Week |
Important Dates |
Sections |
Topics |
Homework |
1 |
Jan 17, 18, 19 |
1.1, 1.2, 1.3 |
Real number system. Ordered field axioms. Supremum, infimum. |
#1.2.0-1.2.3; 1.2.4(a,b,d,e); (a,c) of 1.2.5, 1.2.7, 1.2.8 |
2 |
Jan 24, 25, 26 |
1.3, 1.4 |
Properties of sup, inf. Density of rationals. Mathematical induction. |
#1.3.0-1.3.8, 1.3.10, 1.3.11; 1.4.2-1.4.5, 1.4.8
submit for grade on Feb 2: #1.3.0(c), 1.3.6(a), 1.3.7(b), 1.3.10, 1.4.4(b) |
3 |
Jan 31, Feb 1, 2
Drop with no grade: Feb 3 |
1.4, 1.5 |
Binomial formula. Inverse functions. Images and preimages. DeMorgan's Laws. |
#1.5.1, 1.5.2(b,d), 1.5.3(a,b,c,d), 1.5.4, 1.5.5, 1.5.6(b), 1.5.7
submit for grade on Feb 9: #1.4.3(c), 1.4.8, 1.5.1(a,b) for the function in ε), 1.5.5(iii), 1.5.7 (a)=>(b) |
4 |
Feb 7, 8, 9 |
1.6 |
Countable and uncountable sets. |
#1.6.0, 1.6.1, 1.6.2, 1.6.4, 1.6.5
submit for grade on Feb 16: #1.6.0(c,d), 1.6.1, 1.6.3, 1.6.5(a)
|
5 |
Feb 14, 15, 16 |
2.1, 2.2 |
Limits of sequences and their properties. |
#2.1.0-2.1.8, 2.2.0-2.2.9
submit for grade on Feb 23: #2.1.0(a,c), 2.1.2(c), 2.2.2(b), 2.2.3(d), 2.2.6 |
6 |
Feb 21, 22, 23 |
2.3, 2.4 |
Monotone convergence and Bolzano-Weierstrass theorems. Cauchy sequences. |
#2.3.0, 2.3.1, 2.3.5-2.3.7, 2.4.0, 2.4.2-2.4.5, 2.4.7, 2.4.8 |
7 |
Feb 28 (Exam 1 on 1.1-2.2), Mar 1, 2 |
2.5, 3.1 |
lim sup, lim inf. Limits of functions. |
#2.5.1, 2.5.7
submit for grade on Mar 9: #2.3.5, 2.3.6, 2.4.3(c), 2.4.5, 2.5.7 |
8 |
Mar 7, 8, 9 |
3.1, 3.2, 3.3 |
Properties of limits of functions. Continuity. Extreme Value Theorem. |
#3.1.0, 3.1.1, 3.1.4-3.1.6, 3.2.1-3.2.3, 3.2.7, 3.3.1
submit for grade on Mar 23: #3.1.1(a), 3.1.5, 3.1.6, 3.2.1(b), 3.3.1(d) |
Mar 12-19: Spring Break |
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9 |
Mar 21, 22, 23 |
3.3, 3.4, 4.1, 4.2 |
Intermediate Value Theorem. Uniform continuity. Differentiability. |
#3.3.0(a,b,c), 3.3.2-3.3.5, 3.4.1, 3.4.2, 3.4.4, 3.4.5(a,b), 3.4.6, 4.1.0(a,b), 4.1.2, 4.1.4, 4.1.8, 4.2.2, 4.2.4-4.2.6
submit for grade on Mar 30: #3.3.0(a), 3.3.4, 3.4.2(c), 3.4.5(b), 4.1.4
|
10 |
Mar 28, 29, 30
| 4.1-4.4 |
Mean Value and Taylor's theorems. L'Hospital's rule. |
#4.3.1(a,b)-4.3.6, 4.4.1-4.4.3, 4.4.5(a-f)
submit for grade on Apr 13: #4.3.1(b), 4.3.4, 4.3.5, 4.4.2, 4.4.5(f)
|
11 |
Apr 4, 5, 6 (Exam 2 on 2.3-4.2) |
5.1 |
Review. Riemann integrable functions. |
|
12 |
Apr 11, 12, 13
Withdrawal deadline: Apr 14 |
5.1, 5.2 |
Riemann integral and its properties. |
#5.1.0(a,b,c), 5.1.2(a,b,c(α)), 5.1.4, 5.2.0(a,b,c), 5.2.3 |
13 |
Apr 18, 19, 20 |
5.2, 5.3 |
Fundamental Theorem of Calculus. Integration by parts. Change of variables. |
#5.3.1 submit for grade on Apr 25: #5.1.2(b,c(α)), 5.1.4, 5.2.3(b),5.3.1(b) |
14 |
Apr 25, 26, 27 |
6.1-6.4 |
Series. |
#6.1.1, 6.1.3, 6.4.1(c,d,e); (a-c) of 6.1.0, 6.1.2, 6.2.1, 6.2.2, 6.3.1, 6.4.2 submit for grade on May 4: #6.1.3(c), 6.4.1(c), 6.3.1(b), 5.2.7, 3.3.3 |
15 |
May 2, 3, 4 |
Series. Review. |
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16 |
May 9 (Tuesday), 12:30-2:30 p.m.: Final Exam |