MA 4010: Analysis of functions of a single variable

All the updates related to MA 4010 are announced here.

### Class timings:

Tuesday: 12:00 am to 01:30 pm

Thursday: 12:00 am to 01:30 pm

Saturday: 10:00 am to 11:30 am (Tutorial)

Tuesday: 03:00 pm to 04:30 pm (Office hours)

### Examination and Grades:

The grades will be decided by the marks obtained in the assignments, mid-term, surprise tests, the final examination, and also by the performance in the class.

A google spread sheet, with all the marks obtained
up to that point, was shared with you to assess yourself about your performance in the course^{1}.

## Syllabus:

Real number system: Field properties, ordered properties, completeness axiom, Archimedean property, subsets of R, infimum, supremum, extended real numbers.

Finite, countable and uncountable sets, decimal expansion.

Sequences of real numbers, subsequences, monotone sequences, limit infimum, limit supremum, convergence of sequences.

Metric spaces, limits in metric spaces. Functions of single real variable, limits of functions.

Continuity of functions, uniform continuity, continuity & compactness, connectedness, monotonic functions, limit at infinity.

Differentiation, properties of derivatives, chain rule, Rolle's theorem, mean-value theorems, L'Hospital's rule. Derivatives of higher order, Taylor's theorem.

Definition and existence of Riemann integral, properties, differentiation and integration.

Revision of series, sequences and series of functions, pointwise and uniform convergence, uniform convergence of continuous functions, uniform convergence

and differentiability, equicontinuity, pointwise and uniform boundedness, Ascoli's theorem, Weierstrass approximation theorem, Fourier series.
## References:

- W. Rudin, Principles of Mathematical Analysis, McGraw-Hill international editions (Math Series), 3rd Edition, 1976.
- S. R. Ghorpade and B. V. Limaye, A course in calculus and real analysis, Springer, New York, Springer International Ed., New Delhi, 2006.
- R. R. Goldberg, Methods of Real Analysis, Oxford & IBH Publishing Co. Pvt Ltd, 1970.
- Kenneth A. Ross, Elements of Analysis: The Theory of Calculus, Springer-Verlag, UTM, 1980.

## Assignments:

The assignments have to be submitted right after the class on the respective due dates. The assignments can be submitted after the due date and time as well,
but only 50% of the marks will be credited into your account, unless you have a valid reason for the late submission.
- Assignment 1: Updated on: 21.08.2015, Due on 27.08.2015.
- Assignment 2: Updated on: 27.08.2015, Due on 08.09.2015.
- Problem Sheet 1
- Assignment 3: Updated on: 07.09.2015, Due on 08.10.2015.
- Assignment 4: Updated on: 15.09.2015, Due on 13.10.2015.
- Problem Sheet 2
- Assignment 5: Updated on: 15.10.2015, Due on 29.10.2015.
- Assignment 6: Updated on: 26.10.2015, Due on 10.11.2015.

### Anonymous Feedback

Please let me know what I'm doing right and what I'm doing wrong. Constructive feedback is always welcome. Don't hesitate to propose changes. Give anonymous feedback at the following link.

Some of the assignments and tutorial sheets are being prepared by Mr. Siva Rama Krishna, a tutorial assistant for MA 4010 in July - Nov 2015.

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