# Lectures and Homework 642:550, Summer 2008

All work is due two class meetings after it is assigned.  Exercises from the textbook are identified by a section number of the form #.#, or by #.R to signify the review problems at the end of a chapter.  My supplements, available from the "Resources" section of this site, are designated by S.#.

This page will not show the content of future meetings, but a link to a complete schedule from Summer 2007 is attached.  The course is not expected to differ significantly from previous years. Note that there will be a short exam each week to enforce the pace of the course.  The first two of these will be on Tuesday to allow relevant homework to be evaluated before the exam.  After that, the exam will be on Monday.  In all cases, the exam will be given at the start of class and take no more than half of the meeting time.

1. Monday, June 23:  Prerequisites.
• 2.4: 18, 20.
• 2.R: 11.
• 3.1: 16, 38.
• S.1: A, B.
2. Tuesday, June 24:  Determinants.
• 4.2: 4, 18, 34.
• 4.3: 1&2, 8, 36.
3. Thursday, June 26:  More determinants; introduction to eigenvalues.
• 4.4: 2, 18.
• 4.R: 15.
• S.3: A, B, C.
• 5.1: 1&2&3, 14.
4. Monday, June 30:  Finding eigenvectors.
• 5.2: 2, 4, 8.
• S.4: B, C, D.
• 5.3: 14.
5. Tuesday, July 01:  Exam #1 (based on homework 1 and 2); Complex Matrices.
• 5.5: 6, 7&8, 26, 49.
• 5.R: 15.
6. Thursday, July 03:  Differential Equations.
• S.5: B, C, F, U, W.
7. Monday, July 07:  Schur's theorem; QR factorization.
• S.6: A,B, C, D.
• 3.4: 14, 16, 28.
8. Tuesday, July 08:  Exam #2 (based on homework 3 and 4); the Perron-Frobenius theorem.
• S7: A, B, C, D.
9. Thursday, July 10:  Quadratic forms.
• 6.1: 2, 14.
• 6.2: 2, 6, 14, 28.
10. Monday, July 14:  Exam #3 (based on homework 5 and 6); Least squares; Singular Value Decomposition.
• 3.3: 6, 18, 22. Note that part b of exercise 18 asks for a least squares solution.
• 6.3: 1&2, 18. Note that part c of exercise 2 asks to relate the SVD in part b to the four fundamental subspaces of A.
11. Tuesday, July 15:  Minimum principles.
• 6.4: 6 and the following variants: (A) change the diagonal to 3, 1; (B) change the off diagonal terms to 2; (C) make both changes.
12. Thursday, July 17:  The Finite Element method.
• 6.5: NONE.
13. Monday, July 21:  Exam #4 (based on homework 7 and 8); Calculating characteristic polynomials.
• S.9: (to be continued)
14. Tuesday, July 22:  Calculating characteristic polynomials; numerical linear algebra.
• S.9: A, B, C.
• 7.1: NONE.
• 7.2: NONE.
• S.10: NONE.
15. Thursday, July 24:  More numerical linear algebra.
• 7.3: NONE.
• 7.4: NONE.
16. Monday, July 28:  Exam #5 (based on homework 9 and 10); Start of review.
• XX: NONE.
17. Tuesday, July 29:  Review.
• XX: NONE.
18. Thursday, July 31:  Final Exam.