General Syllabus Note: This is a suggested syllabus. The exact timing of mid-term exams and coverage of topics is determined by the individual course instructors.
| Lecture | Reading | Topics |
|---|---|---|
| 1 | 1.1 | Linear Systems, Method of Elimination |
| 1.2 | Matrices | |
| 2 | 1.3 | Dot Product |
| 1.4 | Matrix Multiplication | |
| 3 | 1.5 | Solving Linear Systems, Row Echelon Form |
| 4 | 1.6 | Inverse of a Matrix |
| 5 | 1.7 | LU Factorization |
| 6 | 3.1 | Definition and Properties of the Determinant of a Matrix |
| 7 | 3.2 | Cofactor Expansion, Matrix Inverse by Determinants |
| 8 | 4.1 | Vectors in R2 |
| 4.2 | Vectors in Rn; dot product and norm | |
| 9 | 4.3 | Introduction to Linear Transformations |
| 5.1 | Applications to Computer Graphics | |
| 10 | Midterm Exam | |
| 11 | 6.1 | Vector spaces |
| 6.2 | Subspaces | |
| 12 | 6.3 | Linear Independence |
| 13 | 6.4 | Basis and Dimension |
| 14 | 6.5 | Homogeneous Systems, General Solution to Ax = b |
| 15 | 6.6 | Row Space, Column Space, and Rank of a Matrix |
| 16 | 6.8 | Orthogonal Bases, Gram-Schmidt Process |
| 17 | 6.9 | Orthogonal Complements, Four Fundamental Subspaces |
| 18 | 6.9 | Orthogonal Projections |
| 7.1 | QR Factorization | |
| 19 | 7.2 | Application: Least Squares Fitting of Data |
| 20 | Midterm Exam # 2 | |
| 21 | 8.1 | Eigenvalues and Eigenvectors |
| 22 | 8.1 | Characteristic Polynomial |
| 23 | 8.2 | Diagonalization of a Matrix |
| 24 | 8.3 | Eigenvalues/Eigenvectors for Symmetric Matrices |
| 25 | 8.3 | Diagonalization of a Symmetric Matrix |
| 26 | 9.2 | Homogeneous Linear Differential Equations |
| 27 | 9.4 | Quadratic Forms |
| 28 | Catch up and review | |
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