Topics, reading and
homework assignments are given below. Beyond a week or two out the
schedule is tentative (or non-existent: it's my first time teaching
this class). 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.
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Dates |
Topics |
Reading |
Homework |
Miscellaney |
|---|---|---|---|---|
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8/28 - 8/30 |
Points, vectors and geometry of R^n |
Jones chap 1 Text 1.0, 1.1, 1.4 |
The sections in the text also discuss matrices and cross product. No need to worry about those just yet. |
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9/2 - 9/6 |
Open/closed sets and convergent sequences |
Text 1.5 (up to but not including uniform continuity) |
There will be an undergraduate reading group on discrete geometry this semester. The first meeting is this Thursday 9/5 from 4-5 PM in Hayes-Healy 258. The plan is to meet every Thursday at the same time thereafter. |
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9/9 - 9/13 |
Continuity and the Bolzano-Weirstrass and Extreme Value Theorems |
Text 1.6 See also sections 9-11 and 13-15 in these notes that I wrote for another course. |
The first Math for Everyone talk is this Thursday 9/12 at 5 PM. Lance Fortnow from Georgia Tech will speak on The P versus NP question. Here is a list of ideas for paper topics. |
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9/16 - 9/20 |
Fundamental Theorem of Algebra Partial derivatives, linear transformations |
Text 1.3, 1.7 |
Note the change in topic. We voted and I heard you... Note also that I will henceforth use Wed, rather than Thurs for tutorials but hold office hours after class Thursday. |
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9/23 - 9/27 |
(Total) derivatives, the Jabobian matrix and continuous differentiability. |
Text 1.8, 1.9 |
The one credit course Problem Solving in Math meets Tuesday afternoons and is aimed at practicing for the Putnam exam. It's too late to sign up for the course, but if you're interested in taking the Putnam and getting some practice, you're welcome to attend anyhow. |
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9/30 - 10/4 |
Parametrized curves and tangent vectors; gradients and critical points |
Jones notes: 2A, 2C-E, 2G, 2H, 2K |
Jones chapter 2 is also all about derivatives of mappings, but he orders the material differently, beginning with special cases and more motivation. Mathematica notebooks concerning curves and level sets |
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10/7 - 10/11 |
The chain rule & proof Proof that continuously differentiable implies differentiable. |
|
review sheet for the midterm. |
Mathematica notebook concerning the chain rule The next Math for Everyone event is Thursday 10/10 from 5-6 PM. This time it's a panel discussion: What to do with a math degree after Notre Dame? |
|
10/14 -10/18 |
1st order ODE |
Apostol I, 8.1-8.3 |
Midterm 10/17 from 12:30-1:45 in DBRT 116 |
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|
10/28 - 11/1 |
Separable and linear 1st order ODEs. The existence and uniqueness theorem |
Apostol I, 8.4, 8.23 (also 8.6 and 8.27 for applications) |
The dfield software by Polking et al is very handy for drawing direction fields and plotting solution curves Mathematica notebook about Picard iteration |
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|
11/4 - 11/8 |
Qualitative analysis for autonomous ODEs Higher order linear ODEs |
Notes concerning the existence and uniqueness theorem. Handout(s) |
The next Math for Everyone event is Thursday 11/8 from 5-6 PM. Alex Kasman from the College of Charleston will speak. The title of his talk is A Glimpse of Soliton Theory. Just to see if you're still paying attention |
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11/11-11/15 |
More ODE Newton's method, inverse function theorem |
More ODE, Hubbards' 2.8 and 2.9 (don't worry about Lipshitz conditions and Kantorovich's theorem) |
A Mathematica notebook that implements Newton's method for non-linear systems of two equations in two unknowns.
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11/18 - 11/22 |
Inverse and Implicit function theorems |
Hubbards 2.10 (I only care about the short versions of the theorems. |
I extended the deadline for homework 10 til Monday 11/23. |
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11/25 - 11/26 |
Hypersurfaces and the 'intrinsic gradient' |
Jones, chapter 5A,EF |
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Homework 11 will be due Monday 12/9. |
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12/2 - 12/6 |
Constrained optimization |
Jones, chapter 5BCD |
The last Math for Everyone event of the semester is a talk by Lisa Traynor from Bryn-Mawr College: All Tied Up in Knots. Takes place Thursday 12/5 at 5 PM in 101 Jordan. Here is a short Mathematica notebook concerning the quadrilateral e.g. from class |
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12/9 – 12/12 |
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review sheet for the final |
No class on Thursday 12/12. Instead I will hold a review session for the final from 7-9 PM on Monday Dec 16 in Hayes-Healy 125 (across from my office). Here is a Mathematica notebook concerning parametrizations of the sphere and the torus. |
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