02895 a2200241 4500008004500000020001800045082001900063100002900082245003100111250001100142260002900153300001500182440004700197504021800244520174600462650003102208650005002239650003902289650006502328942001202393999001902405952022902424160816b2015 xxu||||| |||| 00| 0 eng d a9783319177700 a515bP8R3-2015 aPugh, Charles C.9335555 aReal mathematical analysis a2nd ed bSpringerc2015aNew York axi, 478 p. aUndergraduate Texts in Mathematics9335556 aTable of Contents:
Chapter I Real Numbers
Chapter II A Taste of Topology
Chapter III Functions of a Real Variable
Chapter IV Function Spaces
Chapter V Multivariable Calculus
Chapter VI Lebesgue Theory
aBased on an honors course taught by the author at UC Berkeley, this introduction to undergraduate real analysis gives a different emphasis by stressing the importance of pictures and hard problems. Topics include: a natural construction of the real numbers, four-dimensional visualization, basic point-set topology, function spaces, multivariable calculus via differential forms (leading to a simple proof of the Brouwer Fixed Point Theorem), and a pictorial treatment of Lebesgue theory. Over 150 detailed illustrations elucidate abstract concepts and salient points in proofs. The exposition is informal and relaxed, with many helpful asides, examples, some jokes, and occasional comments from mathematicians, such as Littlewood, Dieudonné, and Osserman. This book thus succeeds in being more comprehensive, more comprehensible, and more enjoyable, than standard introductions to analysis.
New to the second edition of Real Mathematical Analysis is a presentation of Lebesgue integration done almost entirely using the under graph approach of Burkill. Payoffs include: concise picture proofs of the Monotone and Dominated Convergence Theorems, a one-line/one-picture proof of Fubini's theorem from Cavalieri’s Principle, and, in many cases, the ability to see an integral result from measure theory. The presentation includes Vitali’s Covering Lemma, density points — which are rarely treated in books at this level — and the almost everywhere differentiability of monotone functions. Several new exercises now join a collection of over 500 exercises that pose interesting challenges and introduce special topics to the student keen on mastering this beautiful subject.
(http://www.springer.com/gp/book/9783319177700#aboutBook) aMathematical analysis9661 aMathematics - Real numbers - Topology9335557 aFunctions - Real variables9335558 aMultivariable calculus - Lebesgue theory - Exercises9335559 2ddccBK c204360d204360 00102ddc406515_000000000000000_P8R32015708NFIC9342730aVSLbVSLcSlot 1373 (0 Floor, East Wing)d2016-08-04e12g2825.37kSlot 1373 (0 Floor, East Wing)l3m5o515 P8R3-2015p192630r2019-10-15s2019-09-03v3531.72yBK