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Author: Graeme L. Cohen
Publisher: Cambridge University Press
ISBN: 9780511755125
Category : Mathematics
Languages : en
Pages : 333
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Book Description
Designed for one-semester courses at the senior undergraduate level, this book is written for mathematics students and teachers, as well as others needing to learn mathematical analysis for engineering, physics, biology or finance. Nominal divisions between pure and applied mathematics have been merged to provide easier access. Applications are included from differential and integral equations, systems of linear algebraic equations, approximation theory, numerical analysis and quantum mechanics.
Author: Graeme L. Cohen
Publisher: Cambridge University Press
ISBN: 9780511755125
Category : Mathematics
Languages : en
Pages : 333
Get Book
Book Description
Designed for one-semester courses at the senior undergraduate level, this book is written for mathematics students and teachers, as well as others needing to learn mathematical analysis for engineering, physics, biology or finance. Nominal divisions between pure and applied mathematics have been merged to provide easier access. Applications are included from differential and integral equations, systems of linear algebraic equations, approximation theory, numerical analysis and quantum mechanics.
Author: E. T. Whittaker
Publisher: Cambridge University Press
ISBN: 9780521588072
Category : Mathematics
Languages : en
Pages : 620
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Book Description
This classic text is known to and used by thousands of mathematicians and students of mathematics thorughout the world. It gives an introduction to the general theory of infinite processes and of analytic functions together with an account of the principle transcendental functions.
Author: Gerald B. Folland
Publisher: John Wiley & Sons
ISBN: 1118626397
Category : Mathematics
Languages : en
Pages : 309
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Book Description
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.
Author: Graeme Laurence Cohen
Publisher:
ISBN: 9780511070129
Category : Mathematical analysis
Languages : en
Pages : 333
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Book Description
Designed for one-semester courses for senior undergraduates, this book approaches topics initially through convergence of sequences in metric space. However, the alternative topological approach is also described. Applications are included from differential and integral equations, systems of linear algebraic equations, approximation theory, numerical analysis and quantum mechanics.
Author: William J. Terrell
Publisher: American Mathematical Soc.
ISBN: 1470451352
Category : Education
Languages : en
Pages : 607
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Book Description
A Passage to Modern Analysis is an extremely well-written and reader-friendly invitation to real analysis. An introductory text for students of mathematics and its applications at the advanced undergraduate and beginning graduate level, it strikes an especially good balance between depth of coverage and accessible exposition. The examples, problems, and exposition open up a student's intuition but still provide coverage of deep areas of real analysis. A yearlong course from this text provides a solid foundation for further study or application of real analysis at the graduate level. A Passage to Modern Analysis is grounded solidly in the analysis of R and Rn, but at appropriate points it introduces and discusses the more general settings of inner product spaces, normed spaces, and metric spaces. The last five chapters offer a bridge to fundamental topics in advanced areas such as ordinary differential equations, Fourier series and partial differential equations, Lebesgue measure and the Lebesgue integral, and Hilbert space. Thus, the book introduces interesting and useful developments beyond Euclidean space where the concepts of analysis play important roles, and it prepares readers for further study of those developments.
Author: Shmuel Kantorovitz
Publisher: Oxford University Press on Demand
ISBN: 0198526563
Category : Psychology
Languages : en
Pages : 447
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Book Description
This text is based on lectures given by the author in measure theory, functional analysis, Banach algebras, spectral theory (of bounded and unbounded operators), semigroups of operators, probability and mathematical statistics, and partial differential equations.
Author: John J. Benedetto
Publisher: Springer Science & Business Media
ISBN: 0817646566
Category : Mathematics
Languages : en
Pages : 575
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Book Description
This textbook and treatise begins with classical real variables, develops the Lebesgue theory abstractly and for Euclidean space, and analyzes the structure of measures. The authors' vision of modern real analysis is seen in their fascinating historical commentary and perspectives with other fields. There are comprehensive treatments of the role of absolute continuity, the evolution of the Riesz representation theorem to Radon measures and distribution theory, weak convergence of measures and the Dieudonné–Grothendieck theorem, modern differentiation theory, fractals and self-similarity, rearrangements and maximal functions, and surface and Hausdorff measures. There are hundreds of illuminating exercises, and extensive, focused appendices on functional and Fourier analysis. The presentation is ideal for the classroom, self-study, or professional reference.
Author: Wolfgang Tutschke
Publisher: CRC Press
ISBN: 1584884789
Category : Mathematics
Languages : en
Pages : 480
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Book Description
Like real analysis, complex analysis has generated methods indispensable to mathematics and its applications. Exploring the interactions between these two branches, this book uses the results of real analysis to lay the foundations of complex analysis and presents a unified structure of mathematical analysis as a whole. To set the groundwork and mitigate the difficulties newcomers often experience, An Introduction to Complex Analysis begins with a complete review of concepts and methods from real analysis, such as metric spaces and the Green-Gauss Integral Formula. The approach leads to brief, clear proofs of basic statements - a distinct advantage for those mainly interested in applications. Alternate approaches, such as Fichera's proof of the Goursat Theorem and Estermann's proof of the Cauchy's Integral Theorem, are also presented for comparison. Discussions include holomorphic functions, the Weierstrass Convergence Theorem, analytic continuation, isolated singularities, homotopy, Residue theory, conformal mappings, special functions and boundary value problems. More than 200 examples and 150 exercises illustrate the subject matter and make this book an ideal text for university courses on complex analysis, while the comprehensive compilation of theories and succinct proofs make this an excellent volume for reference.
Author: Voxman
Publisher: Routledge
ISBN: 1351468677
Category : Mathematics
Languages : en
Pages : 428
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Book Description
Advanced Calculus: An Introduction to Modem Analysis, an advanced undergraduate textbook,provides mathematics majors, as well as students who need mathematics in their field of study,with an introduction to the theory and applications of elementary analysis. The text presents, inan accessible form, a carefully maintained balance between abstract concepts and applied results ofsignificance that serves to bridge the gap between the two- or three-cemester calculus sequence andsenior/graduate level courses in the theory and appplications of ordinary and partial differentialequations, complex variables, numerical methods, and measure and integration theory.The book focuses on topological concepts, such as compactness, connectedness, and metric spaces,and topics from analysis including Fourier series, numerical analysis, complex integration, generalizedfunctions, and Fourier and Laplace transforms. Applications from genetics, spring systems,enzyme transfer, and a thorough introduction to the classical vibrating string, heat transfer, andbrachistochrone problems illustrate this book's usefulness to the non-mathematics major. Extensiveproblem sets found throughout the book test the student's understanding of the topics andhelp develop the student's ability to handle more abstract mathematical ideas.Advanced Calculus: An Introduction to Modem Analysis is intended for junior- and senior-levelundergraduate students in mathematics, biology, engineering, physics, and other related disciplines.An excellent textbook for a one-year course in advanced calculus, the methods employed in thistext will increase students' mathematical maturity and prepare them solidly for senior/graduatelevel topics. The wealth of materials in the text allows the instructor to select topics that are ofspecial interest to the student. A two- or three ll?lester calculus sequence is required for successfuluse of this book.
Author: Avner Friedman
Publisher: Courier Corporation
ISBN: 9780486640624
Category : Mathematics
Languages : en
Pages : 276
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Book Description
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.
