Teaching
In this semester (Autumn-2024), I am teaching a course MAC-405/ MA 409 on "Real Analysis" to BS-MS 4th year and M.Sc. 1st year students. The content of the course is the following:
Course Outlines: Derivatives in several variable calculus, Clairaut’s theorem, the inverse function theorem, the implicit function theorem, integration on n-dimensional Euclidean plane, Stokes’ Theorem. Metric spaces, convergence of sequences, open and closed subsets, continuity, Cauchy sequences, completeness, Baire category theorem, contraction mapping theorem, connectedness, compactness, Heine-Borel theorem. Weierstrass approximation theorem, review of the Riemann and the Riemann-Stieltjes integrals, fundamental theorem of calculus, first and second mean value theorems. Inner and outer measures, measurable sets, measurable functions, Lebesgue integration.
No. of hours per week 3 hours (lecture) 1 hour (tutorial)
Lecture Mon. & Wed. 10 am and Thurs. 11:05 am (APJ AKB-001)
Tutorial Friday 12:05 pm (TA: Mr. Harshit Bajpai) (APJ AKB-501)
Timing for students 4:30-5:30 pm (with prior appointment)
Lecture Notes:I have taught following courses at IIT Roorkee:
