Dates |
Lectures |
Topics |
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Chapter 1. The Real and Complex Number Systems
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1/7
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Lecture 1
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Introduction. Ordered Sets.
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1/9
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Lecture 2
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Fields
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1/11
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Lecture 3
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The Real Field
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1/14
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Lecture 4
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The Complex Field
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1/16
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Lecture 5
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Euclidean Spaces
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Chapter 2. Basic Topology
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1/18
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Lecture 6
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Finite, Countable, and Uncountable Sets
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1/23
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Lecture 7
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Metric Spaces
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1/25
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Lecture 8
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Metric Spaces (continued)
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1/28
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Lecture 9
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Compact Sets
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1/30
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Lecture 10
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Compact Sets (continued). Perfect Sets. Connected Sets.
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2/1
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Lecture 11
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First midterm exam
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Chapter 3. Numerical Sequences and Series
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2/4
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Lecture 12
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Convergent Sequences
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2/6
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Lecture 13
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Subsequnces.
Cauchy Sequences.
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2/8
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Lecture 14
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Upper and Lower Limits.
Some Special Sequences.
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2/11
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Lecture 15
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Series.
Series of Nonnegative Terms.
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2/13
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Lecture 16
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Series of Nonnegative Terms
(continued)
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2/15
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Lecture 17
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The Number e
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2/20
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Lecture 18
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The Root and Ratio Tests
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2/22
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Lecture 19
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Power Series.
Summation by Parts.
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2/25
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Lecture 20
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Absolute Convergence.
Addition and Multiplication of Series.
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2/27
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Lecture 21
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Rearrangements
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3/1
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Lecture 22
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Second midterm exam
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Chapter 4. Continuity
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3/4
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Lecture 23
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Limits of Funtions.
Continuous Functions.
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3/6
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Lecture 24
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Continuous Functions (continued).
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3/8
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Lecture 25
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Continuity and Compactness
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3/11
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Lecture 26
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Continuity and Connectness.
Discontinuity.
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3/13
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Lecture 27
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Monotonic Functions.
Infinite Limits and Limits at Inifinite.
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3/15
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Lecture 28
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Review
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