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 Rⁿ 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 Rⁿ
• 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: 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/​