Semester plan, for TMA4110 - Calculus 3, spring 2014
The references can all be found in the course text, Differential Equations, Linear Algebra and its Applications.
| Week | Subjects | References |
|---|---|---|
| 2 | Complex numbers | Adams AI |
| 3 | The complex exponential function. Second-order equations. | Adams AII, Polking 4.1 |
| 4 | Linear homogeneous equations with constant coefficients. Harmonic motion. Inhomogeneous equations, the method of undetermined coefficients | Polking 4.3-4.5 |
| 5 | 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 |
| 6 | Vector equations. The Matrix equation Ax=b. Solution sets of linear systems. Applications of linear systems. | Lay 1.3-1.6 |
| 7 | Linear Independence. Linear transformations. Matrices of linear transformations. Linear models | Lay 1.7-1.10 |
| 8 | Matrix operations. Inverse matrices | Lay 2.1-2.3 |
| 9 | Determinants. Cramer's rule | Lay 3.1-3.3 |
| 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 |
| 12 | Eigenvectors and eigenvalues. The characteristic equation. Diagonalization. Complex eigenvalues | Lay 5.1-5.3, 5.5 |
| 13 | Systems of linear differential equations. Inner product, length and orthogonality | Polking 4.2, Lay 5.7, 6.1-6.2 |
| 14 | Orthogonal projections. The Gram-Schmidt process. Least-square problems. Applications to linear models. | Lay 6.3-6.6 |
| 15 | Diagonalization of symmetric matrices. Quadratic forms. Exam from August 2012. | Lay 7.1-7.2 |