## Linear Algebra

### Volledige vakbeschrijving

Linear algebra is the branch of mathematics which is primarily concerned with problems involving linearity of one kind or another. This is reflected by the three main themes around which this introductory course is centred. The first theme is concerned with what can be recognized without doubt as the most frequently occurring mathematical problem in practical applications: how to solve a system of linear equations. For this problem a complete solution procedure is developed which provides the student with a way to deal with such problems systematically, regardless of the number of equations or the number of unknowns. The second theme addresses linear functions and mappings, which can be studied naturally from a geometric point of view. This involves geometric ‘objects’ such as points, lines and planes, and geometric ‘actions’ such as rotation, reflection, projection and translation. One of the main tools of linear algebra is offered by matrices and vectors, for which a basic theory of matrix-vector computation is developed. This allows one to bring these two themes together in a common framework, in what turns out to be an exceptionally fruitful way. By introducing the notions of vector spaces, inner products and orthogonality, a deeper understanding of the scope of these techniques is developed, opening up a large array of rather diverse application areas. The third theme surfaces when the point of view is shifted once more, now from the geometric point of view to the dynamic perspective, where the focus is on the effects of iteration (i.e., the repeated application of a linear mapping). This involves a basic theory of eigenvalues and eigenvectors, which have many applications in various branches of science as will be discussed. Many examples and exercises shall be provided to clarify the issues and to develop practical computational skills. They also serve to demonstrate practical applications where the results of this course can be successfully employed.### Doelstellingen van dit vak

• In this course we provide an introduction to the main topics of linear algebra. Emphasis is on an understanding of the basic concepts and techniques, and on developing the practical, computational skills to solve problems from a wide range of application areas.### Voorwaarden

Basic high school skills in mathematics (equations, functions, graphs,…) See SCI-M.### Aanbevolen literatuur

• Lay, David C. (2012). Linear Algebra and Its Applications. (4th ed.). Pearson. ISBN 13: 978-0-321-62335-5.**Instructional format**

Frontal, but interactive instruction and active training in comprehending the instructed material by spending a lot of time on problem solving, either individually or jointly with other participants. There are no tutor groups for this course. During all contact hours instruction and practice will alternate in line with the progress of the material in the book.

**Examination**

Three written tests on parts of the course and for those who do not pass these tests, there will be a written exam on the entire course.

**This course is a prerequisite for the following course(s):**

• SCI2032 Physics II • SCI3001 Advanced Mathematics

SCI2019

Periode 5

8 apr 2024

7 jun 2024

Studiepunten:

5.0Taal van de opleiding:

EngelsCoördinator:

Onderwijsmethode:

PBL, Presentation(s), Lecture(s), Assignment(s), Paper(s)Evaluatiemethoden:

Final paper, Attendance, Participation, Written exam, Oral exam, Take home exam