Excursions in classical analysis : pathways to advanced problem solving and undergraduate research /

Excursions in Classical Analysis will introduce students to advanced problem solving and undergraduate research in two ways: it will provide a tour of classical analysis, showcasing a wide variety of problems that are placed in historical context, and it will help students gain mastery of mathematic...

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Détails bibliographiques
Cote:Libro Electrónico
Auteur principal: Chen, Hongwei
Collectivité auteur: Mathematical Association of America
Format: Électronique eBook
Langue:Inglés
Publié: Washington, DC : Mathematical Association of America, ©2010.
Collection:Classroom resource materials.
Sujets:
Mathematical analysis > Problems, exercises, etc.
Analyse mathématique > Problèmes et exercices.
MATHEMATICS > Calculus.
MATHEMATICS > Mathematical Analysis.
Mathematical analysis
Problems and exercises
Accès en ligne:Texto completo
Table des matières:
  • Two classical inequalities
  • A new approach for proving inequalities
  • Means generated by an integral
  • The L'Hôpital monotone rule
  • Trigonometric identities via complex numbers
  • Special numbers
  • On a sum of cosecants
  • The gamma products in simple closed forms
  • On the telescoping sums
  • Summation of subseries in closed form
  • Generating functions for powers of Fibonacci numbers
  • Identities for the Fibonacci powers
  • Bernoulli numbers via determinants
  • On some finite trigonometric power sums
  • Power series of (arcsin [italic]x)²
  • Six ways to sum [Greek lowercase]Zeta(2)
  • Evaluations of some variant Euler sums
  • Interesting series involving binomial coefficients
  • Parametric differentiation and integration
  • Four ways to evaluate the Poisson integral
  • Some irresistible integrals.

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