A First Course in Real Analysis - Livres de poche

EAN (ISBN-13): 9781461264330
ISBN (ISBN-10): 1461264332
Version reliée
Livre de poche
Date de parution: 2012
Editeur: Springer

Livre dans la base de données depuis 2014-10-09T22:41:17+02:00 (Paris)
Page de détail modifiée en dernier sur 2023-09-15T09:21:39+02:00 (Paris)
ISBN/EAN: 9781461264330

ISBN - Autres types d'écriture:
1-4612-6433-2, 978-1-4612-6433-0
Autres types d'écriture et termes associés:
Auteur du livre: berberian, sterling
Titre du livre: first course real analysis

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Données de l'éditeur

Auteur: Sterling K. Berberian
Titre: Undergraduate Texts in Mathematics; A First Course in Real Analysis
Editeur: Springer; Springer US
240 Pages
Date de parution: 2012-09-07
New York; NY; US
Imprimé / Fabriqué en
Langue: Anglais
53,49 € (DE)
54,99 € (AT)
59,00 CHF (CH)
POD
XI, 240 p.

BC; Hardcover, Softcover / Mathematik/Analysis; Reelle Analysis, Real-Variablen; Verstehen; Finite; Mean value theorem; Rack; Riemann integral; boundary element method; calculus; character; derivative; form; function; proof; real analysis; sets; system; theorem; Real Functions; BB; EA; BA

1 Axioms for the Field ? of Real Numbers.- §1.1. The field axioms.- §1.2. The order axioms.- §1.3. Bounded sets, LUB and GLB.- §1.4. The completeness axiom (existence of LUB’s).- 2 First Properties of ?.- §2.1. Dual of the completeness axiom (existence of GLB’s).- §2.2. Archimedean property.- §2.3. Bracket function.- §2.4. Density of the rationals.- §2.5. Monotone sequences.- §2.6. Theorem on nested intervals.- §2.7. Dedekind cut property.- §2.8. Square roots.- §2.9. Absolute value.- 3 Sequences of Real Numbers, Convergence.- §3.1. Bounded sequences.- §3.2. Ultimately, frequently.- §3.3. Null sequences.- §3.4. Convergent sequences.- §3.5. Subsequences, Weierstrass-Bolzano theorem.- §3.6. Cauchy’s criterion for convergence.- §3.7. limsup and liminf of a bounded sequence.- 4 Special Subsets of ?.- §4.1. Intervals.- §4.2. Closed sets.- §4.3. Open sets, neighborhoods.- §4.4. Finite and infinite sets.- §4.5. Heine-Borel covering theorem.- 5 Continuity.- §5.1. Functions, direct images, inverse images.- §5.2. Continuity at a point.- §5.3. Algebra of continuity.- §5.4. Continuous functions.- §5.5. One-sided continuity.- §5.6. Composition.- 6 Continuous Functions on an Interval.- §6.1. Intermediate value theorem.- §6.2. n’th roots.- §6.3. Continuous functions on a closed interval.- §6.4. Monotonic continuous functions.- §6.5. Inverse function theorem.- §6.6. Uniform continuity.- 7 Limits of Functions.- §7.1. Deleted neighborhoods.- §7.2. Limits.- §7.3. Limits and continuity.- §7.4. ?,?characterization of limits.- §7.5. Algebra of limits.- 8 Derivatives.- §8.1. Differentiability.- §8.2. Algebra of derivatives.- §8.3. Composition (Chain Rule).- §8.4. Local max and min.- §8.5. Mean value theorem.- 9 Riemann Integral.- §9.1. Upper and lower integrals: the machinery.- §9.2. First properties of upper and lower integrals.- §9.3. Indefinite upper and lower integrals.- §9.4. Riemann-integrable functions.- §9.5. An application: log and exp.- §9.6. Piecewise pleasant functions.- §9.7.Darboux’s theorem.- §9.8. The integral as a limit of Riemann sums.- 10 Infinite Series.- §10.1. Infinite series: convergence, divergence.- §10.2. Algebra of convergence.- §10.3. Positive-term series.- §10.4. Absolute convergence.- 11 Beyond the Riemann Integral.- §11.1 Negligible sets.- §11.2 Absolutely continuous functions.- §11.3 The uniqueness theorem.- §11.4 Lebesgue’s criterion for Riemann-integrability.- §11.5 Lebesgue-integrable functions.- §A.1 Proofs, logical shorthand.- §A.2 Set notations.- §A.3 Functions.- §A.4 Integers.- Index of Notations.