Download or read book A Modern Introduction to Mathematical Analysis written by Alessandro Fonda and published by Springer Nature. This book was released on 2023-03-21 with total page 442 pages. Available in PDF, EPUB and Kindle. Book excerpt: This textbook presents all the basics for the first two years of a course in mathematical analysis, from the natural numbers to Stokes-Cartan Theorem. The main novelty which distinguishes this book is the choice of introducing the Kurzweil-Henstock integral from the very beginning. Although this approach requires a small additional effort by the student, it will be compensated by a substantial advantage in the development of the theory, and later on when learning about more advanced topics. The text guides the reader with clarity in the discovery of the many different subjects, providing all necessary tools – no preliminaries are needed. Both students and their instructors will benefit from this book and its novel approach, turning their course in mathematical analysis into a gratifying and successful experience.
Download or read book Mathematical Analysis written by Andrew Browder and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 348 pages. Available in PDF, EPUB and Kindle. Book excerpt: Among the traditional purposes of such an introductory course is the training of a student in the conventions of pure mathematics: acquiring a feeling for what is considered a proof, and supplying literate written arguments to support mathematical propositions. To this extent, more than one proof is included for a theorem - where this is considered beneficial - so as to stimulate the students' reasoning for alternate approaches and ideas. The second half of this book, and consequently the second semester, covers differentiation and integration, as well as the connection between these concepts, as displayed in the general theorem of Stokes. Also included are some beautiful applications of this theory, such as Brouwer's fixed point theorem, and the Dirichlet principle for harmonic functions. Throughout, reference is made to earlier sections, so as to reinforce the main ideas by repetition. Unique in its applications to some topics not usually covered at this level.
Download or read book Foundations of Mathematical Analysis written by Richard Johnsonbaugh and published by Courier Corporation. This book was released on 2012-09-11 with total page 450 pages. Available in PDF, EPUB and Kindle. Book excerpt: Definitive look at modern analysis, with views of applications to statistics, numerical analysis, Fourier series, differential equations, mathematical analysis, and functional analysis. More than 750 exercises; some hints and solutions. 1981 edition.
Download or read book Intermediate Mathematical Analysis written by Anthony E. Labarre and published by Courier Corporation. This book was released on 2008-01-01 with total page 276 pages. Available in PDF, EPUB and Kindle. Book excerpt: Geared toward those who have studied elementary calculus, this book stresses concepts rather than techniques. It prepares students for a first demanding course in analysis, dealing primarily with real-valued functions of a real variable. Complex numbers appear only in supplements and the last two chapters. 1968 edition.
Download or read book Mathematical Analysis of Physical Problems written by Philip Russell Wallace and published by Courier Corporation. This book was released on 1984-01-01 with total page 644 pages. Available in PDF, EPUB and Kindle. Book excerpt: This mathematical reference for theoretical physics employs common techniques and concepts to link classical and modern physics. It provides the necessary mathematics to solve most of the problems. Topics include the vibrating string, linear vector spaces, the potential equation, problems of diffusion and attenuation, probability and stochastic processes, and much more. 1972 edition.
