In this semester (Autumn-2022), I am teaching a course MAN 503/ MA 409 on "Real Analysis" to IDD 4th year and M.Sc. 1st year students.
The content of the course is the following:
Riemann-Stieltjes integrals, their properties, Integration and differentiation, fundamental theorem of calculus, first and second mean value theorems, Integration of vector-valued functions.
Linear transformations, derivatives in several variable calculus, partial and directional derivatives, chain rule, double derivatives
and Clairaut's theorem, the inverse function theorem, the implicit function theorem, integration on n-dimensional Euclidean space, Stoke's theorem.
Metric spaces, convergence of sequences, open and closed subsets, continuity, Cauchy sequences, compactness, iteration and the contraction mapping theorem.
Length of open sets and closed sets, inner ans outer measure, measurable sets, properties of measurable sets, measurable functions.
No. of hours per week 3 hours (lecture) 1 hour (tutorial)
I have taught following courses at IIT Roorkee
Lecture: Theory of PDEsCourse (MAN-508)
Theory of Partial Differential Equations ( MAN-518 )
Spring
Theory of Differential Equations ( MAN-903 )
Spring
Advanced Numerical Analysis/Finite Element Methods ( MAN-642/MAN-630 )
Autumn
Selected Topics in Analysis ( MAN-901 )
Spring
Functional Analysis ( MAN-611 )
Autumn
Mathematics I ( MA 001 )
Autumn
Real Analysis II ( MA 503 )
Autumn
Theory of Partial Differential Equations ( MA 506 )
Spring
