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 R^{n}. 

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 R^{m} to R^{n.} 

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. 