A First Course in Real Analysis (Undergraduate Texts in Mathematics) - Erstausgabe

EAN (ISBN-13): 9780387942179
ISBN (ISBN-10): 0387942173
Gebundene Ausgabe
Taschenbuch
Erscheinungsjahr: 2007
Herausgeber: Springer
256 Seiten
Gewicht: 0,549 kg
Sprache: eng/Englisch

Buch in der Datenbank seit 2007-12-30T17:01:17+01:00 (Berlin)
Detailseite zuletzt geändert am 2024-02-13T16:49:23+01:00 (Berlin)
ISBN/EAN: 9780387942179

ISBN - alternative Schreibweisen:
0-387-94217-3, 978-0-387-94217-9
Alternative Schreibweisen und verwandte Suchbegriffe:
Autor des Buches: sterling, berberian
Titel des Buches: first course analysis, real analysis, this real

---

Daten vom Verlag:

Autor/in: Sterling K. Berberian
Titel: Undergraduate Texts in Mathematics; A First Course in Real Analysis
Verlag: Springer; Springer US
240 Seiten
Erscheinungsjahr: 1994-06-24
New York; NY; US
Sprache: Englisch
53,49 € (DE)
54,99 € (AT)
59,00 CHF (CH)
Available
XI, 240 p.

BB; 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; BC

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.