Preliminary semester plan, for TMA4110 - Calculus 3, fall 2012

This plan is tentative and can (and probably will) be changed during the semester.

34 Complex numbersAdams AI
35 The complex exponential function. Second-order equations. Adams AII, Polking 4.1
36 Linear homogeneous equations with constant coefficients. Harmonic motion. Inhomogeneous equations, the method of undetermined coefficients Polking 4.3-4.5
37 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
38 Vector equations. The Matrix equation Ax=b. Solution sets of linear systems. Applications of linear systems. Lay 1.3-1.6
39 Linear Independence. Linear transformations. Matrices of linear transformations. Linear models Lay 1.7-1.10
40 Matrix operations. Inverse matrices Lay 2.1-2.3
41 Determinants. Cramer's rule Lay 3.1-3.3
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 from August 2012.Lay 7.1-7.2
2012-11-15, tokemeie