MAT-01266 Mathematics 2, 5 cr
Vastuuhenkilö
Robert Piche
Opetus
| Toteutuskerta | Periodi | Vastuuhenkilö | Suoritusvaatimukset |
| MAT-01266 2019-01 | 2 |
Dmytro Baidiuk Robert Piche Jaakko Pihlajasalo |
Final exam, homework, weekly exercises, and MATLAB Fundamentals self-paced training course in MATLAB Academy. |
Osaamistavoitteet
In this course the student learns the basic theory and methods of linear algebra and matrix analysis. The student learns how to prove theorems and solve problems using mathematical methods and to present solutions orally and in written form.
Sisältö
| Sisältö | Ydinsisältö | Täydentävä tietämys | Erityistietämys |
| 1. | Vectors in R^n: the dot product, length, angle, orthogonality, and projection onto a vector. Lines and planes. | ||
| 2. | Systems of linear equations: solving using Gaussian elimination. | Gauss-Jordan method. Row equivalence. | |
| 3. | Spanning sets and linear independence, subspaces, basis, rank, and dimension. | ||
| 4. | Matrices: matrix algebra, matrix product, the transpose, the inverse, the determinant, the cross product. Eigenvalues and eigenvectors. | Different representations of matrix product. Linear transformation and the standard matrix. The scalar triple product. Similarity and diagonalization. | Markov chains |
| 5. | Orthogonality, orthogonal matrices, orthogonal complement, orthogonal projection. Least squares approximation. | Gram-Schmidt process. Orthogonal diagonalization. The four fundamental spaces of a matrix. | |
| 6. | Basic competence in using Matlab to solve mathematical problems. |
Oppimateriaali
| Tyyppi | Nimi | Tekijä | ISBN | URL | Lisätiedot | Tenttimateriaali |
| Book | Linear Algebra, A Modern Introduction (2nd ed.) | Poole | Available in library for period-loan. | Yes |
Esitietovaatimukset
| Opintojakso | P/S | Selite |
| MAT-01166 Mathematics 1 | Mandatory |
Vastaavuudet
Opintojakso ei vastaan mitään toista opintojaksoa