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Real Analysis I

NPTEL and IIT Palakkad via Swayam


This is an introductory course on Real Analysis designed for undergraduate students of Mathematics. The only pre-requisite is a knowledge of Calculus at high school level so students of the Sciences or Engineering who want a deeper understanding of Calculus or want to pursue subjects such as Theoretical Physics, Computational Complexity, Statistics, etc. would also benefit from this course.
UG Students of Mathematics, the Sciences or Engineering
PREREQUISITES :12th Standard Mathematics
INDUSTRIES SUPPORT :Google, DeepMind, Microsoft Research



Week 1:Introduction, Set Theory and LogicWeek 2:The Real Numbers as an Ordered FieldWeek 3:Completeness of the Reals and ConsequencesWeek 4:Sequences and Series
Week 5:Sequences and Series continuedWeek 6:A Taste of TopologyWeek 7:Limits and ContinuityWeek 8:Continuity and Topological Properties
Week 9:Differentiation and Basic PropertiesWeek 10:Differentiation Continued and Definition of Riemann IntegralWeek 11:The Fundamental Theorem of CalculusWeek 12:Uniform Convergence, Power Series and Taylor Series

Taught by

Prof. Jaikrishnan J

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