Content, progress and pedagogy of the
module
Purpose
Linear algebra is a fundamental tool for virtually all engineering
mathematics.
Learning objectives
Knowledge
- Shall have knowledge about definitions, results and techniques
within the theory of systems of linear equations
- Shall be able to demonstrate insight into linear
transformations and their connection with matrices
- Shall have obtained knowledge about the computer tool MATLAB
and how it can be used to solve various problems in linear
algebra
- Shall have acquired knowledge of simple matrix operations
- Shall know about invertible matrices and invertible linear
mappings
- Shall have knowledge of the vector space R^{n}
and various subspaces
- Must have knowledge of linear dependence and independence of
vectors and the dimension and bases of subspace
- Must have knowledge of the determinant of matrices
- Must have knowledge of Eigen values and eigenvectors of
matrices and their use
- Must have knowledge of projections and orthonormal bases
- Must have knowledge of first order differential equations, and
on systems of linear differential equations
Skills
- Must be able to apply theory and calculation techniques for
systems of linear equations to determine solvability and to provide
complete solutions and their structure
- Must be able to represent systems of linear equations using
matrix equations, and vice versa
- Must be able to determine and apply the reduced Echelon form of
a matrix
- Must be able to use elementary matrices for Gaussian
elimination and inversion
of matrices - Must be able to determine linear dependence or linear
independence of small sets of vectors
- Must be able to determine the dimension of and basis for small
subspaces
- Must be able to determine the matrix for a given linear
transformation, and vice versa
- Must be able to solve simple matrix equations
- Must be able to calculate the inverse of small matrices
- Must be able to determine the dimension of and basis for kernel
and column spaces
- Must be able to compute determinants and could use the result
of calculation
- Must be able to calculate Eigen values and eigenvectors for
simple matrices
- Must be able to determine whether a matrix is diagonalizable,
and if so, implement a diagonalization for simple matrices
- Must be able to compute the orthogonal projection onto a
subspace of R^{n}
- Must be able to solve separable and linear first order
differential equations, in general, and with initial
conditions
Competences
- Shall demonstrate development of his/her knowledge of,
understanding of, and ability to make use of, mathematical theories
and methods within relevant technical fields
- Shall, given certain pre-conditions, be able to make
mathematical deductions and arguments based on concepts from
linear algebra
Type of instruction
The programme is based on a combination of academic,
problem-oriented and interdisciplinary approaches and organised
based on the following work and evaluation methods that combine
skills and reflection: • Lectures • Classroom instruction • Project
work • Workshops • Exercises (individually and in groups) • Teacher
feedback • Reflection • Portfolio work
Extent and expected workload
Since it is a 5 ECTS course module, the work load is expected to
be 150 hours for the student
Exam
Exams
Name of exam | Linear Algebra |
Type of exam | Written or oral examination |
ECTS | 5 |
Permitted aids | With certain aids, see list below
Unless otherwise stated in the course description in Moodle, it is
permitted to bring all kinds of (engineering) aids including books,
notes and advanced calculators. If the student brings a computer,
it is not permitted to have access to the Internet and the teaching
materials from Moodle must therefore be down loaded in advance on
the computer. It is emphasized that no form of electronic
communication must take place. |
Assessment | 7-point grading scale |
Type of grading | Internal examination |
Criteria of assessment | As stated in the Joint Programme Regulations.
http://www.engineering.aau.dk/uddannelse/studieadministration/ |