**Announcements:**

**Final Exam.**
As it says in the syllabus the final exam is Wednesday, May 8,
10:30-1:15. It will not be
cumulative and will cover only chapters 9 and 10. You should be familiar with the
following results from the book, and how to prove them, either as we did in
class or as done in the book (these are sometimes different). By “familiar with” I do not
mean that you should simply memorize the proofs. The goal is to understand *why* the result is true and have an idea
of *how* it is proved. Once you have an
outline of the strategy in your head, the details should not be too hard to
piece together. This is where
ideally I would like each of you to be with regard to this material.

Thm. 9.1.1, Coro. 9.1.1, Thm. 9.2.1, Coro. 9.2.1, Thm. 9.2.4, Thm. 9.3.1,
Thm. 9.3.2

Thm. 10.1.1, Thm. 10.2.1, Thm. 10.2.2, Coro. 10.2.1, Thm 10.2.4, Thm.
10.3.1, Thm. 10.3.2, Coro. 10.3.1, Thm. 10.4.3, Thm. 10.5.1.

Some of the questions may be to prove parts of the more complicated
theorems. To study for the exam you
should sit down with each theorem or corollary and see if you can prove it from
scratch. By thinking through the
process yourself, you will be better able to reconstruct the proof on demand,
and you will *own the result*!!

**Class on Monday 5/6.**
There will be class on Monday 5/6.
I will finish up the change of variables formula. You will not want to miss the cool trick
at the end! The rest of the time
will be for questions or anything else you want.

**Midterm Exam rescheduled. **Your midterm exam will be given in class on **Monday, March 18**
because of the class cancellation of March 6. The exam will consist entirely of proofs
that have been done in class, and will cover Sections 5.1-5.6, 8.1-8.2. Any definitions that you need will be
supplied on the exam.

**Deadlines.**
Please be aware of all relevant deadlines.

**Course syllabus:**

pdf,

**Section outlines:**

Section 5.1 Series of Constants I pdf, Series of Constants II, pdf.

Section 5.2 Convergence Tests for Positive Term Series, pdf.

Section 5.3 Products of Series, pdf

Section 5.5-5.6 The Weierstrass M-Test and Power Series, pdf

Section 8.1 Euclidean Space, pdf

Section 8.2 Open Sets and Closed Sets, pdf

Section 8.3 Compact Sets, pdf

Section 9.1 Limits of Functions, pdf

Section 9.2-9.3 Continuous Functions, pdf

Section 10.1 Linear Transformations and Norms, pdf

Section 10.2 Differentiable Functions, pdf

Section 10.3 The Chain Rule, pdf

Section 10.4 Inverse Functions, pdf

Section 10.5 Implicit Functions, pdf

Section 11.1 Definition of the Integral, pdf

Section 11.2 Lebesgue Null Sets and Jordan Null Sets, pdf

Section 11.3 Lebesgue’s Criterion, pdf

Section 11.4 Fubini’s Theorem, pdf

Section 11.5 Change of Variables, pdf

**Class notes:**

**Homework Assignments: (problems in bold must be written up and
handed in.)**

Homework #1 (due Monday 02-04-13): Problems 5.2, 5.3, 5.4, **5.6, 5.7(a)-(d), 5.8**. Solutions

Homework #2 (due Monday 02-11-13): Problems 5.9, 5.10, 5.16, **5.17**, **5.22, 5. 24, 5.26, 5.27.** Solutions

Homework #3 (due Monday 02-18-13): Problems**
**5.39, **5.40, 5.42, **5.43, **5.44**, **5.46, **5.48, 5.50. Solutions

Homework #4 (due Monday 03-04-13): Problems 8.2, 8.3, **8.8**, **8.11(a)-(b)**, **8.14 (a)-(c)**. Solutions

Homework #5 (due Monday 03-18-13): Problems 8.17, **8.24**, **8.26**, **8.31**, 8.28**, 8.34. **Solutions

Homework #6 (due Monday 03-25-13):
Problems **8.35**, 8.38, 8.39, **8.41, 9.4, 9.5, **9.9. Solutions

Homework #7 (due Monday 04-01-13): Problems **9.11****, 9.12, **9.14, **9.18, **9.19,
9.32, **9.34. **Solutions

Homework #8 (due Monday 04-08-13):
Problems **10.1**, **10.4**, 10.5, **10.8**, 10.9,
10.10, **10.11**, 10.12**. **Solutions

Homework #9 (due Monday 04-15-13):
Problems 10.26, **10.30**, **10.38**, **10.39 **Solutions

Homework #10 (due Monday 04-22-13):
Problems 10.45, 10.48, **10.49**, **10.50**, **10.51**, **10.51(a) **Solutions

Homework #11 (due Monday 04-29-13):
Problems 10.57, **10.61**, **10.65**, 10.66, 10.69, 10.70, 10.74 Solutions

**Exam Solutions:**

Midterm Exam 1 (03-06-13): pdf, Solutions

To
contact me, send mail to: *dwalnut@gmu.edu*.