Here is a suggested syllabus for all sections of Math 250 using the standard format.
| Lecture
number |
Textbook
Sections |
Topics |
|---|---|---|
| 1 | 1.1-1.2 | Vectors, Lengths and Dot Products |
| 2.1 | Vectors and Linear equations | |
| 2 | 2.2, 2.3 | The Idea of Elimination;
Elimination using Matrices |
| 3 | 2.4, 2.5 | Rules for Matrix Operations;
Inverse Matrices |
| 4 | 2.6 | Elimination by A=LU Factorization |
| 5 | 2.7 | Transposes and Permutations,
PA=LU Factorization |
| 6 | 3.1 | Spaces of Vectors |
| 7 | 3.2 | Nullspace of A, Echelon Matrices |
| 8 | 3.3, 3.4 | Rank and Row Reduced Form;
Complete Solution to Ax=b |
| 9 | 3.5 | Independence, Basis, and Dimension |
| 10 | 3.6 | Dimensions of the Four Subspaces |
| 11 | Catch up and review | |
| 12 | First Midterm Exam | |
| 13 | 4.1, 4.2 | Orthogonality of the Four Subspaces,
Projections |
| 14 | 4.3 | Least Squares Approximate Solution to Ax=b |
| 15 | 4.4 | Orthogonal Bases,
Gram-Schmidt Algorithm, A=QR Factorization |
| 16 | 5.1 | Determinant Function and its Properties |
| 17 | 5.2 | Permutations and Cofactors |
| 18 | 5.3 | Cramer's Rule, Inverses |
| 19 | 10.1, 6.1 | Complex numbers,
Introduction to Eigenvalues and Eigenvectors |
| 20 | 6.2 | Diagonalizing a Matrix |
| 21 | 6.3 | Applications to Differential Equations |
| 22 | 6.4 | Eigenvalues and Eigenvectors of Symmetric Matrices |
| 23 | Catch up and review | |
| 24 | Second Midterm Exam | |
| 25 | 6.7 | Singular Value Decomposition |
| 26 | 7.1, 7.2 | Linear Transformations and their Matrices |
| 27 | 7.3, 7.4 | Change of Basis;
Dual Basis; Pseudo Inverse |
| 28 | Catch up and review | |