematical tools. The intended audience consists of advanced undergraduates studying mathematics or computer science. The author provides excursions from the standard topics to modern and exciting topics, to illustrate the fact that even first or second year students can understand certain research problems. The text has been divided into ten chapters and covers topics on sets and numbers, linear spaces and metric spaces, sequences and series of numbers and of functions, limits and continuity, differential and integral calculus of functions of one or several variables, constants (mainly pi) and algorithms for finding them, the W - Z method of summation, estimates of algorithms and of certain combinatorial problems. Many challenging exercises accompany the text. Most of them have been used to prepare for different mathematical competitions during the past few years. In this respect, the author has maintained a healthy balance of theory and exercises.

Author : Nicholas J. Daras,Michael Th. Rassias,Nikolaos B. Zographopoulos
Publisher : Springer Nature
Page : 474 pages
File Size : 47,5 Mb
Release : 2024-01-04
Category : Mathematics
ISBN : 9783031464874

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Exploring Mathematical Analysis, Approximation Theory, and Optimization by Nicholas J. Daras,Michael Th. Rassias,Nikolaos B. Zographopoulos Pdf

This book compiles research and surveys devoted to the areas of mathematical analysis, approximation theory, and optimization. Being dedicated to A.-M. Legendre's work, contributions to this volume are devoted to those branches of mathematics and its applications that have been influenced, directly or indirectly, by the mathematician. Additional contributions provide a historical background as it relates to Legendre's work and its association to the foundation of Greece's higher education. Topics covered in this book include the investigation of the Jensen-Steffensen inequality, Ostrowski and trapezoid type inequalities, a Hilbert-Type Inequality, Hardy’s inequality, dynamic unilateral contact problems, square-free values of a category of integers, a maximum principle for general nonlinear operators, the application of Ergodic Theory to an alternating series expansion for real numbers, bounds for similarity condition numbers of unbounded operators, finite element methods with higher order polynomials, generating functions for the Fubini type polynomials, local asymptotics for orthonormal polynomials, trends in geometric function theory, quasi variational inclusions, Kleene fixed point theorems, ergodic states, spontaneous symmetry breaking and quasi-averages. It is hoped that this book will be of interest to a wide spectrum of readers from several areas of pure and applied sciences, and will be useful to undergraduate students, graduate level students, and researchers who want to be kept up to date on the results and theories in the subjects covered in this volume.

Author : Elimhan Mahmudov
Publisher : Springer Science & Business Media
Page : 386 pages
File Size : 42,6 Mb
Release : 2013-03-19
Category : Mathematics
ISBN : 9789491216862

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Single Variable Differential and Integral Calculus by Elimhan Mahmudov Pdf

The book “Single variable Differential and Integral Calculus” is an interesting text book for students of mathematics and physics programs, and a reference book for graduate students in any engineering field. This book is unique in the field of mathematical analysis in content and in style. It aims to define, compare and discuss topics in single variable differential and integral calculus, as well as giving application examples in important business fields. Some elementary concepts such as the power of a set, cardinality, measure theory, measurable functions are introduced. It also covers real and complex numbers, vector spaces, topological properties of sets, series and sequences of functions (including complex-valued functions and functions of a complex variable), polynomials and interpolation and extrema of functions. Although analysis is based on the single variable models and applications, theorems and examples are all set to be converted to multi variable extensions. For example, Newton, Riemann, Stieltjes and Lebesque integrals are studied together and compared.

Author : Anatoly B. Bakushinsky,Mikhail M. Kokurin,Mikhail Yu. Kokurin
Publisher : Walter de Gruyter GmbH & Co KG
Page : 342 pages
File Size : 45,6 Mb
Release : 2018-02-05
Category : Mathematics
ISBN : 9783110557350

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Regularization Algorithms for Ill-Posed Problems by Anatoly B. Bakushinsky,Mikhail M. Kokurin,Mikhail Yu. Kokurin Pdf

This specialized and authoritative book contains an overview of modern approaches to constructing approximations to solutions of ill-posed operator equations, both linear and nonlinear. These approximation schemes form a basis for implementable numerical algorithms for the stable solution of operator equations arising in contemporary mathematical modeling, and in particular when solving inverse problems of mathematical physics. The book presents in detail stable solution methods for ill-posed problems using the methodology of iterative regularization of classical iterative schemes and the techniques of finite dimensional and finite difference approximations of the problems under study. Special attention is paid to ill-posed Cauchy problems for linear operator differential equations and to ill-posed variational inequalities and optimization problems. The readers are expected to have basic knowledge in functional analysis and differential equations. The book will be of interest to applied mathematicians and specialists in mathematical modeling and inverse problems, and also to advanced students in these fields. ContentsIntroductionRegularization Methods For Linear EquationsFinite Difference MethodsIterative Regularization MethodsFinite-Dimensional Iterative ProcessesVariational Inequalities and Optimization Problems

