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Introduction to Analysis of the Infinite

  • E. Hairer
  • G. Wanner
Part of the Undergraduate Texts in Mathematics book series (UTM)

Abstract

This chapter explains the origin of elementary functions and the impact of Descartes’s “Géométrie” on their calculation. The interpolation polynomial leads to Newton’s binomial theorem and to the infinite series for exponential, logarithmic, and trigonometric functions. The chapter ends with a discussion of complex numbers, infinite products, and continued fractions. The presentation follows the historical development of this subject, with the mathematical rigor of the period. The justification of dubious conclusions will be an additional motivation for the rigorous treatment of convergence in Chapter III.

Keywords

Rational Number Continue Fraction Trigonometric Function Infinite Series Cube Root 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Copyright information

© Springer Science+Business Media New York 2008

Authors and Affiliations

  • E. Hairer
    • 1
  • G. Wanner
    • 1
  1. 1.Department of MathematicsUniversity of GenevaGenevaSwitzerland

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