### MATH 316-001 - Advanced Calculus II - Spring 2013

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.

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:

01-23-13.pdf

01-28-13.pdf

01-30-13.pdf

02-04-13.pdf

02-06-13.pdf

02-11-13.pdf

02-13-13.pdf

02-18-13.pdf

02-20-13.pdf

02-25-13.pdf

02-27-13.pdf

03-04-13.pdf

03-18-13.pdf

03-20-13.pdf

03-25-13.pdf

03-27-13.pdf

04-01-13.pdf

04-03-13.pdf

04-08-13.pdf

04-10-13.pdf

04-15-13.pdf

04-17-13.pdf

04-22-13.pdf

04-24-13.pdf

04-29-13.pdf

05-01-13.pdf

05-06-13.pdf

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), 5.8Solutions
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):  pdfSolutions

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