Download or read book An Introduction to Mathematical Analysis for Economic Theory and Econometrics written by Dean Corbae and published by Princeton University Press. This book was released on 2009-02-17 with total page 696 pages. Available in PDF, EPUB and Kindle. Book excerpt: Providing an introduction to mathematical analysis as it applies to economic theory and econometrics, this book bridges the gap that has separated the teaching of basic mathematics for economics and the increasingly advanced mathematics demanded in economics research today. Dean Corbae, Maxwell B. Stinchcombe, and Juraj Zeman equip students with the knowledge of real and functional analysis and measure theory they need to read and do research in economic and econometric theory. Unlike other mathematics textbooks for economics, An Introduction to Mathematical Analysis for Economic Theory and Econometrics takes a unified approach to understanding basic and advanced spaces through the application of the Metric Completion Theorem. This is the concept by which, for example, the real numbers complete the rational numbers and measure spaces complete fields of measurable sets. Another of the book's unique features is its concentration on the mathematical foundations of econometrics. To illustrate difficult concepts, the authors use simple examples drawn from economic theory and econometrics. Accessible and rigorous, the book is self-contained, providing proofs of theorems and assuming only an undergraduate background in calculus and linear algebra. Begins with mathematical analysis and economic examples accessible to advanced undergraduates in order to build intuition for more complex analysis used by graduate students and researchers Takes a unified approach to understanding basic and advanced spaces of numbers through application of the Metric Completion Theorem Focuses on examples from econometrics to explain topics in measure theory
Download or read book Introduction to Analysis written by Maxwell Rosenlicht and published by Courier Corporation. This book was released on 2012-05-04 with total page 270 pages. Available in PDF, EPUB and Kindle. Book excerpt: Written for junior and senior undergraduates, this remarkably clear and accessible treatment covers set theory, the real number system, metric spaces, continuous functions, Riemann integration, multiple integrals, and more. 1968 edition.
Download or read book Spaces An Introduction to Real Analysis written by Tom L. Lindstrøm and published by American Mathematical Soc.. This book was released on 2017-11-28 with total page 384 pages. Available in PDF, EPUB and Kindle. Book excerpt: Spaces is a modern introduction to real analysis at the advanced undergraduate level. It is forward-looking in the sense that it first and foremost aims to provide students with the concepts and techniques they need in order to follow more advanced courses in mathematical analysis and neighboring fields. The only prerequisites are a solid understanding of calculus and linear algebra. Two introductory chapters will help students with the transition from computation-based calculus to theory-based analysis. The main topics covered are metric spaces, spaces of continuous functions, normed spaces, differentiation in normed spaces, measure and integration theory, and Fourier series. Although some of the topics are more advanced than what is usually found in books of this level, care is taken to present the material in a way that is suitable for the intended audience: concepts are carefully introduced and motivated, and proofs are presented in full detail. Applications to differential equations and Fourier analysis are used to illustrate the power of the theory, and exercises of all levels from routine to real challenges help students develop their skills and understanding. The text has been tested in classes at the University of Oslo over a number of years.
Download or read book Elementary Analysis written by Kenneth A. Ross and published by CUP Archive. This book was released on 2014-01-15 with total page 192 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Real Analysis written by Gerald B. Folland and published by John Wiley & Sons. This book was released on 2013-06-11 with total page 368 pages. Available in PDF, EPUB and Kindle. Book excerpt: An in-depth look at real analysis and its applications-now expanded and revised. This new edition of the widely used analysis book continues to cover real analysis in greater detail and at a more advanced level than most books on the subject. Encompassing several subjects that underlie much of modern analysis, the book focuses on measure and integration theory, point set topology, and the basics of functional analysis. It illustrates the use of the general theories and introduces readers to other branches of analysis such as Fourier analysis, distribution theory, and probability theory. This edition is bolstered in content as well as in scope-extending its usefulness to students outside of pure analysis as well as those interested in dynamical systems. The numerous exercises, extensive bibliography, and review chapter on sets and metric spaces make Real Analysis: Modern Techniques and Their Applications, Second Edition invaluable for students in graduate-level analysis courses. New features include: * Revised material on the n-dimensional Lebesgue integral. * An improved proof of Tychonoff's theorem. * Expanded material on Fourier analysis. * A newly written chapter devoted to distributions and differential equations. * Updated material on Hausdorff dimension and fractal dimension.
