| Instructor / Office / Phone # | Xinwei Yu / 527 CAB / (780)4925731 |
| Email ; Webpage | xinwei2@ualberta.ca ; http://www.math.ualberta.ca/~xinweiyu |
| Location / Time | CAB 281/MWF 10--10:50, R 5--5:50. |
| Office Hours | (Updated Mar. 6, 2017) M 2--3:30, R 2--4; Or by appointment |
Important Dates:
| Week |
Dates |
Lecture Notes |
Required
Readings in the Textbook |
Homeworks Due on Thursdays at 5p in Assignment Box |
| 1 |
Jan. 9--13 |
Jan. 9: Introduction. Jan. 11: Functions. Jan. 12: R^N Jan. 13: Topology and Contnuity |
1.3, 1.4, 2.1 2.2, 2.3, 2.4 |
|
| 2 |
Jan. 16--20 |
Jan. 16: Differentiability Jan. 18: Taylor Expansion Jan. 19: Integrability Jan. 20: Discussions; Quiz 1 (Solutions) |
3.1, 3.2, 3.3, 3.4 3.5 4.1, 4.2, 4.4 |
|
| 3 |
Jan. 23--27 |
Jan. 23: Introduction to Implicit Function Theorems Jan. 25: Examples of Implicit Differentiation Jan. 26: Lagrange Multipliers Jan. 27: Proof of IFT I |
3.6, 5.3 |
Homework 1 Due Feb. 2 Solutions |
| 4 |
Jan. 30--Feb. 3 |
Jan. 30: Proof of IFT II Feb. 1: Proof of IFT III Feb. 2: Examples; Q&A. Feb. 3: Quiz 2 (Solutions); Global inverse function theorem |
5.1 5.2 |
|
| 5 |
Feb. 6--10 |
Feb. 6: Arc length; Feb. 8: Surface area; Feb. 9: Examples; Feb. 10: Line integrals of the second kind. |
6.2 6.5 6.3 |
Homework 2 Due Feb. 16 Solutions |
| 6 |
Feb. 13--17 |
Feb. 13: Surface integrals of the second kind Feb. 15: Green and Stokes Feb. 16: Review for Quiz 3; Feb. 17: Quiz 3 (Solutions); Gauss |
6.6 6.4, 6.6, 6.7 6.2; 6.3; 6.5; 6.6 6.7 |
|
| Reading
week |
||||
| 7 |
Feb. 27--Mar. 3 |
Feb. 27: Overview of 2nd half of the course; Infinite series: Definitions Mar. 1: Infinite series: Cauchy and comparison Mar. 2: Infinite series: Tests Mar. 3: Subtle issues |
7.1 |
Homework 3 Due Mar. 9 Solutions |
| 8 |
Mar. 6--Mar. 10 |
Mar. 6: : Improper integrals; Mar. 8: Improper integrals cont. Mar. 9: Review for Quiz 4 Mar. 10: Quiz 4 (Solutions); Integral of (sin x)/x |
7.2 |
|
| 9 |
Mar. 13--Mar. 17 |
Mar. 13: Infinite series of functions: Introduction Mar. 15: Uniform convergence Mar. 16: Uniform convergence (cont.) Mar. 17: Tests |
8.1 |
Homework 4 Due Mar. 23 Solutions |
| 10 |
Mar. 20--Mar. 24 |
Mar. 20: Power series: Introduction Mar. 22: Power series; Properties Mar. 23: Review for Quiz 5 Quiz 5 (Solutions); Taylor expansion |
8.2 |
|
| 11 |
Mar. 27--Mar.31 |
Mar. 27: Review of Quiz 5 Mar. 29: Fourier Series Expansion Mar. 30: Dirichlet Kernel and Partial Sum Mar. 31: Other Properties of Fourier Series |
8.3 |
Homework 5 Due Apr. 6 Solutions |
| 12 |
Apr. 3--7 |
Apr. 3: Proof of Change of Variables; Apr. 5: Proof of Change of Variabels (cont.) Apr. 6: Review for Quiz 6 Quiz 6 (Solutions); Proof of Change of Variables (cont.) |
6.1 |
|
| 13 |
Apr. 10--12 |
Apr. 10: Review; Q&A; Apr. 12: Review; Q&A. |
||