Math 601

Section 603

Instructor: Jim Belk (jbelk@math.tamu.edu).

Time & Room: MWF 1:50–2:40 in Zachry 104a.

Announcements

Monday Office Hours

I will be having office hours on Monday in my office:

Monday 2–5 pm in Milner 124

Practice Problem with Solutions

Here are some practice problems for the final exam:

Final Exam

Here are the date and time for the final:

Tuesday, December 11 from 3:30 to 5:30 pm (same room that we held class in)

Some notes:

The final exam is comprehensive (half linear algebra and half vector calculus), although there will be at least one entire problem on Gauss' Divergence Theorem.
The final exam will be about twice as long as the four in-class exams. Since there are two hours, it ought to be slightly less rushed than the in-class exams have been.
The final exam counts twice as much as each of the in-class exams. It is 2/7 of your grade (with 1/7 for each of the in-class exams, and 1/7 for homework).
You may bring four index cards OR an 8.5 x 11 sheet of paper filled with notes (front and back).
As with the other exams, you may use a basic scientific calculator only.

Divergence Theorem

Gauss' Divergence Theorem will be covered on the final exam. I've written up some notes on this subject, including some material that I didn't get to talk about in class:

Divergence Theorem Notes

Here are the recommended book problems on the divergence theorem:

TAMU: Section 7.3, # 7, 9
Schaum's Outline: Chapter 6, #17, 18, 52, 53, 55

Course Materials

Note

I'm not sure that any of the links here will work next year. If you want to have long-term access to any of the course documents, you should make sure download them to your files.

Old Exams

Here are the solutions to the four exams:

Here are the practice problems for these exams with solutions:

Practice Test for the First Exam (and Solutions)
Practice Problems for the Second Exam (and Solutions)
Practice Problems for the Third Exam (and Solutions)
Practice Problems for the Fourth Exam (and Solutions)

Old Homework Assignments

Homework 1 was due Friday, August 31. Here are the solutions.
Homework 2 was due Friday, September 7. Here are the solutions.
Homework 3 was due Monday, September 17. Here are the solutions.
Homework 4 was due Friday, September 28. Here are the solutions.
There was no homework 5.
Homework 6 was due Friday, October 5. Here are the solutions.
Homework 7 was due Friday, October 12. Here are the solutions.
Homework 8 was due Friday, October 26. Here are the solutions

Homework 9 was due Friday, November 2. Here are the solutions
Homework 10 was due Friday, November 16. Here are the solutions
Homework 11 was due Wednesday, November 28. Here are the solutions

Notes

Here are all of the notes I have ever written up:

First-Day Handout

Click here for the first-day handout.

Syllabus

The syllabus for the course is online here.

Resources

Wikipedia pages

System of linear equations
Euclidean subspace: You can ignore the "operations on subspaces".
Null space: You can ignore the "relation to the row space" section.
Row space: You can ignore the "relation to the null space" and "generalization to coimage".
Column space: You can ignore the "relation to the left null space".

Online tools

Feel free to use these on the homework assignments. The two row-reduction tools are the first two hits if you Google "row-reducer".

Online Row Reducer: Really cool applet that animates the steps of the row reduction. Handles fractions.
Matrix Row-Reducer: Reduces any matrix to reduced echelon form.
Linear Algebra Toolkit: Toolkit for solving various types of linear algebra problems.
JAVA Vector Field Analyzer II

Free book

There is a free online linear algebra textbook by Jim Hefferon. You may find it useful as a secondary resource.

Linear algebra lectures

These are the lectures for an MIT linear algebra course by Gilbert Strang, hosted by Google Video. (You can download the original versions from the MIT OpenCourseWare website, but they require RealPlayer.)

Lecture 1: Geometry of Linear Equations
Lecture 2: Elimination with Matrices
Lecture 3: Multiplication and Inverse Matrices
Lecture 4: Factorization into A = LU (Note: We are not covering this topic.)
Lecture 5: Transposes, Permutations, Spaces R^n
Lecture 6: Column Space and Nullspace
Lecture 7: Solving Ax = 0: Pivot Variables, Special Solutions
Lecture 8: Solving Ax = b: Row Reduced Form R
Lecture 9: Independence, Basis, and Dimension
Lecture 10: The Four Fundamental Subspaces
Lecture 18: Properties of Determinants
Lecture 19: Determinant Formulas and Cofactors
Lecture 20: Cramer's Rule, Inverse Matrix, and Volume
Lecture 20: Cramer's Rule, Inverse Matrix, and Volume
Lecture 21:Eigenvalues and Eigenvectors
Lecture 22: Diagonalization and Powers of A

Feedback

One of the main difficulties in teaching is getting feedback from students. Please let me know how I'm doing by filling out the following form as often as you can. You can also use this form to comment about the book, the homework, the tests, etc.