Time: | Tue & Thur 11 a.m. - 12:15 p.m. | ||||||
Room: | GSM 230 (Graduate School of Management/ Parish Library) moved to SMLC 124 | ||||||
Instructor Info: | Anna Skripka, skripka [at] math [dot] unm [dot] edu | ||||||
Office hours: | Tue and Thur 3:30 - 4:45 p.m., and by appointment, SMLC 212 |
Week |
Important Dates |
Lectures |
Topics |
Homework |
1 |
Jan 13, 15 |
Munkres 1.3, 1.4.
Lecture 1 |
Review of Math 510 analysis in Rn. |
2 |
Jan 20, 22 |
Munkres 1.1, 1.2, 2.5. Lecture 2
|
Review of linear algebra. Directional derivatives. |
3 |
Jan 27, 29; Drop with no grade: Jan 30 |
Munkres 2.5, 2.6, 2.7. Lecture 3 |
Differentiability of functions mapping Rm to Rn. |
|
4 |
Feb 3, 5 |
Wade 11.5, 11.7, 11.1, Rudin 9.42. Lecture 4 |
Taylor's formula. Local extremum. Differentiation of integrals. |
|
5 |
Feb 10, 12 |
Munkres 2.8, or Wade 11.6, or Rudin 9.24. L 5 |
Inverse function theorem. Prepare for Exam 1 |
|
6 |
Feb 17, 19 (Exam 1) |
Munkres 2.9. Lecture 6 |
Implicit function theorem. |
|
7 |
Feb 24, 26 |
Munkres 3.10, 3.11. Lecture 7 |
Integration over a rectangle. |
|
8 |
Mar 3, 5 |
Munkres 3.11, 3.12. Lecture 8 |
Set of discontinuities of measure 0. Fubini's theorem. |
|
9 |
Mar 17, 19 |
Munkres 3.13. Lecture 9 |
Integration over a bounded set. |
|
10 |
Mar 24, 26 |
Munkres 3.14, 4.17. Lecture 10 |
Rectifiable sets. Fubini's theorem for simple regions. Change of variables and its applications. Prepare for Exam 2 |
|
11 |
Mar 31, Apr 2 (Exam 2)
| Munkres 4.17, 3.15. Lecture 11 |
Change of variables for improper integrals. Proof strategy. |
|
12 |
Apr 7, 9; Withdrawal deadline: Apr 10 |
Munkres 4.16, 4.18, 4.19. Lecture 12 |
Partition of unity. Proof of the change of variables theorem. |
|
13 |
Apr 14, 16 |
Wade, Chapter 13. Lecture 13 |
Line and surface integrals. Fundamental theorems of vector calculus. |
|
14 |
Apr 21, 23 |
Wade, Chapter 13. Lecture 14 |
Applications of Green's, Stokes', and the Divergence theorems. Proofs in particular cases. |
|
15 |
Apr 28, 30 |
Munkres, overview of Chapters 5,6,7. L 15 |
Differential forms. Stokes' theorem for manifolds. |