Math 20860, Spring `15

Schedule


Topics, reading and homework assignments are given below. Beyond a week or two out the schedule is tentative (or non-existent). Hence I will update this page very often. It is your responsibility to check it frequently to see what's going on in class. In particular, you will find all new homework assignments here, and soon after you turn in an assignment, I will post solutions for you to look at.

Dates

Topics

Reading

Homework

Miscellaney

1/12-1/16

Determinants

Shifrin 7.3

Alt, LADW 3.1-3.3, 3.5 and/or Jones 3F

Homework 1

solutions


1/19-1/23

Eigenvalues and diagonalization

Shifrin 9.2

Alt, Jones 4A or LADW 4.1

Homework 2

solutions


1/26-1/30

Second derivative test

Shifrin 5.3, 9.4

Alt Jones 3BE, 4DE

Homework 3

solutions

My rendition of the proof of the spectral theorem.

2/2-2/6

Integration on rectangles

Shifrin 7.1 (Alt Jones 9A-E)

Homework 4

solutions

Mathematica notebook concerning the second derivative test.

Concerning integration, note that I'm using Shifrin's definition of partition but then Jones' definition of Riemann integral. The two are not actually that far apart.

2/9-2/13

Fubini's Theorem

Integration over more general regions

Shifrin 7.2 (Alt Jones 9F-H)

Shifrin 7.1 (Alt Jones 9I, 10B-D)

Homework 5

solutions

Here is a summary of Riemann integration via step functions.

2/16-2/20

Change of variables

Shifrin 7.6 (Alt Jones 10F-I)

Review sheet for 1st exam

Math for everyone talk on Thursday, February 19 at 5 PM in DBRT 102: Imaginary Numbers, Unsolvable Equations, and Newton's Method. Speaker is a relative unknown from an obscure university in a small midwestern town.

2/23-2/27

Polar, spherical and cylindrical coordinates

Shifrin 7.3

Homework 6

solutions

1st midterm in class 2/27

3/2-3/6

Arc-length integrals.

1-forms and line integrals

Jones 11A

Jones 12B; Shifrin 8.3

Homework 7

solutions

Happy spring break!

3/16-3/20

FTC for curves

Green's Theorem

Closed and exact 1-forms

Shifrin 8.3; Jones 12A, C-F

Homework 8

solutions

Take heart. This happened over spring break.

I will have a research visitor here on Tuesday & Thursday this week, so I will have to cancel office hours on Wed. I will be in my office from 2-3:30 on Thursday afternoon instead.

Math for everyone talk by Arielle Saber of Bowdoin College on Thursday, March 19 at 5 PM in DBRT 102: Mathy Words in the Italian Renaissance:  Niccol├│ Tartaglia's Poetic Solution to the Cubic Equation.

3/23-27

Green's Theorem

Cross-product

Parametrized surfaces and Surface area



Shifrin 1.5 (alt Jones, chapter 7)


Homework 9

solutions

There will be a four day Undergraduate Summer School in Mathematics at Notre Dame from 5/19-22. The broad topic will be dynamical systems. Applying is easy and funding is available, but the deadline is April 7.

My treatment of surface area is different than both Jones and Shifrin, so you'll need to depend on my lecture for this part.

Mathematica notebook about parametrized surfaces and area

3/30-4/2

Differential k-forms

Shifrin 8.2

Review sheet for 2nd exam, and some summary notes (by Christian Gorski) about integrating on curves and surfaces.


4/7-4/10

More differential k-forms


Homework 10

solutions

2nd exam in class 4/10

4/13-4/17

Integration of differential forms on parametrized submanifolds (esp. surfaces)

Shifrin 8.4


Homework 11

solutions


4/20-4/24

Stokes Theorem.

Shifrin 8.5, 8.6


I am moving my Wed 4/22 office hours to Mon 4/27 from 5:30-7:30 (I'll put a note about the room on my office door)

4/27-4/29



Review sheet for the final exam

The Math Club is holding an integration bee Tuesday 4/28 at 7:30 PM in Hayes-Healy 127. Also T-Shirts will be available for pickup and new officers will be introduced.

COS-JAM takes place Friday 4/29. There will be two sessions of math talks (1-2:30 and 3:30-5) both in 310 Jordan. I encourage you to attend one or both of these sessions to hear about what upperclass students have been up to mathematically.

No office hours Wed 4/29

Final exam, Thursday May 7 from 4:15-6:15 in Hayes-Healy 229 (our usual lecture room).