Download or read book Introduction to Real Analysis written by Christopher Heil and published by Springer. This book was released on 2019-07-20 with total page 386 pages. Available in PDF, EPUB and Kindle. Book excerpt: Developed over years of classroom use, this textbook provides a clear and accessible approach to real analysis. This modern interpretation is based on the author’s lecture notes and has been meticulously tailored to motivate students and inspire readers to explore the material, and to continue exploring even after they have finished the book. The definitions, theorems, and proofs contained within are presented with mathematical rigor, but conveyed in an accessible manner and with language and motivation meant for students who have not taken a previous course on this subject. The text covers all of the topics essential for an introductory course, including Lebesgue measure, measurable functions, Lebesgue integrals, differentiation, absolute continuity, Banach and Hilbert spaces, and more. Throughout each chapter, challenging exercises are presented, and the end of each section includes additional problems. Such an inclusive approach creates an abundance of opportunities for readers to develop their understanding, and aids instructors as they plan their coursework. Additional resources are available online, including expanded chapters, enrichment exercises, a detailed course outline, and much more. Introduction to Real Analysis is intended for first-year graduate students taking a first course in real analysis, as well as for instructors seeking detailed lecture material with structure and accessibility in mind. Additionally, its content is appropriate for Ph.D. students in any scientific or engineering discipline who have taken a standard upper-level undergraduate real analysis course.
Download or read book Foundations of Modern Analysis written by Avner Friedman and published by Courier Corporation. This book was released on 1982-01-01 with total page 276 pages. Available in PDF, EPUB and Kindle. Book excerpt: Measure and integration, metric spaces, the elements of functional analysis in Banach spaces, and spectral theory in Hilbert spaces — all in a single study. Only book of its kind. Unusual topics, detailed analyses. Problems. Excellent for first-year graduate students, almost any course on modern analysis. Preface. Bibliography. Index.
Download or read book Mathematical Physics written by Sadri Hassani and published by Springer Science & Business Media. This book was released on 2002-02-08 with total page 1052 pages. Available in PDF, EPUB and Kindle. Book excerpt: For physics students interested in the mathematics they use, and for math students interested in seeing how some of the ideas of their discipline find realization in an applied setting. The presentation strikes a balance between formalism and application, between abstract and concrete. The interconnections among the various topics are clarified both by the use of vector spaces as a central unifying theme, recurring throughout the book, and by putting ideas into their historical context. Enough of the essential formalism is included to make the presentation self-contained.
Download or read book An Introduction to Mathematical Analysis written by Robert A. Rankin and published by Elsevier. This book was released on 2016-06-06 with total page 625 pages. Available in PDF, EPUB and Kindle. Book excerpt: An Introduction to Mathematical Analysis is an introductory text to mathematical analysis, with emphasis on functions of a single real variable. Topics covered include limits and continuity, differentiability, integration, and convergence of infinite series, along with double series and infinite products. This book is comprised of seven chapters and begins with an overview of fundamental ideas and assumptions relating to the field operations and the ordering of the real numbers, together with mathematical induction and upper and lower bounds of sets of real numbers. The following chapters deal with limits of real functions; differentiability and maxima, minima, and convexity; elementary properties of infinite series; and functions defined by power series. Integration is also considered, paying particular attention to the indefinite integral; interval functions and functions of bounded variation; the Riemann-Stieltjes integral; the Riemann integral; and area and curves. The final chapter is devoted to convergence and uniformity. This monograph is intended for mathematics students.
Download or read book A Modern Introduction to Geometries written by Annita Tuller and published by . This book was released on 1967 with total page 236 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book A Modern Introduction to Probability and Statistics written by F.M. Dekking and published by Springer Science & Business Media. This book was released on 2006-03-30 with total page 485 pages. Available in PDF, EPUB and Kindle. Book excerpt: Suitable for self study Use real examples and real data sets that will be familiar to the audience Introduction to the bootstrap is included – this is a modern method missing in many other books
Download or read book An Introduction to Modern Analysis written by Vicente Montesinos and published by Springer. This book was released on 2015-05-04 with total page 884 pages. Available in PDF, EPUB and Kindle. Book excerpt: Examining the basic principles in real analysis and their applications, this text provides a self-contained resource for graduate and advanced undergraduate courses. It contains independent chapters aimed at various fields of application, enhanced by highly advanced graphics and results explained and supplemented with practical and theoretical exercises. The presentation of the book is meant to provide natural connections to classical fields of applications such as Fourier analysis or statistics. However, the book also covers modern areas of research, including new and seminal results in the area of functional analysis.
