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Real Analysis and Applications
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Real Analysis and Applications

Real Analysis and Applications

Frank Morgan

198 pages, parution le 26/01/2006

Résumé

Real Analysis and Applications starts with a streamlined, but complete, approach to real analysis. It finishes with a wide variety of applications in Fourier series and the calculus of variations, including minimal surfaces, physics, economics, Riemannian geometry, and general relativity. The basic theory includes all the standard topics: limits of sequences, topology, compactness, the Cantor set and fractals, calculus with the Riemann integral, a chapter on the Lebesgue theory, sequences of functions, infinite series, and the exponential and Gamma functions. The applications conclude with a computation of the relativistic precession of Mercury's orbit, which Einstein called "convincing proof of the correctness of the theory [of General Relativity]."

The text not only provides clear, logical proofs, but also shows the student how to derive them. The excellent exercises come with select solutions in the back. This is a text that makes it possible to do the full theory and significant applications in one semester.

L'auteur - Frank Morgan

Frank Morgan is Dennis Meenan Third Century Professor of Mathematics at Williams College and Second Vice-President of the Mathematical Association of America (MAA). He has received one of the first MAA Haimo awards for distinguished teaching, MIT's Baker teaching award, and an honorary doctorate from Cedar Crest College. Morgan went to MIT and Princeton, taught for ten years at MIT (where he served as Undergraduate Mathematics Chair), and came to Williams in 1987, where he has served as chair and as founding director of an NSF undergraduate research program. Morgan's three other books all now have new editions: Geometric Measure Theory: a Beginner's Guide; Riemannian Geometry: a Beginner's Guide; and Calculus Lite.

Sommaire

  • Real numbers and limits
  • Topology
  • Calculus
  • Fourier series
  • The calculus of variations
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Caractéristiques techniques

  PAPIER
Éditeur(s) American Mathematical Society (AMS)
Auteur(s) Frank Morgan
Parution 26/01/2006
Nb. de pages 198
Format 18 x 26
Couverture Relié
Poids 535g
Intérieur Noir et Blanc
EAN13 9780821838419
ISBN13 978-0-8218-3841-9

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