Mathematics 223, Fall 2007

TuTh 11:40am--12:55pm Malott 251

W 7:30pm--9:55pm Malott 532

Professor Tara Holm
Office: Malott 589
Phone: 607-255-2392

Office Hours:

Tuesday & Thursday 1:00-1:30pm
Wednesday 1:30-2:30pm
By appointment

If you have any questions, please come by my office, or send me email!!

General Information

TA: Igors Gobovickis
TA's office hours: Monday 3:00-4:00pm, Friday 4:00-5:00pm in Malott 218

Topics: Linear algebra and multivariable differential calculus.

Text: Hubbard & Hubbard, Vector Calculus, Linear Algebra, and Differential Forms, 3rd Edition. You can buy it from MatrixEditions or the Cornell bookstore.
A Student's Solutions Manual for the third edition is now available! You can pick up a copy at the Cornell bookstore, or online at MatrixEditions. In the latter case, you can have a $5 discount if you enter the voucher "Cornell" when ordering. This discount will be good through the end of September.

Syllabus: Available in PDF.

Questionnaire from the first lecture: Available in PDF.

Homework Assignments

The first Problem Set is due on 4 September 2007. (Initially I wrote 7 September by mistake; you can still turn in the problem set until 7 September without penalty.)
The second Problem Set is due on 11 September 2007.
The third Problem Set is due on 18 September 2007 IN CLASS!!!. There are (partial) solutions availble! If you have any other questions, email me or ask in recitation!
The fourth Problem Set is due on 2 October 2007 IN CLASS!!!.
The fifth Problem Set is due on Thursday 11 October 2007 in class.
The sixth Problem Set is due on 16 October 2007 in class.
The seventh Problem Set is due on 23 October 2007 in class.
The eighth Problem Set is due on 30 October 2007 in class.
The ninth Problem Set is due on 13 November 2007 in class.
The tenth Problem Set is due on 20 November 2007 in class.
The last Problem Set is due (for extra credit) on 29 November 2007 in class.

Prelims

The Second Prelim is due on 6 November 2007 in class!
The Solutions are available.

Lectures

Please take 15 or 20 minutes before each lecture to read the sections of the books that will be covered. It will help tremendously if you are familiar with the terminology and theorems that will be covered in class.

Date	Lecture Material	Notes from Lecture
Week 1
8/23/07	1.1, 1.2: Points and Vectors, Matrices
Week 2
8/28/07	1.2, 1.3: Matrices, Transformations	Some questions from lecture
8/30/07	1.3, 1.4: Transformations, Geometry of Euclidean space	Some questions from lecture
Week 3
9/4/07	2.1, 2.2: Row reduction, solving equations	Some notes following lecture
9/5/07	Recitation: Induction proofs	Induction handout
9/6/07	2.3: Matrix Inverses, elementary matrices	Some notes and extra exercises
Week 4
9/11/07	2.4: Linear combinations, span, and linear independence
9/13/07	2.5: Kernels, images, and the dimension formula
Week 5
9/18/07	2.6: Abstract vector spaces	Some notes and extra exercises
9/20/07	Prelim 1
Week 6
9/25/07	2.6,1.5: Limits of functions, continuity
9/27/07	1.5 continued
Week 7
10/2/07	1.6,1.7: Four big theorems; Differential calculus	Some extra comments
10/4/07	1.7,1.8: More derivatives
Week 8
10/9/07	No Class -- Fall Break
10/11/07	1.9: Mean Value Theorem, Criteria for derivatives	Notes on the Mean Value Theorem Multidimensional Rolle's
Week 9
10/16/07	2.7: Eigenvectors and eigenvalues
10/18/07	2.8,2.9: Newton's method, superconvergence
Week 10
10/23/07	2.10,3.1: Inverse and Implicit function theorems, manifolds	Reference for IFTs
10/25/07	3.1,3.2: More about manifolds, tangent spaces
Week 11
10/30/07	3.3,3.4: Taylor polynomials
11/1/07	3.4,3.5: More on Taylor polynomials; Quadratic forms
Week 12
11/6/07	3.5: Quadratic forms
11/8/07	3.6: Classifying critical points	Some notes on quadrics
Week 13
11/13/07	3.7: Constrained critical points and Lagrange multipliers
11/15/07	3.7: More Lagrange multipliers, catch up!
Week 14
11/20/07	3.8: Geometry of curves and surfaces	Some notes on Dynkin diagrams NYTimes article
11/22/07	No Class -- Thanksgiving Break
Week 15
11/27/07	3.8: More curves and surfaces
11/29/07	Catch up!
12/7/07	FINAL EXAM!!