the theory of calculus Ross, Kenneth A. creator Lopez, Jorge M. text bibliography nyu New York Springer c2013 2013 2nd ed. monographic eng

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xi, 409 p. : ill. For over three decades, this best-selling classic has been used by thousands of students in the United States and abroad as a must-have textbook for a transitional course from calculus to analysis. It has proven to be very useful for mathematics majors who have no previous experience with rigorous proofs. Its friendly style unlocks the mystery of writing proofs, while carefully examining the theoretical basis for calculus. Proofs are given in full, and the large number of well-chosen examples and exercises range from routine to challenging. The second edition preserves the book's clear and concise style, illuminating discussions, and simple, well-motivated proofs. New topics include material on the irrationality of pi, the Baire category theorem, Newton's method and the secant method, and continuous nowhere-differentiable functions. 1. Introduction -- 2. Sequences -- 3. Continuity -- 4. Sequences and series of functions -- 5. Differentiation -- 6. Integration -- 7. Capstone -- Appendix on set notation -- Selected hints and answers. Kenneth A. Ross ; in collaboration with Jorge M. López. Includes bibliographical references (pages 397-401) and indexes. Calculus QA303 .R63 2013 9781461462705 (hbk.) 1461462703 (hbk.) 2013950414 210218 ocn828140570