Lecture plan:
Week 1: Topology of R^n, Differentiability, Partial derivatives. Problem set 1
Week 2: Chain rule, Taylor's approximation, Gen. mean value theorem, Extrema, Hessian, parametrized curves and surfaces Problem set 2
Week 3: Inverse function theorem, Implicit function theorem, Applications Some nice online resources: Geometric content of ImFT and other pages
Here are my handwritten notes for first 3 weeks of lectures : click here
Week 4: Rank theorem, Geometric consequences of ImFT to parametrized subsets of R^n, Lagrange Multiplier method Problem set 3-4 (based on week 3 and 4) Handwritten notes for week 4 of lectures : click here
Quiz 1 on 2nd Sept 2026 4:30-5:30 pm in M3. 📚
Week 5: Integration, Properties of lower and upper sums, measure zero sets. Problem set 5
Notes for week 5: click here
Week 6: Characterization of integrable functions via discontinuities, rectifiable sets, Fubini's theorem Problem set 6 Notes for week 6
Week 7: Sard's theorem Problem set 7 Notes for week 7
Mid-Semester exam on 24th Sept 2026 10 -12 am
Week 8: Topological spaces
Week 9:
Week 10:
Week 11:
Week 12:
Week 13:
Week 14: