Analysis

Literature

The following is a list of books on which the lecture is based. They are available in the library. Although we will not follow a book strictly, the material can be found in them and they may sometimes offer a different approach to the material.

Books relevant for the first term:

• E.T. Copson, Metric Spaces. Cambridge University Press.
• J. Dieudonne, Foundations of modern analysis. Academic Press.
• E. Hewitt, K. Stromberg, Real and abstract analysis. Springer Verlag.
• K. Hoffman, Analysis in Euclidean space. Prentice-Hall.

Books relevant for the second term:

• M.P. do Carmo, Differential Forms and Applications. Springer Verlag.
• J.R. Munkres, Analysis on manifolds. Westview Press.
• M. Spivak, Calculus on manifolds. Benjamin.

The following link contains lecture notes to an Analysis course by Victor Guillemin, provided by MIT Open Courseware, which is also a good reference.

A roadmap on the 4H extra reading material can be found here. Links to books for extra reading material are:

Haggarty, R. (1993) Fundamentals of mathematical analysis by Rod Haggerty. Wokingham: Addison-Wesley, p.224-225,
Hairer, E. and Wanner, G. (1996) Analysis by its history. New York London: Springer, p.281-283,
Simmons, G.F. (1963) Approximation In Introduction to topology and modern analysis. New York: McGraw-Hill, p.153-161