<aside> ⏱ Class Timings: Mondays, Wednesdays, and Fridays, 11:00 - 12:00, LH-4
<aside> ❓ Course Instructor: Gadadhar Misra (Office: L17), TA: Anindya Biswas (email: firstname.lastname@example.org).
<aside> 📓 View homework assignments on this page.
Construction of the field of real numbers and the least upper bound property. Review of sets, countable & uncountable sets.
Metric Spaces: topological properties, the topology of Euclidean space. Sequences and series.
Continuity: definition and basic theorems, uniform continuity, the Intermediate Value Theorem.
Differentiability on the real line: definition, the Mean Value Theorem.
The Riemann-Stieltjes integral: definition and examples, the Fundamental Theorem of Calculus. Sequences and series of functions, uniform convergence, the Weierstrass Approximation Theorem.
Differentiability in higher dimensions: motivations, the total derivative, and basic theorems.
Partial derivatives, characterization of continuously-differentiable functions. The Inverse and Implicit Function Theorems.