MATH V2010:
Linear Algebra
Spring 2003
This page is
www.math.columbia.edu/~bayer/S03/linalg
Section 002 (Bayer)
Tuesdays and Thursdays, 10:35am-11:50am
304 Barnard Hall
Dave Bayer (x42643, 426 Mathematics,
www.math.columbia.edu/~bayer)
Bulletin page |
Directory of Classes :
Mathematics
Office Hours
Prerequisites: Math
V1106 Calculus IIS or Math
V1201 Calculus IIIA or the equivalent.
Text:
Linear Algebra with Applications Sixth Edition, by Steven J. Leon.
Prentice Hall, 1998, ISBN 0130337811.
University bookstore ($105) or
AddALL ($75 and up).
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, February 20, in class
- Second Exam, Thursday, April 3, in class
- Final, Tuesday, May 13, 9am-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.
Please discuss other conflicts with me well in advance of the exam in question.
Master University Examination Schedule
University Academic Calendar
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.
Course materials from previous semesters:
I have taught this course before; you can find old exams and practice materials on the
web pages for previous semesters:
Class Schedule and Homework Assignments
(Homework is not collected. Work as many exercises as necessary to master the material, and bring questions
to office hours or the help room.)
Tuesday, January 21
1.1 Systems of Linear Equations. Exercises 1-8
Thursday, January 23
1.2 Row Echelon Form. Exercises 1-3, 5, 6
Tuesday, January 28
1.3 Matrix Algebra. Exercises 1-10, 12, 20
Thursday, January 30
1.4 Elementary Matrices. Exercises 1-5, 7, 9
Tuesday, February 4
1.5 Partitioned Matrices. Exercises 4, 5, 7-9
Thursday, February 6
2.1 The Determinant of a Matrix. Exercises 1-4, 6
Assignments after this point still refer to Leon's 5th edition, and need to be updated.
Tuesday, February 11
2.2 Properties of Determinants. Exercises 1, 3, 4, 7, 10
Thursday, February 13
2.3 Cramer's Rule. Exercises 1-6
Tuesday, February 18
Thursday, February 20
Tuesday, February 25
3.1 Vector Spaces. Exercises 1-10
Thursday, February 27
3.2 Subspaces. Exercises 1-8
Tuesday, March 4
3.3 Linear Independence. Exercises 1-9
Thursday, March 6
3.4 Basis and Dimension. Exercises 1-8, 11
3.5 Change of Basis. Exercises 1-5, 8-10
Tuesday, March 11
3.6 Rowspace, column space. Exercises 1-7
Thursday, March 13
4.1 Linear transformations, definitions and examples. Exercises 1, 3-5, 12
Tuesday, March 18
Thursday, March 20
Tuesday, March 25
4.2 Matrix representation of linear transformations. Exercises 1-5
Thursday, March 27
4.3 Similarity. Exercises 1, 3-6
Tuesday, April 1
Thursday, April 3
Tuesday, April 8
5.1 The scalar product. Exercises 1-8
5.2 Orthogonal subspaces. Exercises 1, 2
Thursday, April 10
5.3 Inner product spaces. Exercises 1-4
5.4 Least squares problems. Exercises 1-6
Tuesday, April 15
5.5 Orthonormal sets. Exercises 1, 2, 4, 7, 8
5.6 The Gram-Schmidt orthogonalization process. Exercises 1-4
Thursday, April 17
6.1 Eigenvalues and eigenvectors. Exercises 1-5
6.2 Systems of linear differential equations. Exercise 1
Tuesday, April 22
6.3 Diagonalization. Exercises 1-4
Thursday, April 24
6.4 Hermitian matrices. Exercises 1, 4
6.5 Quadratic forms. Exercises 1, 3
Tuesday, April 29
6.6 Positive definite matrices. Exercises 1, 3, 4
Thursday, May 1
Tuesday, May 13