Course Archives Theoretical Statistics and Mathematics Unit
Course:
Function Spaces
Level:
Undergraduate
Time:
Currently not offered
Syllabus
Past Exams
Syllabus:
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 Picards theorem. Uniform convergence. 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:
(a) T. M. Apostol: Mathematical Analysis.
(b) T. M. Apostol: Calculus.
(c) S. Dineen: Multivariate Calculus and Geometry.
(d) R. R. Goldberg: Methods of Real Analysis.
(e) T. Tao: Analysis I & II.
(f) Bartle and Sherbert: Introduction to Real Analysis. (g) H. Royden: Real Analysis.
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Past Exams
Midterm
24.pdf
Semestral
24.pdf
Supplementary and Back Paper
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