Dates |
Lectures |
Topics |
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Chapter 1. The Real and Complex Number Systems
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10/3
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Lecture 1
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Introduction. Ordered Sets.
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10/6
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Lecture 2
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Fields
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10/8
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Lecture 3
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The Real Field
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10/10
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Lecture 4
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The Complex Field
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10/13
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Lecture 5
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Euclidean Spaces
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Chapter 2. Basic Topology
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10/15
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Lecture 6
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Finite, Countable, and Uncountable Sets
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10/17
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Lecture 7
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Metric Spaces
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10/20
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Lecture 8
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Metric Spaces (continued)
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10/22
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Lecture 9
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Compact Sets
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10/24
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Lecture 10
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Midterm I
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10/27
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Lecture 11
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Compact Sets (continued).
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10/29
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Lecture 12
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Compact Sets (continued).
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Chapter 3. Numerical Sequences and Series
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10/31
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Lecture 13
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Convergent Sequences
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11/3
|
Lecture 14
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Subsequnces.
Cauchy Sequences.
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11/5
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Lecture 15
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Upper and Lower Limits.
Some Special Sequences.
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11/7
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Lecture 16
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Series.
Series of Nonnegative Terms.
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11/10
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Lecture 17
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Series of Nonnegative Terms
(continued)
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11/12
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Lecture 18
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The Number e
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11/14
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Lecture 19
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The Root and Ratio Tests
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11/17
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Lecture 20
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Power Series.
Summation by Parts.
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11/19
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Lecture 21
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Absolute Convergence.
Addition and Multiplication of Series.
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11/21
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Lecture 22
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Midterm II
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Chapter 4. Continuity
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11/24
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Lecture 23
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Rearrangements. Limits of Functions.
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11/26
|
Lecture 24
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Limits of functions. Continuous Functions.
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|
12/1
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Lecture 25
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Continuity and Compactness
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12/3
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Lecture 26
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Uniform continuity. Connected sets.
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12/5
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Lecture 27
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Continuity and Connectedness. Intermediate value theorem.
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12/8
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Lecture 28
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Discontinuities. Monotonic Functions.
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12/10
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Lecture 29
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Infinite Limits and Limits at Infinity.
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12/12
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Lecture 30
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Review
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12/15
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Final Exam
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