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Assignments, additional related material will be posted on this page.
Assignments, additional related material will be posted on this page.
Resources:
Resources:
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, continuous maps, limit points and closed sets, order topology, product spaces Notes for week 8
Week 9: Countability axioms, separation axioms, Urysohn's lemma, Tietze extension theorem Notes for week 9 Problem set for week 8-9 material
Week 10: Holidays
Week 11: Connectedness, Path connectedness, local notions, Compactness Problem set 9
Week 12: Tychonoff theorem, local compactness, Compactification Quiz on Friday 6th Nov : 5 to 6 pm
Week 13: Quotient topology, Projective spaces
Week 14: Topological Manifolds, Whitney embedding theorem.
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