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 … | Saff–Snider 1.1–1.4 |
| 35 | … exponential. Powers and roots. Second-order … | Saff–Snider 1.4–1.5, Polking 4.1 |
| 36 | … linear equations. Homogeneous equations with constant coefficients. Harmonic motion | Polking 4.1, 4.3-4.5 |
| 37 | Inhomogeneous equations. Undetermined coefficients. Variation of parameters. Forced harmonic motion | Polking 4.6-4.7 |
| 38 | Systems of linear equation. Row reduction and echelon forms. Vectors. The Matrix equation Ax=b | Lay 1.1-1.4 |
| 39 | Solution sets of linear systems. Applications of linear systems. Linear Independence | Lay 1.5-1.7 |
| 40 | Linear transformations. Matrices of linear transformations. Linear models. Matrix … | Lay 1.8-1.10, 2.1 |
| 41 | … operations. Inverse matrices. Determinants. LU factorization | Lay 2.1-2.3, 2.5, 3.1-3.2 |
| 42 | Vector spaces and subspaces. Null spaces, column spaces and linear transformations. Linear independents sets and bases. Coordinate … | Lay 4.1-4.4 |
| 43 | … systems. Dimensions and ranks. Applications to Markov chains | Lay 4.4-4.6, 4.9 |
| 44 | Eigenvectors and eigenvalues. The characteristic equation. Diagonalization. Complex eigenvalues | Lay 5.1-5.3, 5.5 |
| 45 | Systems of linear differential equations. Inner product, length and orthogonality | Polking 4.2, 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 |