# 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