Pensum
Denne planen er tentativ og kan (og mest sannsynligvis vil) bli endret på i løpet av semesteret. Alle kapitelene er fra læreboka.
| Uke | Tema | Referanse |
|---|---|---|
| 34 | The algebra of complex numbers. Point representations. Polar forms. The complex exponentials. | Saff–Snider 1.1–1.4 |
| 35 | Powers and roots. Systems of linear equation. Row reduction and echelon forms. | Saff–Snider 1.4–1.5, Lay 1.1, 1.2 |
| 36 | Vectors. The Matrix equation Ax=b. Solution sets of linear systems. | Lay 1.3-1.5 |
| 37 | Linear Independence. Linear transformations. Matrices of linear transformations. | Lay 1.7-1.9 |
| 38 | Applications of linear systems. Linear Models. Matrix operations. Inverse of matrices. | Lay 1.6, 1.10, 2.1, 2.2 |
| 39 | Characterization of invertible matrices. Determinants. | Lay 2.3, 3.1, 3.2 |
| 40 | Vector spaces and subspaces. Null spaces, column spaces and linear transformations. Linear independents sets and bases. | Lay 4.1-4.3 |
| 41 | Coordinate systems. Dimensions and ranks. Applications to Markov chains. | Lay 4.4-4.6, 4.9 |
| 42 | Eigenvectors and eigenvalues. The characteristic equation. Diagonalization. Complex eigenvalues. | Lay 5.1-5.3, 5.5 |
| 43 | Second order equations. Homogeneous equations with constant coefficients. Harmonic motion | Polking 4.1, 4.3, 4.4 |
| 44 | Inhomogeneous equations. Undetermined coefficients. Variation of parameters. Forced harmonic motion. Systems of linear differential equations. | Polking 4.5-4.7, 4.2 |
| 45 | Systems of linear differential equaitons. Inner product, length and orthogonality | Lay 5.7, 6.1-6.2 |
| 46 | Orthogonal projections. The Gram-Schmidt process. Least-square problems. Applications to linear models | Lay 6.3-6.6 |
| 47 | Diagonalization of symmetric matrices. Quadratic forms. Exam practice | Lay 7.1-7.2 |