## Real Analysis (Google eBook)This book is written by award-winning author, Frank Morgan. It offers a simple and sophisticated point of view, reflecting Morgan's insightful teaching, lecturing, and writing style. Intended for undergraduates studying real analysis, this book builds the theory behind calculus directly from the basic concepts of real numbers, limits, and open and closed sets in $\mathbf{R n$. It gives the three characterizations of continuity: via epsilon-delta, sequences, and open sets. It givesthe three characterizations of compactness: as "closed and bounded," via sequences, and via open covers. Topics include Fourier series, the Gamma function, metric spaces, and Ascoli's Theorem. This concise text not only provides efficient proofs, but also shows students how to derive them. Theexcellent exercises are accompanied at the back of the book by select solutions. Ideally suited as an undergraduate textbook, this complete book on real analysis will fit comfortably into one semester. Frank Morgan received the first national Haimo teaching award from the Mathematical Association of America. He has also garnered top teaching awards from Rice University (Houston, TX) and MIT (Cambridge, MA). |

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Capítulo 17: Sequencias de funções

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accumulation point boundary point bounded interval Cantor set Cauchy sequence Chapter choose closed and bounded closed sets compact set Compute continuous function convergent subsequence converges absolutely converges pointwise Corollary countable sets define definition derivative differentiable domain endpoints Exercises exp(x f is continuous Figure finite subcover fn(x Fourier series fractal function f functions is continuous give a counterexample Give an example given Greek letter Hence infinitely intersection irrational Let f maximum Mean Value Theorem metric space negative terms nonnegative open cover open sets oscillation positive terms power series Proof Proposition Prove or give radius of convergence rationals real analysis real numbers Riemann integral Riemann sums sequence of functions series converges absolutely set contained set is open sets is compact sinx subintervals subsequence converging subset sup metric Suppose that f term by term totally disconnected uncountable uniform convergence uniformly continuous Weierstrass M-test