Fall 2000

Mathematics 21b - Fall 2000
Linear Algebra
and Differential Equations

Course Head:
Robert Winters
Office: SciCtr 435
Email: rwinters@math.harvard.edu

Final Exam Information:

The Final Exam will be held on Saturday, January 13 at 2:15pm in Harvard 202. To help with your studying for this exam, here are some helpful materials:

There will be an informal review (questions and answers) this Wednesday, Jan 10 from 10am to noon in Sci Ctr 102b. Check back here in case there is a room change.

Midterm Exam 2 Information:

Midterm Exam #2 was on Tues, Nov 21. It covered material from section 3.2 to section 7.2 of the text. The median score on Exam 2 was 80.

Supplements:

Week of Dec 4 - Dec 8:
Supplement: Section 8.3 - Nonlinear Systems and Linearization (scanned, 13 page PDF)
Supplement: Section 8.3 - Nonlinear Systems and Linearization (reformatted 10 page PDF, same content as above)

Supplement: Section 9.1 - Ordinary Linear Differential Equations (scanned, 6 page PDF)
Supplement: Section 9.1 exercises (scanned, 1 page PDF)

Week of Dec 11 to end of course:
Supplement: Section 10 - Further Topics in Differential Equations (scanned, 24 page PDF)

Supplement: Quadratic forms, critical points, principal axes, and the 2nd Derivative Test
Supplement: Matrix of a linear transformation relative to a preferred basis
(and how you might deal with repeated eigenvalues and complex eigenvalues)
Supplement on Least Squares Approximation in Economics

Midterm Exam 1 Information:

Midterm Exam #1 was Mon, Oct 16. It covered material up to and including section 3.1 of the text.
The median score on Exam 1 was 76.

Review Materials for Midterms:
Exam 2 - Fall 1999 (PDF)
Exam 2 Solutions - Fall 1999 (PDF)
Spring 1995 and Fall 1996 Second Midterm Exams (PDF)
Solutions to Spring 1995 Second Midterm Exam (PDF)
Solutions to Fall 1996 Second Midterm Exam (PDF)
Topics for Exam 2
Spring 1998 Exam 1 (HTML)
Spring 1998 Exam 1 Solutions (HTML)
Spring 1998 Exam 1 (PDF)
Spring 1998 Exam 1 Solutions (PDF)