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Undergraduate Texts in Mathematics Kenneth A. Ross Elementary Analysis The Theory of Calculus Second Edition Undergraduate Texts in Mathematics Undergraduate Texts in Mathematics Series Editors: Sheldon Axler SanFrancisco State University, San Francisco, CA, USA Kenneth Ribet University of California, Berkeley, CA, USA Advisory Board: Colin C. Adams, Williams College, Williamstown, MA, USA Alejandro Adem, University of British Columbia, Vancouver, BC, Canada RuthCharney,Brandeis University, Waltham, MA, USA Irene M. Gamba, The University of Texas at Austin, Austin, TX, USA RogerE.Howe,Yale University, New Haven, CT, USA David Jerison, Massachusetts Institute of Technology, Cambridge, MA, USA Jeffrey C. Lagarias, University of Michigan, Ann Arbor, MI, USA Jill Pipher, Brown University, Providence, RI, USA Fadil Santosa, University of Minnesota, Minneapolis, MN, USA AmieWilkinson,University of Chicago, Chicago, IL, USA Undergraduate Texts in Mathematics are generally aimed at third- and fourth- year undergraduate mathematics students at North American universities. These texts strive to provide students and teachers with new perspectives and novel approaches. The books include motivation that guides the reader to an appreciation of interrela- tions among different aspects of the subject. They feature examples that illustrate key concepts as well as exercises that strengthen understanding. For further volumes: http://www.springer.com/series/666 Kenneth A. Ross Elementary Analysis TheTheoryofCalculus Second Edition ´ In collaboration with Jorge M. Lopez, University of ´ Puerto Rico, Rıo Piedras 123
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