This is a textbook suitable for a year-long course in analysis at the ad� vanced undergraduate or possibly beginning-graduate level. It is intended for students with a strong background in calculus and linear algebra, and a strong motivation to learn mathematics for its own sake. At this stage of their education, such students are generally given a course in abstract algebra, and a course in analysis, which give the fundamentals of these two areas, as mathematicians today conceive them. Mathematics is now a subject splintered into many specialties and sub� specialties, but most of it can be placed roughly into three categories: al� gebra, geometry, and analysis. In fact, almost all mathematics done today is a mixture of algebra, geometry and analysis, and some of the most in� teresting results are obtained by the application of analysis to algebra, say, or geometry to analysis, in a fresh and surprising way. What then do these categories signify? Algebra is the mathematics that arises from the ancient experiences of addition and multiplication of whole numbers; it deals with the finite and discrete. Geometry is the mathematics that grows out of spatial experience; it is concerned with shape and form, and with measur� ing, where algebra deals with counting.

From the Back Cover

Mathematical Analysis: An Introduction is a textbook containing more than enough material for a year-long course in analysis at the advanced undergraduate or beginning graduate level. The book begins with a brief discussion of sets and mappings, describes the real number field, and proceeds to a treatment of real-valued functions of a real variable. Separate chapters are devoted to the ideas of convergent sequences and series, continuous functions, differentiation, and the Riemann integral. The middle chapters cover general topology and a miscellany of applications: the Weierstrass and Stone-Weierstrass approximation theorems, the existence of geodesics in compact metric spaces, elements of Fourier analysis, and the Weyl equidistribution theorem. Next comes a discussion of differentiation of vector-valued functions of several real variables, followed by a brief treatment of measure and integration (in a general setting, but with emphasis on Lebesgue theory in Euclidean space). The final part of the book deals with manifolds, differential forms, and Stokes' theorem, which is applied to prove Brouwer's fixed point theorem and to derive the basic properties of harmonic functions, such as the Dirichlet principle.

"About this title" may belong to another edition of this title.

Store Description

Better World Books (https://www.BetterWorldBooks.com) is a for-profit, socially conscious business and a global online bookseller that collects and sells new and used books online, matching each purchase with a book donation. Each sale generates funds for literacy and education initiatives in the U.S., the UK, and around the world. Since its launch in 2003, Better World Books has raised $33 million for libraries and literacy, donated over 32 million books, and reused or recycled more than 397 million books.

Visit Seller's Storefront

Seller's business information

Better World Books Marketplace, Inc.
55740 Currant Road, Mishawaka, IN, 46545, U.S.A.

Sale & Shipping Terms

Terms of Sale

Better World Books (BWB) values your satisfaction and offers you returns within thirty (30) days after the estimated delivery date on most items. All returned items must be in the original condition; used items should include the SKU sticker located on the spine or back of the product.

If you have an incomplete, incorrect, or damaged shipment, please contact our Customer Care team via Abebooks contact seller options before proceeding with the return.Please keep in mind that because we deal mostl...

More Information