Preliminary semester plan, for TMA4110 - Calculus 3, fall 2014
This plan is tentative and can (and probably will) be changed during the semester. The references can all be found in the course text, Differential Equations, Linear Algebra and its Applications.
| 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. | Lay 3.1-3.2, 2.5 |
| 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 |