Solving Problems In Mathematical Analysis Part I

Author : Tomasz Radożycki
Publisher : Springer Nature
Page : 375 pages
File Size : 53,5 Mb
Release : 2020-02-20
Category : Mathematics
ISBN : 9783030358440

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Solving Problems in Mathematical Analysis, Part I by Tomasz Radożycki Pdf

This textbook offers an extensive list of completely solved problems in mathematical analysis. This first of three volumes covers sets, functions, limits, derivatives, integrals, sequences and series, to name a few. The series contains the material corresponding to the first three or four semesters of a course in Mathematical Analysis. Based on the author’s years of teaching experience, this work stands out by providing detailed solutions (often several pages long) to the problems. The basic premise of the book is that no topic should be left unexplained, and no question that could realistically arise while studying the solutions should remain unanswered. The style and format are straightforward and accessible. In addition, each chapter includes exercises for students to work on independently. Answers are provided to all problems, allowing students to check their work. Though chiefly intended for early undergraduate students of Mathematics, Physics and Engineering, the book will also appeal to students from other areas with an interest in Mathematical Analysis, either as supplementary reading or for independent study.

Author : Tomasz Radożycki
Publisher : Springer Nature
Page : 378 pages
File Size : 47,5 Mb
Release : 2020-02-24
Category : Mathematics
ISBN : 9783030385965

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Solving Problems in Mathematical Analysis, Part III by Tomasz Radożycki Pdf

This textbook offers an extensive list of completely solved problems in mathematical analysis. This third of three volumes covers curves and surfaces, conditional extremes, curvilinear integrals, complex functions, singularities and Fourier series. The series contains the material corresponding to the first three or four semesters of a course in Mathematical Analysis. Based on the author’s years of teaching experience, this work stands out by providing detailed solutions (often several pages long) to the problems. The basic premise of the book is that no topic should be left unexplained, and no question that could realistically arise while studying the solutions should remain unanswered. The style and format are straightforward and accessible. In addition, each chapter includes exercises for students to work on independently. Answers are provided to all problems, allowing students to check their work. Though chiefly intended for early undergraduate students of Mathematics, Physics and Engineering, the book will also appeal to students from other areas with an interest in Mathematical Analysis, either as supplementary reading or for independent study.

Author : Tomasz Radożycki
Publisher : Springer
Page : 369 pages
File Size : 51,9 Mb
Release : 2020-02-21
Category : Mathematics
ISBN : 3030358437

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Solving Problems in Mathematical Analysis, Part I by Tomasz Radożycki Pdf

This textbook offers an extensive list of completely solved problems in mathematical analysis. This first of three volumes covers sets, functions, limits, derivatives, integrals, sequences and series, to name a few. The series contains the material corresponding to the first three or four semesters of a course in Mathematical Analysis. Based on the author’s years of teaching experience, this work stands out by providing detailed solutions (often several pages long) to the problems. The basic premise of the book is that no topic should be left unexplained, and no question that could realistically arise while studying the solutions should remain unanswered. The style and format are straightforward and accessible. In addition, each chapter includes exercises for students to work on independently. Answers are provided to all problems, allowing students to check their work. Though chiefly intended for early undergraduate students of Mathematics, Physics and Engineering, the book will also appeal to students from other areas with an interest in Mathematical Analysis, either as supplementary reading or for independent study.

Author : Tomasz Radożycki
Publisher : Springer Nature
Page : 384 pages
File Size : 48,6 Mb
Release : 2020-02-22
Category : Mathematics
ISBN : 9783030368487

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Solving Problems in Mathematical Analysis, Part II by Tomasz Radożycki Pdf

This textbook offers an extensive list of completely solved problems in mathematical analysis. This second of three volumes covers definite, improper and multidimensional integrals, functions of several variables, differential equations, and more. The series contains the material corresponding to the first three or four semesters of a course in Mathematical Analysis. Based on the author’s years of teaching experience, this work stands out by providing detailed solutions (often several pages long) to the problems. The basic premise of the book is that no topic should be left unexplained, and no question that could realistically arise while studying the solutions should remain unanswered. The style and format are straightforward and accessible. In addition, each chapter includes exercises for students to work on independently. Answers are provided to all problems, allowing students to check their work. Though chiefly intended for early undergraduate students of Mathematics, Physics and Engineering, the book will also appeal to students from other areas with an interest in Mathematical Analysis, either as supplementary reading or for independent study.

