Instructor: John D. Trout
Course on canvas.dartmouth.edu.⇗
Syllabus
| Lecture | Date | Read Sections | Description | Lecture Notes, Handouts & Daily HW |
| 1 |
Monday March 31 |
Appendices A, B, C, D |
Course Introduction | |
| 2 |
Wednesday April 2 |
1.1 & 1.2 | Vector Spaces |
lecture-02.pdf Download lecture-02.pdf HW § 1.2 # 1, 4 aceg, 13, 14, 15 |
| 3 |
Friday April 4 |
1.2 & 1.3 |
Vector Spaces & Subspaces |
lecture-03.pdf Download lecture-03.pdf HW § 1.3: # 1, 2 ace, 8, 11, 15 |
| 4 |
Monday April 7 |
1.3 & 1.4 |
Subspaces (cont'd) & Linear Combinations |
lecture-04.pdf Download lecture-04.pdf Lecture 4 notes.pdf Download Lecture 4 notes.pdf HW § 1.4: # 2 ace, 3 ace |
| 5 |
Wednesday April 9 |
1.4 & 1.5 |
Linear Combinations (cont'd) & Linear (In)dependence |
l Download lecture-05.pdf Download ecture-05.pdf Lecture 5 notes.pdf Download Lecture 5 notes.pdf HW § 1.4: # 1, 4 ace, 5 aceg |
| 6 |
Friday April 11 |
1.5 & 1.6 |
Linear (In)dependence (cont'd) & Bases & Dimension |
lecture-06.pdf Download lecture-06.pdf Lecture 6 notes.pdf Download Lecture 6 notes.pdf HW § 1.5: # 1, 2 acegi, 7 HW § 1.6: # 2 ae, 3 ac, 5 |
| 7 |
Monday April 14 |
1.6 & 2.1 |
Bases & Dimensions (cont'd), Linear Transformations |
lecture-07.pdf Download lecture-07.pdf Lecture 7 notes.pdf Download Lecture 7 notes.pdf HW 1.6: # 1, 4, 9, 13, 20 |
| 8 |
Wednesday April 16 |
2.1 Review Appendix B |
Linear Transformations (cont'd) |
lecture-08.pdf Download lecture-08.pdf Lecture 8 notes.pdf Download Lecture 8 notes.pdf Rank-Nullity Example.pdf Download Rank-Nullity Example.pdf Rank-Nullity Example.gcf Download Rank-Nullity Example.gcf (Graph Calc demo) HW § 2.1: # 1, 2, 4, 5, 10, 12, 13 |
| 9 |
Friday April 18 |
2.1 & 2.2 |
Linear Transformations (cont'd)., Coordinate Vectors relative to Ordered Bases |
|
| 10 |
Monday April 21 |
2.2 |
Matrix Representation of Linear Transformations |
lecture-10.pdf Download lecture-10.pdf HW § 2.2: # 1, 2 acdf, 3,5 abe, 13 |
|
11 |
Wednesday April 23 |
2.3 |
Composition of Linear Transformations and Matrix Multiplication |
lecture-11.pdf Download lecture-11.pdf Lecture 11 notes.pdf Download Lecture 11 notes.pdf HW § 2.3: # 1, 2 ab, 3 a, 4 ac, 15 |
|
12 |
Friday April 25 |
2.4 |
Invertibility and Isomorphisms |
lecture-12.pdf Download lecture-12.pdf Lecture 12 Notes.pdf Download Lecture 12 Notes.pdf Matrix Multiply Inverse.pdf Download Matrix Multiply Inverse.pdf Matrix Multiply Inverse.gcf Download Matrix Multiply Inverse.gcf HW § 2.4: # 1, 2, 3 |
| 13 |
Monday, April 28 |
2.5 & 3.1 |
Change of Coordinate Matrix & Elementary Matrix Operations |
lecture-13.pdf Download lecture-13.pdf Lecture 13 notes.pdf Download Lecture 13 notes.pdf HW § 2.5: # 1, 2 ac, 3 ce, 4, 5, 6 a, 13 |
