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.

Week	Subjects	References
02	The algebra of complex numbers. Point representations. Polar forms	Saff-Snider 1.1-1.3
03	The complex exponential. Powers and roots	Saff-Snider 1.4-1.5
04	Second-order linear equations. Homogeneous equations with constant coefficients. Harmonic motion	Polking 4.1, 4.3-4.5
05	Inhomogeneous equations. Undetermined coefficients. Variation of parameters. Forced harmonic motion	Polking 4.6-4.7
06	Systems of linear equation. Row reduction and echelon forms. Vectors. The Matrix equation Ax=b	Lay 1.1-1.4
07	Solution sets of linear systems. Applications of linear systems. Linear Independence	Lay 1.5-1.7
08	Linear transformations. Matrices of linear transformations. Linear models	Lay 1.8-1.10
09	Matrix operations. Inverse matrices. Determinants. LU factorization	Lay 2.1-2.3, 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
13/14	Eigenvectors and eigenvalues. The characteristic equation. Diagonalization. Complex eigenvalues	Lay 5.1-5.3, 5.5
14/15	Systems of linear differential equations. Inner product, length and orthogonality	Polking 4.2, Lay 5.7, 6.1-6.2
15/16	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