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001451140 001__ 1451140
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001451140 019__ $$a1350690436
001451140 020__ $$a9783031157653$$q(electronic bk.)
001451140 020__ $$a3031157656$$q(electronic bk.)
001451140 020__ $$z9783031157646
001451140 020__ $$z3031157648
001451140 0247_ $$a10.1007/978-3-031-15765-3$$2doi
001451140 035__ $$aSP(OCoLC)1350671603
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001451140 049__ $$aISEA
001451140 050_4 $$aQA300
001451140 08204 $$a515$$223/eng/20221116
001451140 1001_ $$aZalduendo, Ignacio,$$eauthor.
001451140 24510 $$aCalculus off the beaten path :$$ba journey through its fundamental ideas /$$cIgnacio Zalduendo.
001451140 264_1 $$aCham :$$bSpringer,$$c[2022]
001451140 264_4 $$c©2022
001451140 300__ $$a1 online resource (xvi, 213 pages) :$$billustrations (some color).
001451140 336__ $$atext$$btxt$$2rdacontent
001451140 337__ $$acomputer$$bc$$2rdamedia
001451140 338__ $$aonline resource$$bcr$$2rdacarrier
001451140 4901_ $$aSpringer undergraduate mathematics series. SUMS readings
001451140 504__ $$aIncludes bibliographical references and index.
001451140 5050_ $$aIntro -- Preface -- Contents -- Introduction -- 2400 Years of Calculus -- Calculus and Education -- 1 The Real Numbers -- The Rational Line -- Density of Q -- Some Basic Notions -- Irrationality of Q -- From Eudoxus to Dedekind -- The Real Line -- Dyadic Series-A Construction of R -- The Scarcity of Q -- The Completeness of R -- Cardinality -- Exercises -- 2 Sequences and Series -- Sequences -- Limits of Sequences -- Cantor's Nested Intervals Theorem -- Subsequences -- Series -- The Harmonic Series -- Series of Positive Terms -- Series with Positive and Negative Terms
001451140 5058_ $$aThe Riemann Series Theorem -- Absolute and Unconditional Convergence -- Exercises -- 3 Functions -- The Elementary Functions -- Polynomials -- Circular Functions -- The Exponential Function: Bernoulli's Inequality -- Irrationality of e -- Convergence of k=1∞(1+ak) and of k=1∞ak -- Hyperbolic Functions -- Injectivity and Inverse Functions -- Curves in the Plane: Parametrized Curves -- The Cycloid -- Pythagorean Triples -- Continuity -- Bolzano and Weierstrass -- Limits -- Limits in Ancient Greece: The Area of a Circle -- Three Important Limits -- Exercises -- 4 The Derivative -- Derivative
001451140 5058_ $$aIntegration and Products: Integration by Parts -- Stirling's Formula -- Integration and Composition: Integration by Substitution -- A Note on Notation -- Length of Curves. The Catenary -- Area Enclosed by a Simple Closed Curve -- Exercises -- 6 More Derivatives -- Second Derivative, Best-Fitting Parabola, and Curvature -- The Taylor Polynomial of Order Two -- Curvature -- Random Walk and the Gauss Curve -- The Taylor Series -- Exercises -- 7 Convexity and the Isoperimetric Inequality -- The Arithmetic-Geometric Inequality -- Convexity -- Young, Hölder, Jensen, Cauchy-Schwarz...
001451140 5058_ $$aThe Isoperimetric Inequality -- Exercises -- 8 More Integrals -- Volume -- Double Integrals -- The Basel Problem -- Solids of Revolution -- Integration of e -- Density Functions, Barycenter, and Expectation -- Center of Mass or Barycenter -- Pappus' Theorem -- The Method -- Surface Area -- Normal Distribution. Gauss, Laplace, and Stirling -- Exercises -- 9 The Gamma Function -- The Gamma Function -- Weierstrass' Formula -- Growth of the Harmonic Series, Again -- Exercises -- Bibliography -- Index
001451140 506__ $$aAccess limited to authorized users.
001451140 520__ $$aThis textbook provides a gentle overview of fundamental concepts related to one-variable calculus. The original approach is a result of the authors forty years of experience in teaching the subject at universities around the world. In this book, Dr. Zalduendo makes use of the history of mathematics and a friendly, conversational approach to attract the attention of the student, emphasizing what is more conceptually relevant and putting key notions in a historical perspective. Such an approach was conceived to help them to overcome potential difficulties in teaching and learning of this subject caused, in many cases, by an excess of technicalities and computations. Besides covering the core of the discipline real number, sequences and series, functions, derivatives, integrals, convexity and inequalities the book is enriched by "side trips" to relevant subjects not usually seen in traditional calculus textbooks, touching on topics like curvature, the isoperimetric inequality, Riemanns rearrangement theorem, Snells law, Buffons needle problem, Gregorys series, random walk and the Gauss curve, and more. An insightful collection of exercises and applications completes this book, making it ideal as a supplementary textbook for a calculus course or the main textbook for an honors course on the subject.
001451140 588__ $$aOnline resource; title from PDF title page (SpringerLink, viewed November 16, 2022).
001451140 650_0 $$aCalculus.
001451140 655_0 $$aElectronic books.
001451140 77608 $$iPrint version: $$z3031157648$$z9783031157646$$w(OCoLC)1337522924
001451140 830_0 $$aSpringer undergraduate mathematics series.$$pSUMS readings.
001451140 852__ $$bebk
001451140 85640 $$3Springer Nature$$uhttps://univsouthin.idm.oclc.org/login?url=https://link.springer.com/10.1007/978-3-031-15765-3$$zOnline Access$$91397441.1
001451140 909CO $$ooai:library.usi.edu:1451140$$pGLOBAL_SET
001451140 980__ $$aBIB
001451140 980__ $$aEBOOK
001451140 982__ $$aEbook
001451140 983__ $$aOnline
001451140 994__ $$a92$$bISE