# 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