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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