Author : Marian Mureşan
Publisher : Springer
Page : 265 pages
File Size : 40,8 Mb
Release : 2017-02-21
Category : Computers
ISBN : 9783319520032

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Introduction to Mathematica® with Applications by Marian Mureşan Pdf

Starting with an introduction to the numerous features of Mathematica®, this book continues with more complex material. It provides the reader with lots of examples and illustrations of how the benefits of Mathematica® can be used. Composed of eleven chapters, it includes the following: A chapter on several sorting algorithms Functions (planar and solid) with many interesting examples Ordinary differential equations Advantages of Mathematica® dealing with the Pi number The power of Mathematica® working with optimal control problems Introduction to Mathematica® with Applications will appeal to researchers, professors and students requiring a computational tool.

Author : Various Authors
Publisher : Taylor & Francis
Page : 4507 pages
File Size : 55,7 Mb
Release : 2022-07-30
Category : Business & Economics
ISBN : 9781351869393

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Routledge Library Editions: The History of Economic Thought by Various Authors Pdf

The volumes in this set, originally published between 1925 and 1990, draw together research by leading academics in the area of the history of economic thought. The volumes encompass many different schools of economic thought, with a focus on individual economic thinkers such as Friedrich Hayek, Adam Smith and Piero Sraffa. This set will be of interest to students of economics, particularly students of the history of economic thought.

Author : Ronald L. Graham,Donald E. Knuth,Oren Patashnik
Publisher : Addison-Wesley Professional
Page : 811 pages
File Size : 55,7 Mb
Release : 1994-02-28
Category : Computers
ISBN : 9780134389981

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Concrete Mathematics by Ronald L. Graham,Donald E. Knuth,Oren Patashnik Pdf

This book introduces the mathematics that supports advanced computer programming and the analysis of algorithms. The primary aim of its well-known authors is to provide a solid and relevant base of mathematical skills - the skills needed to solve complex problems, to evaluate horrendous sums, and to discover subtle patterns in data. It is an indispensable text and reference not only for computer scientists - the authors themselves rely heavily on it! - but for serious users of mathematics in virtually every discipline. Concrete Mathematics is a blending of CONtinuous and disCRETE mathematics. "More concretely," the authors explain, "it is the controlled manipulation of mathematical formulas, using a collection of techniques for solving problems." The subject matter is primarily an expansion of the Mathematical Preliminaries section in Knuth's classic Art of Computer Programming, but the style of presentation is more leisurely, and individual topics are covered more deeply. Several new topics have been added, and the most significant ideas have been traced to their historical roots. The book includes more than 500 exercises, divided into six categories. Complete answers are provided for all exercises, except research problems, making the book particularly valuable for self-study. Major topics include: Sums Recurrences Integer functions Elementary number theory Binomial coefficients Generating functions Discrete probability Asymptotic methods This second edition includes important new material about mechanical summation. In response to the widespread use of the first edition as a reference book, the bibliography and index have also been expanded, and additional nontrivial improvements can be found on almost every page. Readers will appreciate the informal style of Concrete Mathematics. Particularly enjoyable are the marginal graffiti contributed by students who have taken courses based on this material. The authors want to convey not only the importance of the techniques presented, but some of the fun in learning and using them.

Author : Omar Hijab
Publisher : Springer Science & Business Media
Page : 345 pages
File Size : 51,8 Mb
Release : 2007-04-17
Category : Mathematics
ISBN : 9780387693163

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Introduction to Calculus and Classical Analysis by Omar Hijab Pdf

Intended for an honors calculus course or for an introduction to analysis, this is an ideal text for undergraduate majors since it covers rigorous analysis, computational dexterity, and a breadth of applications. The book contains many remarkable features: * complete avoidance of /epsilon-/delta arguments by using sequences instead * definition of the integral as the area under the graph, while area is defined for every subset of the plane * complete avoidance of complex numbers * heavy emphasis on computational problems * applications from many parts of analysis, e.g. convex conjugates, Cantor set, continued fractions, Bessel functions, the zeta functions, and many more * 344 problems with solutions in the back of the book.

Author : Adam Bobrowski
Publisher : Cambridge University Press
Page : 279 pages
File Size : 48,8 Mb
Release : 2020-11-26
Category : Mathematics
ISBN : 9781108495790

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Generators of Markov Chains by Adam Bobrowski Pdf

A clear explanation of what an explosive Markov chain does after it passes through all available states in finite time.

