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❯
Year 1
❯
Term 1
❯
M2 Analysis I Sequences and Series
❯
Lectures
Folder: Year-1/Term-1/M2---Analysis-I---Sequences-and-Series/Lectures
37 items under this folder.
Nov 03, 2025
01. Introduction
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02. Axioms for arithmetic in ℝ
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03. Properties of arithmetic in ℝ
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04. Ordering the real numbers
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05. Inequalities and arithmetic
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06. The modulus of a real number
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07. Complex Numbers
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08. Upper and Lower Bounds
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09. The (nearly) empty section
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10. Supremum, infimum and completeness
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11. Existence of roots
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12. More consequences of completeness
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13. Countability
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14 - More on countability
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15 - Introduction to sequences
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16 - Convergence of a Sequence
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17 - Limits - first key results
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18. Limits - modulus and inequalities
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19 - Bounded and unbounded sequences
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20. Complex Sequence
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21. Subsequences
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22. Algebra of Limits - part one
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23. Algebra of Limits - part two
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24. Orders of Magnitude
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25. Monotonic Sequences
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26. Convergent Subsequence
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27. Cauchy Sequences
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28. Convergence for Series
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29. Series - first results and a first test for convergence
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30. Series - more results and another test for convergence
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31. More on the Comparison Test
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32 . Ratio Test
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33. Integral Tests
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34. Euler's Constant and Rearranging Series
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35. Power Series
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36. Radius of Convergence
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37. Differentiation Theorem
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