| 14 |
Wednesday, April 30 |
3.1 & 3.2 | Elementary Matrix Operations & Rank and Invertible Matrices |
lecture-14.pdf Download lecture-14.pdf Lecture 14 notes.pdf Download Lecture 14 notes.pdf HW § 3.1: # 1, 2, 3 ac HW § 3.2: # 1, 2 ace, 4 a |
|
Thursday, May 1 |
x-hour | More Examples and Some Review! | 2D Linear Transformations.pdf Download 2D Linear Transformations.pdf | |
| 15 |
Friday, May 2 |
3.2 & 3.3 | Inverses of Matrices & Theory of Linear Systems |
lecture-15.pdf Download lecture-15.pdf Lecture 15 notes.pdf Download Lecture 15 notes.pdf HW § 3.2: # 5 aceg HW § 3.3: # 1, 2 ace, 3 ace, 4 b |
| 16 |
Monday, May 5 |
3.4 | Computational Aspects of Linear Systems |
lecture-16.pdf Download lecture-16.pdf Lecture 16 notes.pdf Download Lecture 16 notes.pdf HW § 3.4: # 1, 2 aei, 4 ac, 5, 15 |
|
Wednesday, May 7 |
Midterm Exam | |||
| 17 |
Friday, May 9 |
4.1 & 4.2 |
Determinants of Order 2 and Order n |
lecture-17.pdf Download lecture-17.pdf HW § 4.1: # 1, 2 ac, 12 HW § 4.2: # 1, 3, 5, 7, 11, 15, 29 |
|
Monday, May 12 |
NO CLASS | NO CLASS | ||
| 18 |
Wednesday, May 14 |
4.3 & 4.4 |
Properties of Determinants and Summary |
lecture-18.pdf Download lecture-18.pdf Lecture 18 notes.pdf Download Lecture 18 notes.pdf HW § 4.3: # 1 abcdef, 21 HW § 4.4: # 1, 3 acg, 4 acg |
| 19 |
Friday, May 16 |
5.1 |
Eigenvalues and Eigenvectors |
lecture-19.pdf Download lecture-19.pdf HW § 5.1: # 1, 2 ace, 3 a, 4 abf, 15 |
| 20 |
Monday, May 19 |
5.1 & 5.2 |
Eigenvalues and Eigenvectors, Diagonalizability |
lecture-20.pdf Download lecture-20.pdf HW § 5.2: # 1, 2 aceg, 3 acde, 7, 12 a |
| 21 |
Wednesday, May 21 |
5.2 |
Diagonalizability (cont'd) |
l Download lecture-21.pdf Download ecture-21.pdf HW § 5.2: # 1, 2 aceg, 3 acde, 7, 12 a |
|
x-hour |
Thursday, May 22 |
Canceled |
x-hour will be rescheduled for next week. |
|
|
22 |
Friday, May 23 |
5.4 |
Invariant Subspaces and the Cayley-Hamilton Thm |
lecture-22.pdf Download lecture-22.pdf HW: § 5.4: # 1, 2, 6 ac, 9 ac, 10 ac, 15 |
|
|
Monday, May 26 |
NO CLASS |
Memorial Day |
|
|
23 |
Wednesday, May 28 |
6.1 |
Inner Products and Norms |
lecture-23.pdf Download lecture-23.pdf HW § 6.1: # 1, 2, 3, 10, 16 b |
|
|
Thursday, May 29 |
x-hour | Applications of Linear Algebra | |
| 24 |
Friday May 30 |
6.2 |
Gram-Schmidt Orthogonalization Process |
lecture-24.pdf Download lecture-24.pdf HW § 6.2: # 1, 2 bcgm, 4, 5, 11, 19 ab |
| 25 |
Monday, June 2 |
6.3 |
Adjoint of a Linear Operator |
lecture-25.pdf Download lecture-25.pdf HW § 6.3: # 1, 2 ac , 3 ac, 14, 18 |
| 26 |
Wednesday, June 4 |
6.4 |
Normal and Self-Adjoint Operators |
HW § 6.4: # 1, 2 ace |