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 |
---|---|---|
2 | The algebra of complex numbers. Point representations. Polar forms. The complex exponential | Saff–Snider 1.1–1.4 |
3 | Powers and roots. Second-order linear equations. | Saff–Snider 1.5, Polking 4.1 |
4 | Homogeneous equations with constant coefficients. Harmonic motion. Inhomogeneous equations. Undetermined coefficients. | Polking 4.3-4.5 |
5 | Variation of parameters. Forced harmonic motion. Systems of linear equation. Row reduction and echelon forms. | Polking 4.6-4.7, Lay 1.1 -1.2 |
6 | Vector equation. The Matrix equation Ax=b. Solution sets of linear systems. Applications of linear systems. | Lay 1.3-1.6 |
7 | Linear Independence. Linear transformations. Matrices of linear transformations. | Lay 1.7-1.9 |
8 | Linear models. Matrix operations. Inverse matrices. | Lay 1.10, 2.1-2.2 |
9 | LU factorization. Determinants. | Lay 2.3, 2.5, 3.1-3.2 |
10 | Vector spaces and subspaces. Null spaces, column spaces and linear transformations. Linear independents sets and bases. | Lay 4.1-4.3 |
11 | Coordinate systems. Dimensions and ranks. Applications to Markov chains | Lay 4.4-4.6, 4.9 |
12 | Eigenvectors and eigenvalues. The characteristic equation. Diagonalization. Complex eigenvalues | Lay 5.1-5.3, 5.5 |
13 | Systems of linear differential equations. Inner product, length and orthogonality | Polking 4.2, Lay 5.7, 6.1-6.2 |
14 | Orthogonal projections. The Gram-Schmidt process. Least-square problems. Applications to linear models | Lay 6.3-6.6 |
16-17 | Diagonalization of symmetric matrices. Quadratic forms. Exam practice | Lay 7.1-7.2 |