Course Archives Theoretical Statistics and Mathematics Unit

Course: Analysis I Level: Undergraduate Time: Currently not offered

Syllabus Past Exams Syllabus: (Calculus of one variable) : The language of sets and functions - countable and uncountable sets (see also Algebra 1). 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, ab- solute 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 num- bers, 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: Internal Quiz marks Final Exam marks Total 100 marks Top of the page Past Exams

Midterm 03.pdf 05.pdf 06.pdf 07.pdf 08.pdf 09.pdf 10.pdf 11.pdf 12.pdf 13.pdf 14.pdf 15.pdf 16.pdf 17.pdf 18.pdf 19.pdf 20.pdf 20s.pdf Solution 09.pdf 10.pdf 11.pdf 12.pdf 13.pdf 14.pdf 15.pdf 16.pdf 17.pdf 18.pdf 19.pdf Semestral 01.pdf 02.pdf 03.pdf 05.pdf 06.pdf 07.pdf 08.pdf 09.pdf 10.pdf 11.pdf 12.pdf 13.pdf 14.pdf 15.pdf 16.pdf 17.pdf 18.pdf 19.pdf 20.pdf Solution 09.pdf 10.pdf 11.pdf 12.pdf 13.pdf 14.pdf 15.pdf 16.pdf 17.pdf 18.pdf 19.pdf Supplementary and Back Paper 01.pdf 05.pdf 10.pdf 11.pdf 12.pdf 13.pdf 15.pdf 16.pdf 17.pdf 18.pdf 20.pdf Top of the page

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