Math | B.Sc.S.Y. | Real Analysis-2 | unbounded Functions | Lect.18 | Dr. S. S. Bellale | DSCL

#B. Sc. #M. Sc. #SET #NET #CSIR #UPSE #12th #11th #IIT-JAM #IIT-JEE #Mathematics #SidhshwarBellale #SRTMU #DayanandCollegeLatur #BAMU #SPPU #MU #SU #AMU #DU #BHU #KU #B.Sc. Definition of Metric Space
#Examplesof Metric Space
Riemann Integral,
Introduction,
Definition and existence of the integral,
Definitions,
Inequalities for integrals,
Refinement of partitions,
Darboux's theorem,
Conditions of Integrability,
Deductions,
Integrability of the sum and difference of integrable functions,
Integrability of the product,
Quotient and the modulus of Integrable functions,
The integral as a limit of sums (only definitions of Riemann sums),
Some applications,
Some Integrable functions,
Integration and differentiation,
Fundamental theorem of calculus,
Mean value theorems of integral calculus.
Introduction,
Integration of unbounded functions with finite limits of integrations,
Comparison tests for convergence,
Useful comparison integral,
Examples, General test for convergence,
Absolute convergence