2018/2019

Content, progress and pedagogy of the module

Linear algebra is a fundamental tool for virtually all engineering mathematics.

Learning objectives

Knowledge

• Must have knowledge about definitions, results and techniques within the theory of systems of linear equations
• Must be able to demonstrate insight into linear transformations and their connection with matrices
• Must have obtained knowledge about the computer tool MATLAB and how it can be used to solve various problems in linear algebra
• Must have acquired knowledge of simple matrix operations
• Must know about invertible matrices and invertible linear mappings
• Must 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

Competences

• Must demonstrate development of his/her knowledge of, understanding of, and ability to make use of, mathematical theories and methods within relevant technical fields
• Given certain pre-conditions, must be able to make mathematical deductions and arguments based on concepts from linear algebra

Type of instruction

Refer to the overview of instruction types listed in the start of chapter 3. The types of instruction for this course are decided according to the current Joint Programme Regulations and directions are decided and given by The Study Board of Electronics and IT.

Exam

Exams

 Name of exam Linear Algebra Type of exam Written or oral exam ECTS 5 Assessment 7-point grading scale Type of grading Internal examination Criteria of assessment As stated in the Joint Programme Regulations http:/​/​www.tech.aau.dk/​uddannelse/​Studieadministration/​