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SYLLABUS- B.Sc. OBJ. REAL ANALYSIS,Unit 1Axiomatic study of real numbers, Completeness property in R, Archimedean property, Countable anduncountable sets, Neighbourhood, Interior points, Limit points, Open and closed sets, Derived sets, Dense sets,Perfect sets, Bolzano-Weierstrass theorem.Unit 2Sequences of real numbers, Subsequences, Bounded and monotonic sequences, Convergent sequences,Cauchy's theorems on limit, Cauchy sequence, Cauchy's general principle of convergence, Uniform convergenceof sequences and series of functions, Weierstrass M-test, Abel's and Dirichlet's tests.Unit 3Sequential continuity, Boundeness and intermediate value properties of continuous functions, Uniform continuity,Meaning of sign of derivative, Darboux theorem. Limit and continuity of functions of two variables, Taylor'stheorem for functions of two variables, Maxima and minima of functions of three variables, Lagrange's method ofundetermined multipliers.Unit 4Riemann integral, Integrability of continuous and monotonic functions, Fundamental theorem of integral calculus,Mean value theorems of integral calculus, Improper integrals and their convergence, Comparison test, m-test,Abel's test, Dirichlet's te

Author

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Published

2021

Language

EN