Zoom Discussions & Lectures: | Tue & Thur, 2:00 - 3:15 pm, to be posted on UNMLearn |
Office hours: | by email and by appointment in Zoom |
Professor Info: | Anna Skripka, skripka [at] math [dot] unm [dot] edu |
Week |
Important Dates |
Chapters |
Topics |
Homework |
1 |
Jan 19, 21 |
Munkres 1.3, 1.4, Stein-Shakarchi 1.1. |
Review of Math 510 analysis in Rn and of linear algebra. |
2 |
Jan 26, 28 |
Munkres 1.1, 1.2, 2.5.
|
Review of linear algebra. |
3 |
Feb 2, 4 (HW1)
Drop with no grade: Feb 5 |
Munkres 2.6, 2.7 or Rudin Chapter 9, Wade 11.4. |
Differentiability of functions mapping Rm to Rn. Chain rule. |
|
4 |
Feb 9, 11 (HW2) |
Wade 11.5, 11.7, 11.1. |
Mean value theorem. Taylor's formula. Local extremum. |
HW 3,
|
5 |
Feb 16, 18 (HW3) |
Munkres 2.8, or Wade 11.6, or Rudin 9.24 |
Inverse function theorem. |
HW 4,
|
6 |
Feb 23, 25 (HW4) |
Munkres 2.9 or Rudin 9.28. |
Implicit function theorem. |
|
7 |
Mar 2, 4 (HW5) |
Carothers Ch. 16, Stein & Shakarchi 1.2. |
Summary of Riemann & intro to Lebesgue integration. |
|
8 |
Mar 9, 11 (Exam on topics of weeks 1-6) |
Carothers Ch. 16, Stein & Shakarchi 1.2. |
Outer measure. Review. |
|
9 |
Mar 23, 25 |
Carothers Ch. 16, 17, Stein & Shakarchi 1.3, 1.4. |
Measurable sets and functions. |
|
10 |
Mar 30, Apr 1 |
Carothers Ch. 18, Stein & Shakarchi 2.1. |
Lebesgue integral: simple and nonnegative functions. |
|
11 |
Apr 6, 8 (HW6)
| Carothers Ch. 18, Stein & Shakarchi 2.1, 2.3. |
Lebesgue integral: general case. Convergence. Fubini's theorem. |
|
12 |
Apr 13, 15 (HW7)
Withdrawal deadline: Apr 16 |
Munkres 4.16 - 4.19, Rudin 10.9, Wade 12.4. |
Change of variables and its applications. |
|
13 |
Apr 20, 22 (HW8) |
Wade Ch. 13. |
Line and surface integrals. Fundamental theorems of vector calculus and their applications. |
|
14 |
Apr 27, 29 (HW9) |
Wade, Ch. 13. |
Green's, Stokes', the Divergence theorems. Proofs in particular cases. |
|
15 |
May 4, 6 (HW10) |
Munkres, overview of Ch. 5,6,7. |
Differential forms. Stokes' theorem for manifolds.
Review (see Learn). |
|
16 |
Final Exam: May 11 (Tuesday), 10 am - noon |