# Lecture plan

This plan is tentative and can (and probably will) be changed during the semester. The references can all be found in the textbook.

WeekSubjectsReferences
34 The algebra of complex numbers. Point representations. Polar forms Saff-Snider 1.1-1.3
35 The complex exponential. Powers and roots Saff-Snider 1.4-1.5
36 Second-order 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 Lay 1.8-1.10
41 Matrix 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 Lay 4.1-4.3
43 Coordinate 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 practiceLay 7.1-7.2