Course Archives    Theoretical Statistics and Mathematics Unit
Course: Analysis IV
Time: Currently not offered
Level: Undergraduate
Syllabus
Past Exams


Syllabus (Introduction to Function Spaces): Review of compact metric spaces. C([a; b]) as a complete metric space, the contraction mapping principle. Banachs contraction principle and its use in the proofs of Picars theorem, inverse and implicit function theorems. The Stone-Weierstrass theorem and Arzela-Ascoli theorem for C(X). Periodic functions, Elements of Fourier series - uniform convergence of Fourier series for well behaved functions and mean square convergence for square integrable functions.

Reference Texts:
1. T.M. Apostol: Mathematical Analysis.
2. T.M.Apostol: Calculus
3. S. Dineen: Multivariate Calculus and Geometry.

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Past Exams
Midterm
04.pdf 05.pdf 07.pdf 07a.pdf 09.pdf 10.pdf 11.pdf 12.pdf 13.pdf 15.pdf 16.pdf 17.pdf
Semestral
03.pdf 03a.pdf 04.pdf 07.pdf 09.pdf 10.pdf 11.pdf 12.pdf 13.pdf 15.pdf 16.pdf 17.pdf
Supplementary and Back Paper
09.pdf 10.pdf 11.pdf 12.pdf 15.pdf 17.pdf

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