Fall 2019

<aside> ⏱ Class Timings: Mondays, Wednesdays, and Fridays, 11:00 - 12:00, LH-4

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

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<aside> 📓 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

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

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