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Indian Institute of Science Education and Research Berhampur
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
Suggested Books:
- G. B. Thomas and R. L. Finney, Calculus and Analytic Geometry, 9th edition, Indian student edition, Addison-Wesley, 1998
- T. M. Apostol, Calculus, Volumes 1 and 2, 2nd edition, Wiley Eastern, 1980
- R. Courant, F. John, Introduction to Calculus and Analysis, Volume 1, Classics in Mathematics, Springer, 1989
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