Author : Wiesława J. Kaczor,Maria T. Nowak
Publisher : American Mathematical Soc.
Page : 398 pages
File Size : 44,6 Mb
Release : 2001-01
Category : Mathematics
ISBN : 9780821820513

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Problems in Mathematical Analysis: Continuity and differentiation by Wiesława J. Kaczor,Maria T. Nowak Pdf

We learn by doing. We learn mathematics by doing problems. And we learn more mathematics by doing more problems. This is the sequel to Problems in Mathematical Analysis I (Volume 4 in the Student Mathematical Library series). If you want to hone your understanding of continuous and differentiable functions, this book contains hundreds of problems to help you do so. The emphasis here is on real functions of a single variable. The book is mainly geared toward students studying the basic principles of analysis. However, given its selection of problems, organization, and level, it would be an ideal choice for tutorial or problem-solving seminars, particularly those geared toward the Putnam exam. It is also suitable for self-study. The presentation of the material is designed to help student comprehension, to encourage them to ask their own questions, and to start research. The collection of problems will also help teachers who wish to incorporate problems into their lectures. The problems are grouped into sections according to the methods of solution. Solutions for the problems are provided.

Author : Jiří Gregor,Jaroslav Tišer
Publisher : Springer Science & Business Media
Page : 247 pages
File Size : 47,8 Mb
Release : 2010-12-21
Category : Mathematics
ISBN : 9780857290649

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Discovering Mathematics by Jiří Gregor,Jaroslav Tišer Pdf

The book contains chapters of structured approach to problem solving in mathematical analysis on an intermediate level. It follows the ideas of G.Polya and others, distinguishing between exercises and problem solving in mathematics. Interrelated concepts are connected by hyperlinks, pointing toward easier or more difficult problems so as to show paths of mathematical reasoning. Basic definitions and theorems can also be found by hyperlinks from relevant places. Problems are open to alternative formulations, generalizations, simplifications, and verification of hypotheses by the reader; this is shown to be helpful in solving problems. The book presents how advanced mathematical software can aid all stages of mathematical reasoning while the mathematical content remains in foreground. The authors show how software can contribute to deeper understanding and to enlarging the scope of teaching for students and teachers of mathematics.

Author : Ovidiu Furdui
Publisher : Springer Science & Business Media
Page : 289 pages
File Size : 40,7 Mb
Release : 2013-05-30
Category : Mathematics
ISBN : 9781461467625

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Limits, Series, and Fractional Part Integrals by Ovidiu Furdui Pdf

This book features challenging problems of classical analysis that invite the reader to explore a host of strategies and tools used for solving problems of modern topics in real analysis. This volume offers an unusual collection of problems — many of them original — specializing in three topics of mathematical analysis: limits, series, and fractional part integrals. The work is divided into three parts, each containing a chapter dealing with a particular problem type as well as a very short section of hints to select problems. The first chapter collects problems on limits of special sequences and Riemann integrals; the second chapter focuses on the calculation of fractional part integrals with a special section called ‘Quickies’ which contains problems that have had unexpected succinct solutions. The final chapter offers the reader an assortment of problems with a flavor towards the computational aspects of infinite series and special products, many of which are new to the literature. Each chapter contains a section of difficult problems which are motivated by other problems in the book. These ‘Open Problems’ may be considered research projects for students who are studying advanced calculus, and which are intended to stimulate creativity and the discovery of new and original methods for proving known results and establishing new ones. This stimulating collection of problems is intended for undergraduate students with a strong background in analysis; graduate students in mathematics, physics, and engineering; researchers; and anyone who works on topics at the crossroad between pure and applied mathematics. Moreover, the level of problems is appropriate for students involved in the Putnam competition and other high level mathematical contests.

