Linear Algebra

2018/2019

Content, progress and pedagogy of the module

Learning objectives

Knowledge

  • Have knowledge about definitions, results and techniques in the theory of systems of linear equations
  • Be able to demonstrate insight into linear transformations and their connection to matrices
  • Have obtained knowledge about the computer program, MATLAB, and its application related to linear algebra
  • Have acquired knowledge about simple matrix operations
  • Have knowledge about invertible matrices and invertible linear transformation
  • Have knowledge about the vector space Rn and its subspaces
  • Have knowledge about linearly dependent vectors and linearly independent vectors, and the dimension and basis subspaces
  • Have knowledge about the determinant of a matrix
  • Have knowledge about eigenvalues and eigenvectors of matrices and their application
  • Have knowledge about projections and orthonormal bases
  • Have knowledge about first-order differential equations, and systems of linear differential equations

Skills

  • Be able to apply theory and calculation techniques for systems of linear equations to determine solvability and determine complete solutions and their structure
  • Be able to represent systems of linear equations by means of matrix equations, and vice versa
  • Be able to determine and apply the reduced echelon form of a matrix
  • Be able to use elementary matrices in connection with Gauss elimination and inversion of matrices
  • Be able to determine linear dependence or linear independence of sets of few vectors
  • Be able to determine dimension of and basis of subspaces
  • Be able to determine the matrix for a given linear transformation, and vice versa
  • Be able to solve simple matrix equations
  • Be able to calculate the inverse of small matrices
  • Be able to determine the dimension of and basis for kernel and column spaces
  • Be able to calculate determinants and apply the result of this calculation
  • Be able to calculate eigenvalues and eigenvectors for simple matrices
  • Be able to determine whether a matrix is diagonalizable, and if so, be able to diagonalize a simple matrix
  • Be able to calculate the orthogonal projection onto a subspace of Rn
  • Be able to solve separable and linear first order differential equations, in general, and with initial conditions

Competences

  • Be able to develop and strengthen knowledge, comprehension and application of mathematical theories and methods in other subject areas
  • Given certain pre-conditions, be able to make mathematical deductions and arguments based on concepts from linear algebra

Type of instruction

Lectures with exercises.

Extent and expected workload

Since it is a 5 ECTS course, the work load is expected to be 150 hours for the student.

Exam

Exams

Name of examLinear Algebra
Type of exam
Written or oral exam
ECTS5
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.
Assessment7-point grading scale
Type of gradingInternal examination
Criteria of assessmentAs stated in the Joint Programme Regulations.

Facts about the module

Danish titleLineær algebra
Module codeN-EN-B2-4
Module typeCourse
Duration1 semester
SemesterSpring
ECTS5
Empty-place SchemeYes
Location of the lectureCampus Aalborg, Campus Esbjerg
Responsible for the module

Organisation

Study BoardStudy Board of Energy
DepartmentDepartment of Energy Technology
FacultyFaculty of Engineering and Science