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. Top of the page Past Exams

Midterm 24.pdf Semestral 24.pdf Supplementary and Back Paper Top of the page

[ Semester Schedule ][ Statmath Unit ] [Indian Statistical Institute]