Author : Teodora-Liliana Radulescu,Vicentiu D. Radulescu,Titu Andreescu
Publisher : Springer Science & Business Media
Page : 452 pages
File Size : 52,5 Mb
Release : 2009-06-12
Category : Mathematics
ISBN : 9780387773797

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Problems in Real Analysis by Teodora-Liliana Radulescu,Vicentiu D. Radulescu,Titu Andreescu Pdf

Problems in Real Analysis: Advanced Calculus on the Real Axis features a comprehensive collection of challenging problems in mathematical analysis that aim to promote creative, non-standard techniques for solving problems. This self-contained text offers a host of new mathematical tools and strategies which develop a connection between analysis and other mathematical disciplines, such as physics and engineering. A broad view of mathematics is presented throughout; the text is excellent for the classroom or self-study. It is intended for undergraduate and graduate students in mathematics, as well as for researchers engaged in the interplay between applied analysis, mathematical physics, and numerical analysis.

Author : Wieslawa J. Kaczor,Maria T. Nowak
Publisher : American Mathematical Soc.
Page : 400 pages
File Size : 45,7 Mb
Release : 2000
Category : Mathematical analysis
ISBN : 0821884433

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Problems in Mathematical Analysis by Wieslawa J. Kaczor,Maria T. Nowak Pdf

Author : Alina Sîntămărian,Ovidiu Furdui
Publisher : Springer Nature
Page : 543 pages
File Size : 53,7 Mb
Release : 2021-10-25
Category : Mathematics
ISBN : 9783030771393

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Sharpening Mathematical Analysis Skills by Alina Sîntămărian,Ovidiu Furdui Pdf

This book gathers together a novel collection of problems in mathematical analysis that are challenging and worth studying. They cover most of the classical topics of a course in mathematical analysis, and include challenges presented with an increasing level of difficulty. Problems are designed to encourage creativity, and some of them were especially crafted to lead to open problems which might be of interest for students seeking motivation to get a start in research. The sets of problems are comprised in Part I. The exercises are arranged on topics, many of them being preceded by supporting theory. Content starts with limits, series of real numbers and power series, extending to derivatives and their applications, partial derivatives and implicit functions. Difficult problems have been structured in parts, helping the reader to find a solution. Challenges and open problems are scattered throughout the text, being an invitation to discover new original methods for proving known results and establishing new ones. The final two chapters offer ambitious readers splendid problems and two new proofs of a famous quadratic series involving harmonic numbers. In Part II, the reader will find solutions to the proposed exercises. Undergraduate students in mathematics, physics and engineering, seeking to strengthen their skills in analysis, will most benefit from this work, along with instructors involved in math contests, individuals who want to enrich and test their knowledge in analysis, and anyone willing to explore the standard topics of mathematical analysis in ways that aren’t commonly seen in regular textbooks.

Author : Asuman G. Aksoy,Mohamed A. Khamsi
Publisher : Springer Science & Business Media
Page : 257 pages
File Size : 40,6 Mb
Release : 2010-03-10
Category : Mathematics
ISBN : 9781441912961

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A Problem Book in Real Analysis by Asuman G. Aksoy,Mohamed A. Khamsi Pdf

Education is an admirable thing, but it is well to remember from time to time that nothing worth knowing can be taught. Oscar Wilde, “The Critic as Artist,” 1890. Analysis is a profound subject; it is neither easy to understand nor summarize. However, Real Analysis can be discovered by solving problems. This book aims to give independent students the opportunity to discover Real Analysis by themselves through problem solving. ThedepthandcomplexityofthetheoryofAnalysiscanbeappreciatedbytakingaglimpseatits developmental history. Although Analysis was conceived in the 17th century during the Scienti?c Revolution, it has taken nearly two hundred years to establish its theoretical basis. Kepler, Galileo, Descartes, Fermat, Newton and Leibniz were among those who contributed to its genesis. Deep conceptual changes in Analysis were brought about in the 19th century by Cauchy and Weierstrass. Furthermore, modern concepts such as open and closed sets were introduced in the 1900s. Today nearly every undergraduate mathematics program requires at least one semester of Real Analysis. Often, students consider this course to be the most challenging or even intimidating of all their mathematics major requirements. The primary goal of this book is to alleviate those concerns by systematically solving the problems related to the core concepts of most analysis courses. In doing so, we hope that learning analysis becomes less taxing and thereby more satisfying.

