Math 412: Real Analysis

Spring 2009

General Information

Instructor: Chris Staecker (Personal Homepage)

Email: cstaecker@messiah.edu

Office: Frey 327

Office Hours: M 1-3, W 2-4, F 8-9

Textbook: Gaskill & Narayanaswami, Elements of Real Analysis, first edition.

Class Meetings: MWF 11:30 - 12:30, Frey 250

Final Exam: 8:00 - 10:00, Tuesday May 12

Other Materials

• Syllabus (61KB pdf) LaTeX source
• Answer for 2.2 #13 (35KB pdf) LaTeX source

Coming Attractions

2/11: Homework #1 due

Section 0.1 1a,c,d, 2a, 3a, 4, 10a,b
Section 0.4 2b,d,f,l,r, 4, 10, 12, 16a,f, 33, 36, 38 (use #37 here)
Section 0.5 4, 5

2/18: Homework #2 due

Section 0.6 1, 2, 3, 10a,b, 16
Section 1.1 4b,f,m,n,w, 7, 13, 15, 20

2/25: Homework #3 due

Section 1.2 1, 2, 8, 11a,b, 13a,c,d,e,f (these are all false, give counterexamples)
Section 1.3 1b,c,d,n (for n, use the result from problem 22, section 0.4), 2b,d, 3, 4, 16 (just state, don't prove your theorem), 23
Section 2.1 1, 4, 6a,d,h,k (in each part, just pick one of +∞ or -∞), 7a,b,e,f,h,i, 11 (prove it)

3/4: Homework #4 due

Section 2.2 1a,d, 3 (show directly- dont use theorems from 2.3), 5, 6, 13 (ignore the "further"), 14 (use theorems from 2.3 to make it easier)
Section 2.3 1a (just prove "+"), 13, 15 (just prove ⇒)

3/6: Exam #1

 

3/11: Homework #5 due

Section 2.4 1b,c,i, (for these, prove the limits exist or do not exist) 2, 6 ("one to one" means f(x) = f(y) ⇒ x=y), 9, 15
Section 2.5 1h, 2b (assume sin(x) is continuous), 9, 14 (just max), 16 (use 9), 20 (use 9 again)

3/25: Homework #6 due

Section 2.6 10, 14 (to show f is continuous from the right at some y, use the IVT with c=f(y)+ε), 15, 17 (first try it with λ = μ = 1), 23, 24, 26

4/1: Homework #7 due

Section 3.1 1d,h,i, 8, 9, 10a, 12, 15, 16, 17, 18, 21 (no "what about")

4/8: Homework #8 due

Section 3.2 4, 9, 17a,b,d (describe the subsequence), 18, 22, 23, 24
Section 3.3 2, 5, 6, 15

4/15: Homework #9 due

Section 3.4 8b,c,d,f,m,t, 13a,b,c,d, 15, 17, 18

4/17: Exam #2

 

4/29: Homework #10 due

Section 3.5 7, 10, 21
Section 6.1 6, 7, 15, 16a,i,o,p,q, 19, 28c,e
Section 6.2 3, 5, 7a,b,c,l,r

5/12: Final exam: 8:00 - 10:00