| Class |
Date |
Day |
Title |
Sections |
Announcements |
| Lecture 01 |
9/08 |
W |
The Geometry of Linear Equations. |
1.1-2.1 |
| Lecture 02 |
9/10 |
F |
Elimination with Matrices. |
2.2-2.3 |
| Lecture 03 |
9/13 |
M |
Matrix Operations and Inverses. |
2.4-2.5 |
| Lecture 04 |
9/15 |
W |
A = LU and A = LDU Factorization. |
2.6 |
Problem Set 1 Due 9/16 |
| Lecture 05 |
9/17 |
F |
Permutations, Dot Products, and Transposes. |
2.7 |
| Lecture 06 |
9/20 |
M |
Vector Spaces and Subspaces. |
3.1 |
| Lecture 07 |
9/22 |
W |
The Nullspace: Solving Ax=0. |
3.2 |
Problem Set 2 Due 9/23. |
| Lecture 08 |
9/24 |
F |
Solving $Ax=b$ for nonsquare $A$, Row-reduced Echelon Form. |
3.3-3.4 |
| Lecture 09 |
9/27 |
M |
Independence, Dimension, and Bases. |
3.5 |
| Lecture 10 |
9/29 |
W |
The Four Fundamental Subspaces. |
3.6 |
Problem Set 3 Due 9/30. |
| Lecture 11 |
10/01 |
F |
EXAM REVIEW. |
3.6 |
| Exam 1 |
10/04 |
M |
EXAM: Chapters 1 to 3.5 |
|
| Lecture 12 |
10/06 |
W |
Graphs and Networks. |
8.2 |
Problem Set 4 Due 10/07. |
| Lecture 13 |
10/08 |
F |
Orthogonality and Subspaces |
4.1 |
|
10/11 |
M |
COLUMBUS DAY |
|
| Lecture 14 |
10/13 |
W |
Projections. |
4.2 |
Problem Set 5 Due 10/14 |
| Lecture 15 |
10/15 |
F |
Least Squares Approximations. |
4.3 |
| Lecture 16 |
10/18 |
M |
Orthonormal Bases, Gram-Schmidt, and $A=QR$. |
4.4 |
| Lecture 17 |
10/20 |
W |
Fourier Series and Orthogonal Polynomials. |
8.5 |
Problem Set 6 Due 10/21 |
| Lecture 18 |
10/22 |
F |
Properties of Determinants. |
5.1 |
| Lecture 19 |
10/25 |
M |
Formulas for Determinants; Jacobians. |
5.2-5.3 |
| Lecture 20 |
10/27 |
W |
Eigenvalues and Eigenvectors. |
6.1 |
Problem Set 7 Due 10/28 |
| Lecture 21 |
10/29 |
F |
Similar Matrices, Diagonalization, and Powers of $A$ |
6.6, 6.2 |
| Lecture 22 |
11/01 |
M |
EXAM REVIEW |
|
| Exam 2 |
11/03 |
W |
EXAM: Chapter 1 to 5.3 and 8.2,8.5 |
|
| Lecture 23 |
11/05 |
F |
Markov Matrices |
8.3 |
| Lecture 24 |
11/08 |
M |
Differential Equations |
6.3 |
| Lecture 25 |
11/10 |
W |
Symmetric Matrices. |
6.4 |
Problem Set 8 Due 11/11 |
| Lecture 26 |
11/12 |
F |
Positive Definite Matrices. |
6.5 |
| Lecture 27 |
11/15 |
M |
Defective Matrices: Jordan Forms and Generalized Eigenvectors. |
6.6 |
| Lecture 28 |
11/17 |
W |
Singular Value Decompositions. |
6.7 |
Problem Set 9 Due 11/18. |
| Lecture 29 |
11/19 |
F |
Matrices in Engineering. |
8.1 |
| Lecture 30 |
11/22 |
M |
Linear Operators on Functions. |
|
| Lecture 31 |
11/24 |
W |
Sparse Matrices and Iterative Methods. |
9.3 |
Problem Set 10 Due 11/29. |
|
11/26 |
F |
THANKSGIVING. |
|
|
| Lecture 32 |
11/29 |
M |
EXAM REVIEW. |
|
| Exam 3 |
12/01 |
W |
EXAM: Chapters 1 to 6.7 and 8.1, 8.3, 8.5. |
|
| Lecture 33 |
12/03 |
F |
Numerical Linear Algebra |
9.1-9.2 |
| Lecture 34 |
12/06 |
M |
Complex Matrices and FFTs |
10.1-10.3 |
| Lecture 35 |
12/08 |
W |
Course Review. |
| Final Exam |
TBD |
|
|
|
18.06 Linear Algebra, Spring 2011