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

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

^Week^Subjects^References|
| 34| Complex numbers|Adams 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 |