Schedule
Classes normally meet Tuesdays and Thursdays at 11:25 AM in PH 109.
Completed lecture topics through October 8 have been checked against the Panopto recordings. Future topics are provisional and will be updated as assignments, quizzes, holidays, and examination details are finalized.
August
| Week | Date | Topic | Slides / Materials |
|---|---|---|---|
| 1 | Tue Aug 18 | Course introduction; linear systems and solution sets; reversible equation operations | Why Linear Algebra? Systems and Matrices |
| Thu Aug 20 | Dot product and matrix multiplication; augmented matrices, elimination and pivots; geometry of solution sets | Systems and Matrices | |
| 2 | Tue Aug 25 | Dot-product cosine formula; resistance-circuit systems; row operations as matrix multiplication; LU preview | Systems and Matrices |
| Thu Aug 27 | Undoing elimination; homogeneous systems; inverses and Gauss–Jordan reduction | Inverses and Invertibility |
September
| Week | Date | Topic | Slides / Materials |
|---|---|---|---|
| 3 | Tue Sep 1 | Inverse algebra and singularity; solving versus forming an inverse; Leontief and covariance/precision applications | Inverses and Invertibility |
| Thu Sep 3 | Diagonal, triangular, tridiagonal and symmetric matrices; permutations and PLU; companion notebook on reusable factors and solve cost | Matrix Structure and Transformations Companion notebook |
|
| Mon Sep 7 | Assignment 1 due | WileyPLUS: Systems and Matrix Operations | |
| 4 | Tue Sep 8 | Linear transformations and basis images; diagonal actions, Householder reflections, projections and rotations; Givens introduction | Matrix Structure and Transformations |
| Thu Sep 10 | Invertibility review; matrix transformations companion notebook; determinants: signed scale, elimination, PLU and swap parityQuiz 1 | Matrix Structure and Transformations DeterminantsCovers Systems and Matrices Inverses and Invertibility |
|
| 5 | Tue Sep 15 | Test 1 review: permutations/PLU, rotations, reflections, projections and inverses; revisit the determinant area proof | Matrix Structure and Transformations Determinants |
| Thu Sep 17 | Test 1 | Covers Systems of Linear Equations and Matrices Inverses and Invertibility Matrix Structure and Transformations |
|
| 6 | Tue Sep 22 | Determinants companion notebook; invertibility, products, eigenvalues, and computation; parameter-dependent determinants, Wronskians, Jacobians, and polar area factor; Euclidean vector-space preview | Determinants Determinants notebook Euclidean Vector Spaces |
| Thu Sep 24 | Points versus vectors and linear combinations; homogeneous directions and affine solution sets; elimination examples; nearest-point projection and worked distance example | Euclidean Vector Spaces | |
| Fri Sep 25 | Assignment 2 due | WileyPLUS: Inverses and Determinants | |
| 7 | Tue Sep 29 | Nearest-point practice; cross products, their determinant pattern and area interpretation; plane normals and triangle area; triple product; vector-space preview | Euclidean Vector Spaces |
October
| Week | Date | Topic | Slides / Materials |
|---|---|---|---|
| 7 | Thu Oct 1 | Vector-space axioms and scalar fields; polynomial, function, differential-equation, and Fourier examples; affine solution spaces; zero-vector test and the role of the operationsQuiz 2 | Vector Spaces, Subspaces, and SpanCovers Determinants Euclidean Vector Spaces through projection onto an affine line Cross products excluded |
| 8 | Tue Oct 6 | Subspace tests; span as linear combinations; plane-span membership and redundant generators | Vector Spaces, Subspaces, and Span |
| Thu Oct 8 | Polynomial-span coefficient tests and a singular example; coordinates and a square-to-parallelogram map; linear independence, redundant generators, and polynomial and R³ basis examples | Vector Spaces, Subspaces, and Span Bases, Dimension, and Coordinates |
|
| Fri Oct 9 | Assignment 3 due | WileyPLUS: Euclidean Vector Spaces | |
| Mon Oct 12 | Midterm course evaluation due |
Complete in Canvas or use your invitation email |
|
| 9 | Tue Oct 13 | No Class — Fall Break | |
| Thu Oct 15 | Independence and bases: resume at “Example: independent Fourier modes”; revisit deferred coordinate applicationsQuiz 3 | Bases, Dimension, and CoordinatesCovers Euclidean Vector Spaces Vector Spaces, Subspaces, and Span |
|
| 10 | Tue Oct 20 | ||
| Thu Oct 22 | |||
| Fri Oct 23 | Assignment 4 due | Details TBD | |
| 11 | Tue Oct 27 | ||
| Thu Oct 29 | Test 2 | Coverage TBD |
November
| Week | Date | Topic | Slides / Materials |
|---|---|---|---|
| 12 | Tue Nov 3 | ||
| Thu Nov 5 | |||
| Fri Nov 6 | Assignment 5 due | Details TBD | |
| 13 | Tue Nov 10 | ||
| Thu Nov 12 | Quiz 4 | Coverage TBD | |
| 14 | Tue Nov 17 | ||
| Thu Nov 19 | |||
| Fri Nov 20 | Assignment 6 due | Details TBD | |
| 15 | Tue Nov 24 | ||
| Thu Nov 26 | No Class — Thanksgiving holiday |
December
| Week | Date | Topic | Slides / Materials |
|---|---|---|---|
| 16 | Tue Dec 1 | Quiz 5 | Coverage TBD |
| Thu Dec 3 |
The official last day of classes is Saturday, December 5. Because the course meets on Tuesdays and Thursdays, Thursday, December 3 is the final regular class meeting.
Final examinations
Final examinations occur during the following week.
| Week | Date | Topic | Slides / Materials |
|---|---|---|---|
| 17 | TBA | Final Exam — time and location TBA | Whole course; greater emphasis on material not covered by Test 1 or Test 2 |