000			02730nmm a22002655i 4500
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008			150729s2015 sz | s |||| 0|eng d
020			_a9783319177717 _9978-3-319-17771-7
082			_a515.42 _223
100			_aPugh, Charles Chapman. _919994
245			_aReal Mathematical Analysis _h[electronic resource] / _cby Charles Chapman Pugh.
250			_a2nd ed. 2015.
260			_aCham : _bSpringer International Publishing : _bImprint: Springer, _c2015.
300			_aXI, 478 p. 1 illus. in color. _bonline resource.
505			_aReal Numbers -- A Taste of Topology -- Functions of a Real Variable -- Function Spaces -- Multivariable Calculus -- Lebesgue Theory.
520			_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 undergraph 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.
650			_aMeasure theory. _919995
650			_aFunctions of real variables. _919996
650			_aSequences (Mathematics). _919997
650			_aMeasure and Integration. _919998
650			_aReal Functions. _919999
650			_aSequences, Series, Summability. _920000
856			_uhttps://doi.org/10.1007/978-3-319-17771-7
942			_cEBK
999			_c13592 _d13592