### Fall 2019

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⏱ **Class Timings:** Mondays, Wednesdays, and Fridays, 11:00 - 12:00, LH-4

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❓ Course Instructor: Gadadhar Misra (Office: L17),
TA: Anindya Biswas (email: anindyab@iisc.ac.in).

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📓 **View homework assignments on this page.**

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### Topics

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.

Higher-order derivatives.

### References

- Rudin, W.,
*Principles of Mathematical Analysis*, McGraw-Hill, 1986.
- Apostol, T. M.,
*Mathematical Analysis*, Narosa, 1987.

### Other Links