| When | What |
Where |
| Week 1 (1/21 - 1/23) |
Introductions and Practical Stuff
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The set of natural numbers and the set of rational numbers
| 1, 2
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The set of Real Numbers
| 3
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| Week 2 (1/29 - 1/30) |
The Completeness Axiom
| 4 |
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The symbors for + infinity and - infinity
| 5 |
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Week 3 (2/04 - 2/06) |
Limits of Sequences
| 7 |
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A discussion about proofs
| 8 |
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Limit theorems for sequences
| 9 |
| Week 4 (2/11 - 2/13) |
Monotone sequences and Cauchy sequences
| 10 |
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Subsequences
|
11
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| Week 5 (2/18 - 2/20) |
limsup's and liminf's, Review 1
| 12 |
| Midterm 1 (2/20) |
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| Week 6 (2/25- 2/27) |
Series
|
14
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| Alternating series and integral tests
| 15 |
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| Week 7 (3/03 - 3/05) |
Continuous functions
|
17
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Properties of continuous functions
| 18 |
| Week 8 (3/10 - 3/12 ) |
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Uniform continuity
|
19
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Limits of functions
| 20 |
| Week 9 (3/17 - 3/19 ) |
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Power Series
|
23
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Uniform convergence
| 24 |
| Week 10 (3/24 - 3/26) |
Spring Break |
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| Week 11 (3/31 - 4/02) |
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More on uniform convergence
|
25
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Integration and differentiation of power series
|
26
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| Week 12 (4/07 - 4/09) |
Basic properties of the derivative
| 28 |
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| Midterm 2 (4/09) |
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| Week 13 ( 4/14 - 4/16) | The mean value theorem
| 29 |
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Taylor's Theorem
|
31
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| Week 14 ( 4/21 - 4/23) |
The Riemann Integral
| 32 |
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Properties of the Riemann Integral
|
33
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| Week 15 (4/28 - 4/30) |
The Fundamental Theorem of Calculus
| 34 |
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Examples and Review
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| Week 16 (5/05 - 5/07 ) |
RRR week
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| Week 17 (5/12 - 5/14) |
Final Exam: Wed, May 13, 11:30A - 2:30P
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