SYLLABUS
Interior points, limit points, open sets, closed sets, bounded sets, connected sets, compact sets; completeness of R, Power series (of real variable) including Taylor’s and Maclaurin’s, domain of convergence, term-wise differentiation and integration of power series.
Course Curriculum
SET THEORY | |||
Sets | 01:26:00 | ||
Relation and Functions | 00:47:00 | ||
Countability of Sets | 00:32:00 | ||
REAL NUMBERS | |||
Real Numbers | 01:32:00 | ||
TOPOLOGY ON REAL LINE | |||
Metric Space | 01:09:00 | ||
Open Sets | 01:10:00 | ||
Closed Sets | 00:18:00 | ||
Limit Points of Sets | 01:20:00 | ||
Compactness and Connectedness | 00:30:00 | ||
REAL SEQUENCES | |||
Introduction to Real Sequences | FREE | 01:03:00 | |
Monotonic Sequence | 00:37:00 | ||
Cauchy Theorems on Limits | 00:19:00 | ||
Limit Points | 01:00:00 | ||
Subsequence | 00:11:00 | ||
Cauchy Sequence | 00:16:00 | ||
INFINITE SERIES | |||
Introduction to Infinite Series | 00:52:00 | ||
Test of Convergence of Infinite Series | 01:34:00 | ||
Alternating Series | 00:12:00 | ||
POWER SERIES | |||
Power Series | 00:32:00 |
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