This page is
www.math.columbia.edu/~bayer/F00/linalg.html
Prerequisites: Math
V1106 Calculus IIS or Math
V1201 Calculus IIIA or the equivalent.
Text:
Linear Algebra with Applications Fifth Edition, by Steven J. Leon.
Prentice Hall, 1998, ISBN 0138493081.
Columbia University Bookstore,
or check
AddALL to find the best price online.
This semester we will cover chapters 1, 2, 3, 4, 5, 6.
Exams: There will be two exams (30 points each) and a final (40 points).
- First Exam, Thursday, October 5, 2000, in class.
- Second Exam, Thursday, November 9, 2000, in class.
- Final, Thursday, December 21, 2000, 9:00am-NOON.
These dates do not coincide with any religious holiday which causes suspension of
New York City's alternate side parking regulations; see
NYC Parking Calendar.
See also bnaibrith.org/caln.html.
Please discuss other conflicts with me well in advance of the exam in question.
Master University Examination Schedule
2000-2001 University Academic Calendar
Office Hours are posted at www.math.columbia.edu/~bayer.
I have no more office hours for the Fall 2000 semester. Please go to the
Help Room for
assistance with Linear Algebra, or contact me by email.
Course materials: Course materials are posted in Acrobat PDF format. Your browser
can be trained to automatically open these files with Acrobat Reader, a free program which you can
download from http://www.adobe.com/products/acrobat/readermain.html.
- inverse.pdf describes a quick hand method for computing
3 by 3 inverses.
(TeX sources, for instructors wishing to borrow format:
midterm1_F00.tex,
practice2_F00.tex,
midterm2_F00.tex.)
Class Schedule and Homework Assignments:
- Tuesday, September 5, 2000:
1.1 Systems of Linear Equations. Exercises 1-8.
- Thursday, September 7:
1.2 Row Echelon Form. Exercises 1-3, 5, 6, 19.
- Tuesday, September 12:
1.3 Matrix Algebra. Exercises 1-10, 12, 20, 30.
- Thursday, September 14:
1.4 Elementary Matrices. Exercises 1-5, 7, 9, 15.
- Tuesday, September 19:
1.5 Partitioned Matrices. Exercises 4, 5, 7-10.
- Thursday, September 21:
2.1 The Determinant of a Matrix. Exercises 1-4, 6, 10.
- Tuesday, September 26:
2.2 Properties of Determinants. Exercises 1, 3, 4, 7, 10.
- Thursday, September 28:
2.3 Cramer's Rule. Exercises 1-6.
- Tuesday, October 3:
exam review
- Thursday, October 5: First exam
- Tuesday, October 10:
3.1 Vector Spaces. Exercises 1-10.
- Thursday, October 12:
3.2 Subspaces. Exercises 1-8.
- Tuesday, October 17:
3.3 Linear Independence. Exercises 1-9.
- Thursday, October 19:
3.4 Basis and Dimension. Exercises 1-8, 11
3.5 Change of Basis. Exercises 1-5, 8-10
- Tuesday, October 24:
3.6 Rowspace, column space. Exercises 1-7
- Thursday, October 26:
4.1 Linear transformations, definitions and examples. Exercises 1, 3-5, 12.
4.2 Matrix representation of linear transformations. Exercises 1-5.
- Tuesday, October 31:
4.3 Similarity. Exercises 1, 3-6.
- Thursday, November 2:
exam review.
- Tuesday, November 7: no class; Election Day
- Thursday, November 9: Second exam
- Tuesday, November 14:
5.1 The scalar product. Exercises 1-8
5.2 Orthogonal subspaces. Exercises 1, 2
- Thursday, November 16:
5.3 Inner product spaces. Exercises 1-4
5.4 Least squares problems. Exercises 1-6
- Tuesday, November 21:
5.5 Orthonormal sets. Exercises 1, 2, 4, 7, 8
5.6 The Gram-Schmidt orthogonalization process. Exercises 1-4
- Thursday, November 23: no class; Thanksgiving
- Tuesday, November 28:
6.1 Eigenvalues and eigenvectors. Exercises 1-5
6.2 Systems of linear differential equations. Exercise 1
- Thursday, November 30:
6.3 Diagonalization. Exercises 1-4
6.4 Hermitian matrices. Exercises 1, 4
- Tuesday, December 5:
6.5 Quadratic forms. Exercises 1, 3
6.6 Positive definite matrices. Exercises 1, 3, 4
- Thursday, December 7:
exam review.
- Thursday, December 21, 2000: Final Exam, 9:00am-Noon