Real Analysis
Graduate Course, ISI & IISc, 2022
Lecture notes consists of materials from my coursework both at ISI and IISc.
- Lec-1: Set Theory.
- Lec-2: Natural and Rational numbers.
- Lec-3: Ordered Fields.
- Lec-4: Construction of Real numbers.
- Lec-5: Properties of Real numbers
- Lec-6: Cardinality
- Lec-7: Metric Topology
- Lec-8: Introduction to Compactness
- Lec-9: Topics on Compactness
- Lec-10: Connectedness
- Lec-11: Sequences
- Lec-12: Topics on Sequences
- Lec-13: Series
- Lec-14: Topics in Series
- Lec-15: Series: Sum, Product and Rearrangements
- Lec-16: Limits and Continuity
- Lec-17: Continuity and Topology
- Lec-18: Discontinuities
- Lec-19: Differentiation
- Lec-20: Mean Value Theorems
- Lec-21: Reimann Integration
- Lec-22: Further topics on Reimann Integration
- Lec-23: Uniform Convergence
- Lec-24: Equi-Continuity
- Lec-25: Arzela-Ascolli Theorem
- Lec-26: Weierstrass Approximation Theorem
- Lec-27: Introduction to Multivariable Calculus
- Lec-28: Directional Derivatives