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Real Analysis

  • Răzvan GelcaEmail author
  • Titu Andreescu
Chapter

Abstract

Real analysis starts with a treatment of sequences and series, including, among other things, applications to the Cauchy criterior of convergence, the Chesáro-Stolz theorem, Cantor’s nested intervals theorem, and the telescopic method. This is followed by a long treatment of one-variable real analysis: limits, continuity, differentiability, convexity, and computations and applications of integrals, with a discussion of Taylor and Fourier series. The subchapter on multivariable real analysis contains applications of partial derivatives, computation of integrals, and the theorems of Green, Kelvin-Stokes and Gauss-Ostrogradsky. The chapter concludes with functional and differential equations.

Copyright information

© Springer International Publishing AG 2017

Authors and Affiliations

  1. 1.Department Mathematics and StatisticsTexas Tech UniversityLubbockUSA
  2. 2.MathematicsUniversity of Texas at DallasRichardsonUSA

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