Mathematical Analysis An Introduction [Paperback]

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.This book introduces analysis, from the basics of mathematical proposition and proof to differentiation, integration and more. Includes Stokes theorem and such applications as Brouwer's fixed point theorem, and the Dirichlet principle for harmonic functions.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 analÓ5