Course Archives Theoretical Statistics and Mathematics Unit
Course: Analysis I
Instructor: B V Rajarama Bhat
Room: G24
Level: Undergraduate
Time: Currently offered
Syllabus
Past Exams


Syllabus (Calculus of one variable): The language of sets and functions - countable and uncountable sets (see also Algebra I). Real numbers - least upper bounds and greatest lower bounds. Sequences - limit points of a sequence, convergent sequences; bounded and monotone sequences, the limit superior and limit inferior of a sequence. Cauchy sequences and the completeness of R. Series - convergence and divergence of series, absolute and conditional convergence. Various tests for convergence of series. (Integral test to be postponed till after Riemann integration is introduced in Analysis II.) Connection between infinite series and decimal expansions, ternary, binary expansions of real numbers, calculus of a single variable - continuity; attainment of supremum and infimum of a continuous function on a closed bounded interval, uniform continuity. Differentiability of functions. Rolle's theorem and mean value theorem. Higher derivatives, maxima and minima. Taylor's theorem - various forms of remainder, infinite Taylor expansions.

Evaluation:
Midterm Exam 40 marks
Assignment 10 marks
Final Exam 50 marks
Total 100 marks


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Past Exams
Midterm
03.pdf 05.pdf 06.pdf 07.pdf 09.pdf 10.pdf 11.pdf 12.pdf 13.pdf 14.pdf 15.pdf 16.pdf 17.pdf
Solution
09.pdf 10.pdf 11.pdf 12.pdf 13.pdf 14.pdf 15.pdf 16.pdf 17.pdf
Semestral
01.pdf 02.pdf 03.pdf 05.pdf 06.pdf 07.pdf 09.pdf 10.pdf 11.pdf 12.pdf 13.pdf 14.pdf 15.pdf 16.pdf 17.pdf
Solution
09.pdf 10.pdf 11.pdf 12.pdf 13.pdf 14.pdf 15.pdf 16.pdf 17.pdf
Supplementary and Back Paper
01.pdf 05.pdf 10.pdf 11.pdf 12.pdf 13.pdf 15.pdf 16.pdf 17.pdf

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[ Semester Schedule ][ Statmath Unit ] [Indian Statistical Institute]