Author : Jean-Paul Penot
Publisher : Springer
Page : 669 pages
File Size : 48,7 Mb
Release : 2016-12-18
Category : Mathematics
ISBN : 9783319324111

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Analysis by Jean-Paul Penot Pdf

This textbook covers the main results and methods of real analysis in a single volume. Taking a progressive approach to equations and transformations, this book starts with the very foundations of real analysis (set theory, order, convergence, and measure theory) before presenting powerful results that can be applied to concrete problems. In addition to classical results of functional analysis, differential calculus and integration, Analysis discusses topics such as convex analysis, dissipative operators and semigroups which are often absent from classical treatises. Acknowledging that analysis has significantly contributed to the understanding and development of the present world, the book further elaborates on techniques which pervade modern civilization, including wavelets in information theory, the Radon transform in medical imaging and partial differential equations in various mechanical and physical phenomena. Advanced undergraduate and graduate students, engineers as well as practitioners wishing to familiarise themselves with concepts and applications of analysis will find this book useful. With its content split into several topics of interest, the book’s style and layout make it suitable for use in several courses, while its self-contained character makes it appropriate for self-study.

Author : O. Hijab
Publisher : Springer Science & Business Media
Page : 336 pages
File Size : 53,5 Mb
Release : 1997
Category : Calculus
ISBN : 0387949267

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Introduction to Calculus and Classical Analysis by O. Hijab Pdf

As an excellent, easy-to-understand introduction to analysis, this book involves rigorous analysis, computational dexterity, and a breadth of applications, making it ideal for undergraduate majors. The book contains many remarkable features, including a heavy emphasis on computational problems and applications from many parts of analysis. The work completely avoids treating complex numbers. Nearly 350 problems with solutions are included in the back of the book.

Author : Sacha Friedli,Yvan Velenik
Publisher : Cambridge University Press
Page : 643 pages
File Size : 51,7 Mb
Release : 2017-11-23
Category : Mathematics
ISBN : 9781107184824

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Statistical Mechanics of Lattice Systems by Sacha Friedli,Yvan Velenik Pdf

A self-contained, mathematical introduction to the driving ideas in equilibrium statistical mechanics, studying important models in detail.

Author : Henri Cohen,Fredrik Strömberg
Publisher : American Mathematical Soc.
Page : 700 pages
File Size : 42,8 Mb
Release : 2017-08-02
Category : Forms (Mathematics).
ISBN : 9780821849477

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Modular Forms: A Classical Approach by Henri Cohen,Fredrik Strömberg Pdf

The theory of modular forms is a fundamental tool used in many areas of mathematics and physics. It is also a very concrete and “fun” subject in itself and abounds with an amazing number of surprising identities. This comprehensive textbook, which includes numerous exercises, aims to give a complete picture of the classical aspects of the subject, with an emphasis on explicit formulas. After a number of motivating examples such as elliptic functions and theta functions, the modular group, its subgroups, and general aspects of holomorphic and nonholomorphic modular forms are explained, with an emphasis on explicit examples. The heart of the book is the classical theory developed by Hecke and continued up to the Atkin–Lehner–Li theory of newforms and including the theory of Eisenstein series, Rankin–Selberg theory, and a more general theory of theta series including the Weil representation. The final chapter explores in some detail more general types of modular forms such as half-integral weight, Hilbert, Jacobi, Maass, and Siegel modular forms. Some “gems” of the book are an immediately implementable trace formula for Hecke operators, generalizations of Haberland's formulas for the computation of Petersson inner products, W. Li's little-known theorem on the diagonalization of the full space of modular forms, and explicit algorithms due to the second author for computing Maass forms. This book is essentially self-contained, the necessary tools such as gamma and Bessel functions, Bernoulli numbers, and so on being given in a separate chapter.

Author : Universitatea "Babeș-Bolyai."
Publisher : Unknown
Page : 960 pages
File Size : 54,5 Mb
Release : 2010
Category : Mathematics
ISBN : UCBK:C089194213

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Studia Universitatis Babeș-Bolyai by Universitatea "Babeș-Bolyai." Pdf

Author : Vassili N. Kolokoltsov
Publisher : Springer
Page : 360 pages
File Size : 55,6 Mb
Release : 2007-12-03
Category : Mathematics
ISBN : 9783540465874

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Semiclassical Analysis for Diffusions and Stochastic Processes by Vassili N. Kolokoltsov Pdf

The monograph is devoted mainly to the analytical study of the differential, pseudo-differential and stochastic evolution equations describing the transition probabilities of various Markov processes. These include (i) diffusions (in particular,degenerate diffusions), (ii) more general jump-diffusions, especially stable jump-diffusions driven by stable Lévy processes, (iii) complex stochastic Schrödinger equations which correspond to models of quantum open systems. The main results of the book concern the existence, two-sided estimates, path integral representation, and small time and semiclassical asymptotics for the Green functions (or fundamental solutions) of these equations, which represent the transition probability densities of the corresponding random process. The boundary value problem for Hamiltonian systems and some spectral asymptotics ar also discussed. Readers should have an elementary knowledge of probability, complex and functional analysis, and calculus.