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Indian Institute of Science Education and Research Berhampur

Mathematics

MTH 101: Calculus of One Variable (3)

Learning Objectives:

This is a core mathematics course for first-semester BS-MS students. The course introduces the basic concepts of differential and integral calculus of one real variable with an emphasis on careful reasoning and understanding of the material.

Course Contents:

Introduction to the real number system, field axioms, order axioms and the completeness axiom

Sequences and series of numbers, convergence of a sequence, Cauchy's criterion, limit of a sequence, supremum and infimum, absolute and conditional convergence of an infinite series, tests of convergence, examples

Limits and continuity, definitions, continuity and discontinuity of a function at a point, left and right continuity, examples of continuous and discontinuous functions, intermediate value theorem, boundedness of a continuous function on a closed interval, uniform continuity

Differentiation, definition and basic properties, Rolle's theorem, mean value theorem, Leibnitz's theorem on successive differentiation, Taylor's theorem

Integration, Riemann integral viewed as an area, partitions, upper and lower integrals, existence of the Riemann integral, basic properties, fundamental theorem of integral calculus, integration by parts, applications

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