### EE 759 – APPLIED MATHEMATICAL ANALYSIS IN ENGINEERING

**Course offered in:**

Autumn 2020

**Instructors:**

Prof. Jayakrishnan Nair

**Course Content:**

- A brief analysis of the set of real numbers, ℝ.
- Sequence & Series (- this includes the following major topics – Sequences, Subsequential limits, Root and Ratio tests, Power series, etc.)
- Continuity (-this includes Intermediate Value Theorem) & Uniform continuity
- Derivatives (- this includes Chain Rule, Mean Value Theorem, L’Hostpital’s rule, etc.)
- Integration
- Fundamental Theorem of Calculus I & II.

[NOTE: These are some additional miscellaneous topics that were covered as a part of this course – Metric Spaces, Taylor’s Theorem, etc.]

**Prerequisites:**

No strict prerequisites. Sophomores were allowed to take this course.

**Feedback on Lectures:**

The course in general was very well structured – making it easy to follow. The lectures were regularly uploaded on every weekend, and live interaction took place in the usual lecture slot – this served as a doubt clearing session. A significant amount of effort was made from the professor’s end to teach the concepts and clear any doubts.

**Feedback on Tutorials, Assignments and Exams:**

Tutorials & Assignments: A set of problems were handed out every week, and submission was expected for every alternate week’s problem set. The questions in these sets were illustrative of the questions in exams.

Exams: A total of 4 quizzes were taken and the best 2 of those were counted for final evaluation. Along with the quizzes, there was mid-semester as well as end-semester exam.

Following is evaluation plan that was used:

Assignments: 10%

Quizzes (best 2 of 4): 20%

Mid-semester exam: 30%

End-semester exam: 40%

**Difficulty:**

On a scale of 1-10, I would rate the course an 8. This is a moderately demanding cours.

**Grading Statistics:**

**Study Material and References:**

The lecture videos (both pre-recorded as well as live) were tremendously useful, and in my opinion, are sufficient for this course. Although individually taking notes in the lectures is encouraged, the lecture notes were made available. Other than these primary resources, “Kenneth A. Ross – Elementary Analysis – The Theory of Calculus” was recommended.

**Comments:**

This course is moderately demanding and it definitely helps to be regular in this course – most of the last minute hacks would probably fail in this course.

**Advanced courses that can be taken after this:**

HS431 – Reading Fiction

**Takeaways from the course:**

This course forms a strong foundation for other courses based on mathematical analysis.

Review by – Sammed Mangale (17d070025@iitb.ac.in)

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