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Advanced Linear Algebra

Code

ME-ALA1

Version

1.0

Offered by

Mechanical Engineering

ECTS

5

Prerequisites

- Introductory linear algebra
- ME/MAT-MAT2

Main purpose

​To give a better understanding of linear algebra with a focus on topics and applications relevant for engineering.

Knowledge

After completing the course, the student can:
  • Define a vector space and explain concepts like basis and dimension
  • Define linear transformations and list important examples
  • Recognize eigenvalue problems

Skills

​After completing the course, the student can:

  • Solve systems of linear equations and account for the structure of the solution set
  • Manipulate vectors and matrices 
  • Solve eigenvalue problems and perform singular value decomposition
  • Write computer code to manipulate data in vector and matrix form

​

Competences

After having completed the course, the student can:

  • Analyse physical systems using linear algebra tools and concepts
  • Implement simple numerical algorithms 
  • Understand technical texts using the language of linear algebra

Topics

Teaching methods and study activities

​The course duration is approximately 12 weeks with 4 lessons per week. The expected work load for the student is approximately 138 hours.

The teaching consists of lectures and problem solving in class. The student must prepare for classes by reading and solving problems. Some problems will involve writing computer code. A selection of problems from throughout the semester will constitute the course assignment.

Resources

​David C. Lay, Linear Algebra and its Applications, Global Edition, latest edition (Pearson)

The student will have the option of using either Matlab (VIA licens) or Python (free)

Evaluation

Examination

Prerequisites for exam:
The course assignment must be handed in before the set deadline. Fail to meet the prerequisites will disqualify entering the examination. As of re-exam, a new deadline will be set before the re-exam.

Exam type:
Individual oral exam based on a randomly drawn topic. Duration is approximately 20 minutes. There is no preparation time. 
Internal co-examiner.
 
Tools allowed:
None

Re-exam:
As the ordinary exam. 


Grading criteria

​Grading based on the Danish 7-point scale.

Additional information

Responsible

Uffe Vestergaard Poulsen

Valid from

8/1/2024 12:00:00 AM

Course type

Keywords

- Vector spaces - Systems of linear equations and their solutions - Determinants - Linear transformations - Eigenvalue problems - Orthogonality and rotations - Singular value decomposition