Revision—and Assessment

  • Jeremy GrayEmail author
Part of the Springer Undergraduate Mathematics Series book series (SUMS)


At this point in the course we have seen a lot of mathematics  emerge: the existence of harmonic functions satisfying certain boundary conditions, trigonometric functions, and complex analytic functions (which, in Riemann’s hands but not those of Weierstrass, have intimate links to harmonic functions). But it is also true that very little of this was solidly established at the time: Dirichlet’s principle was beginning to look too insubstantial to solve Dirichlet’s problem, and with it could fall much of Riemann’s complex analysis. The study of trigonometric series might open the way to new results about real functions, but intuition seemed to offer little guidance.

Copyright information

© Springer International Publishing Switzerland 2015

Authors and Affiliations

  1. 1.Department of Mathematics and StatisticsThe Open UniversityMilton KeynesUK
  2. 2.University of WarwickCoventryUK

Personalised recommendations