| Day |
Material covered in the lecture |
Homework due |
Week 1
April 1st |
§1.1-1.3: Gaussian elminiation |
|
| April 3rd |
§1.1-1.3: Gaussian elminiation |
|
| April 5th |
§1.1-1.3: Gaussian elminiation |
|
Week 2
April 8th |
§1.5-1.6: Matrix operations |
|
| April 10th |
§1.5-1.6: Matrix operations |
|
| April 12th |
§1.7: Linear independence
Quiz |
§1.1: #17, 29, 32, 35
§1.2: #10, 21, 31, 35, 39, 49, 51
§1.3: #4, 12, 18, 23, 24
§1.5: #6, 8c, 10c, 12b, 20, 24, 30, 48 |
Week 3
April 15th |
§1.7: Linear independence |
|
| April 17th |
§1.9: Matrix inverses |
|
| April 19th |
§1.9: Matrix inverses |
§1.6: #3, 11, 26, 27, 40, 47
§1.7: #12, 14, 20, 23, 50, 56 |
Week 4
April 22nd |
§3.1-3.3: Subspaces |
|
| April 24th |
§3.1-3.3: Subspaces |
|
| April 26th |
§3.1-3.3: Subspaces |
§1.9: #4, 8, 10, 20, 38, 39, 55, 70, 76
§3.1: #13, 16, 21, 22 |
Week 5
April 29th |
§3.4-3.5: Bases and dimension |
|
| May 1st |
Review of the midterm |
|
| May 3rd |
Midterm |
§3.2: #6, 10, 11, 21, 28, 33
§3.3: #19, 20, 25, 32, 43, 48, 51, 52 |
Week 6
May 6th |
§3.4-3.5: Bases and dimension |
|
| May 8th |
§3.6-3.7: Orthogonal basis
and linear transformations |
|
| May 10th |
§3.6-3.7: Orthogonal basis
and linear transformations |
§3.4: #1, 9c, 11, 24, 34, 37
§3.5: #4, 6, 9, 18, 26, 32, 33, 34 |
Week 7
May 13th |
§3.8-3.9: Least squares |
|
| May 15th |
§3.8-3.9: Least squares |
|
| May 17th |
§4.1-4.3: Eigenvalues and determinants
Quiz |
§3.6: #4, 6, 10, 16, 22, 28
|
Week 8
May 20th |
§4.1-4.3: Eigenvalues and determinants |
|
| May 22nd |
§4.4-4.5: Eigenvalues, characteristic
polynomial, eigenspaces |
|
| May 24th |
§4.4-4.5: Eigenvalues, characteristic
polynomial, eigenspaces |
§3.7: #3, 10, 14, 22, 28, 30, 34, 36, 44
Also do:
Let \(P_2\) be the vector space of polynomials
of degree less than or equal to \(2\). Show that
the function \(T: P_2 \to \mathbb{R}^2 \) given by
\(T(p(x)) = \begin{bmatrix} \int^1_0 p(x) dx \\ p(0)\end{bmatrix}\) is a linear transformation.
§3.8: #1, 3 |
Week 9
May 27th |
No class |
|
| May 29th |
§4.6-4.7: Complex eigenvalues,
similarity, diagonalization |
|
| May 31st |
§4.6-4.7: Complex eigenvalues,
similarity, diagonalization
Quiz |
§4.1: #2, 10, 14, 17
§4.2: #12, 18, 24, 25, 28, 30
§4.3: #4, 12
§4.4: #14
§4.5: #6, 10, 14 (ignore the part defective), 20, 22 |
Week 10
June 3rd |
§4.8 Applications |
|
| June 5th |
Review for the final |
|
| June 7th |
Review for the final |
§4.7: #5, 7, 25
Also do:
For an \( (n \times n) \) matrix \( A \) the exponential of \(A\)
is defined as \(e^A = \sum_{k = 0}^{\infty} \frac{A^k}{k!}\).
If \(D = \begin{bmatrix} d_1 & 0 & \cdots & 0 \\
0 & d_2 & 0 & \cdots \\
\vdots & 0 & \ddots & 0 \\
0 & \cdots & 0 & d_n \end{bmatrix} \), then
\(e^D = \begin{bmatrix} e^{d_1} & 0 & \cdots & 0 \\
0 & e^{d_2} & 0 & \cdots \\
\vdots & 0 & \ddots & 0 \\
0 & \cdots & 0 & e^{d_n} \end{bmatrix} \).
Let \(A\) be a diagonalizable matrix, that is, \(A= SDS^{-1} \)
where \(D\) is a diagonal matrix; then \(e^A = S e^D S^{-1} \).
Compute \(e^A \) for problems 5 and 7 of 4.7. |