# 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