Multivariable Calculus
Graduate Course, ISI & IISc, 2023
Lecture notes consists of materials from my coursework both at ISI and IISc.
- Lec-1: Introduction to Calculus
- Lec-2: Review of Continuity.
- Lec-3: Derivatives.
- Lec-4: Continuously Differentiable Functions
- Lec-5: Properties of Derivatives
- Lec-6: Product rule and Lipschitz’s property
- Lec-7: Chain rule and Mean Value Theorem
- Lec-8 & Lec-9 & Lec-10: Inverse Function Theorem
- Lec-11 & Lec-12 & Lec-13: Implicit Function Theorem
- Lec-14: Taylor’s Theorem
- Lec-15 & Lec-16: Local Maxima and Minima
- Lec-17: Manifolds
- Lec-18 & Lec-19: Integration
- Lec-20 & Lec-21: Fubini’s Theorem
- Lec-22 & Lec-23: Change of Variables