LEADER 04652nam 22007095 450 001 9910254082003321 005 20200629194445.0 010 $a3-319-28400-2 024 7 $a10.1007/978-3-319-28400-2 035 $a(CKB)3710000000602304 035 $a(SSID)ssj0001658927 035 $a(PQKBManifestationID)16439448 035 $a(PQKBTitleCode)TC0001658927 035 $a(PQKBWorkID)14990149 035 $a(PQKB)11065757 035 $a(DE-He213)978-3-319-28400-2 035 $a(MiAaPQ)EBC5588211 035 $a(Au-PeEL)EBL5588211 035 $a(OCoLC)939900301 035 $a(PPN)192222090 035 $a(EXLCZ)993710000000602304 100 $a20160209d2016 u| 0 101 0 $aeng 135 $aurnn|008mamaa 181 $ctxt 182 $cc 183 $acr 200 10$aIntroduction to Calculus and Classical Analysis$b[electronic resource] /$fby Omar Hijab 205 $a4th ed. 2016. 210 1$aCham :$cSpringer International Publishing :$cImprint: Springer,$d2016. 215 $a1 online resource (XIII, 427 p. 69 illus., 1 illus. in color.) 225 1 $aUndergraduate Texts in Mathematics,$x0172-6056 300 $aBibliographic Level Mode of Issuance: Monograph 311 $a3-319-28399-5 327 $aPreface -- A Note to the Reader -- 1. The Set of Real Numbers -- 2. Continuity -- 3. Differentiation.-4. Integration -- 5. Applications -- 6. Generalizations -- A. Solutions -- References -- Index. 330 $aThis completely self-contained text is intended either for a course in honors calculus or for an introduction to analysis. Beginning with the real number axioms, and involving rigorous analysis, computational dexterity, and a breadth of applications, it is ideal for undergraduate math majors. This fourth edition includes an additional chapter on the fundamental theorems in their full Lebesgue generality, based on the Sunrise Lemma. Key features of this text include: ? Applications from several parts of analysis, e.g., convexity, the Cantor set, continued fractions, the AGM, the theta and zeta functions, transcendental numbers, the Bessel and gamma functions, and many more; ? A heavy emphasis on computational problems, from the high-school quadratic formula to the formula for the derivative of the zeta function at zero; ? Traditionally transcendentally presented material, such as infinite products, the Bernoulli series, and the zeta functional equation, is developed over the reals; ? A self-contained treatment of the fundamental theorems of calculus in the general case using the Sunrise Lemma; ? The integral is defined as the area under the graph, while the area is defined for every subset of the plane; ? 450 problems with all the solutions presented at the back of the text. Reviews: "Chapter 5 is?an astonishing tour de force?" ?Steven G. Krantz, American Math. Monthly "For a treatment?[of infinite products and Bernoulli series] that is very close to Euler?s and even more elementary?" ?V. S. Varadarajan, Bulletin AMS "This is a very intriguing, decidedly unusual, and very satisfying treatment of calculus and introductory analysis. It's full of quirky little approaches to standard topics that make one wonder over and over again, 'Why is it never done like this?'" ?John Allen Paulos, Author of Innumeracy and A Mathematician Reads the Newspaper. 410 0$aUndergraduate Texts in Mathematics,$x0172-6056 606 $aApproximation theory 606 $aSequences (Mathematics) 606 $aSpecial functions 606 $aCombinatorics 606 $aApproximations and Expansions$3https://scigraph.springernature.com/ontologies/product-market-codes/M12023 606 $aSequences, Series, Summability$3https://scigraph.springernature.com/ontologies/product-market-codes/M1218X 606 $aSpecial Functions$3https://scigraph.springernature.com/ontologies/product-market-codes/M1221X 606 $aCombinatorics$3https://scigraph.springernature.com/ontologies/product-market-codes/M29010 615 0$aApproximation theory. 615 0$aSequences (Mathematics). 615 0$aSpecial functions. 615 0$aCombinatorics. 615 14$aApproximations and Expansions. 615 24$aSequences, Series, Summability. 615 24$aSpecial Functions. 615 24$aCombinatorics. 676 $a511.4 700 $aHijab$b Omar$4aut$4http://id.loc.gov/vocabulary/relators/aut$058868 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910254082003321 996 $aIntroduction to calculus and classical analysis$983075 997 $aUNINA