Author : Boris P. Demidovič
Publisher : Beekman Books Incorporated
Page : 496 pages
File Size : 48,6 Mb
Release : 1976
Category : Mathematics
ISBN : 0846407612

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Problems in Mathematical Analysis by Boris P. Demidovič Pdf

Author : Wiesława J. Kaczor,Maria T. Nowak
Publisher : American Mathematical Soc.
Page : 396 pages
File Size : 43,5 Mb
Release : 2000
Category : MATHEMATICS
ISBN : 9780821820506

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Problems in Mathematical Analysis: Real numbers, sequences, and series by Wiesława J. Kaczor,Maria T. Nowak Pdf

Solutions for all the problems are provided."--BOOK JACKET.

Author : James F. Epperson
Publisher : John Wiley & Sons
Page : 672 pages
File Size : 53,6 Mb
Release : 2021-07-21
Category : Mathematics
ISBN : 9781119604747

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An Introduction to Numerical Methods and Analysis by James F. Epperson Pdf

The new edition of the popular introductory textbook on numerical approximation methods and mathematical analysis, with a unique emphasis on real-world application An Introduction to Numerical Methods and Analysis helps students gain a solid understanding of a wide range of numerical approximation methods for solving problems of mathematical analysis. Designed for entry-level courses on the subject, this popular textbook maximizes teaching flexibility by first covering basic topics before gradually moving to more advanced material in each chapter and section. Throughout the text, students are provided clear and accessible guidance on a wide range of numerical methods and analysis techniques, including root-finding, numerical integration, interpolation, solution of systems of equations, and many others. This fully revised third edition contains new sections on higher-order difference methods, the bisection and inertia method for computing eigenvalues of a symmetric matrix, a completely re-written section on different methods for Poisson equations, and spectral methods for higher-dimensional problems. New problem sets—ranging in difficulty from simple computations to challenging derivations and proofs—are complemented by computer programming exercises, illustrative examples, and sample code. This acclaimed textbook: Explains how to both construct and evaluate approximations for accuracy and performance Covers both elementary concepts and tools and higher-level methods and solutions Features new and updated material reflecting new trends and applications in the field Contains an introduction to key concepts, a calculus review, an updated primer on computer arithmetic, a brief history of scientific computing, a survey of computer languages and software, and a revised literature review Includes an appendix of proofs of selected theorems and a companion website with additional exercises, application models, and supplemental resources An Introduction to Numerical Methods and Analysis, Third Edition is the perfect textbook for upper-level undergraduate students in mathematics, science, and engineering courses, as well as for courses in the social sciences, medicine, and business with numerical methods and analysis components.

Author : James F. Epperson
Publisher : John Wiley & Sons
Page : 308 pages
File Size : 44,8 Mb
Release : 2021-09-03
Category : Mathematics
ISBN : 9781119604594

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Solutions Manual to accompany An Introduction to Numerical Methods and Analysis by James F. Epperson Pdf

A solutions manual to accompany An Introduction to Numerical Methods and Analysis, Third Edition An Introduction to Numerical Methods and Analysis helps students gain a solid understanding of a wide range of numerical approximation methods for solving problems of mathematical analysis. Designed for entry-level courses on the subject, this popular textbook maximizes teaching flexibility by first covering basic topics before gradually moving to more advanced material in each chapter and section. Throughout the text, students are provided clear and accessible guidance on a wide range of numerical methods and analysis techniques, including root-finding, numerical integration, interpolation, solution of systems of equations, and many others. This fully revised third edition contains new sections on higher-order difference methods, the bisection and inertia method for computing eigenvalues of a symmetric matrix, a completely re-written section on different methods for Poisson equations, and spectral methods for higher-dimensional problems. New problem sets—ranging in difficulty from simple computations to challenging derivations and proofs—are complemented by computer programming exercises, illustrative examples, and sample code. This acclaimed textbook: Explains how to both construct and evaluate approximations for accuracy and performance Covers both elementary concepts and tools and higher-level methods and solutions Features new and updated material reflecting new trends and applications in the field Contains an introduction to key concepts, a calculus review, an updated primer on computer arithmetic, a brief history of scientific computing, a survey of computer languages and software, and a revised literature review Includes an appendix of proofs of selected theorems and author-hosted companion website with additional exercises, application models, and supplemental resources