# Applied linear algebra

Course Code : | 1000WETTLA |

Study domain: | Mathematics |

Academic year: | 2017-2018 |

Semester: | 1st semester |

Contact hours: | 30 |

Credits: | 3 |

Study load (hours): | 84 |

Contract restrictions: | No contract restriction |

Language of instruction: | Dutch |

Exam period: | exam in the 1st semester |

Lecturer(s) | Werner Peeters |

### 1. Prerequisites *

- competences corresponding the final attainment level of secondary school

an active knowledge of

- Dutch

- general knowledge of the use of a PC and the Internet

general notion of the basic concepts of

Use of a general word processor and a spreadsheet; basic knowledge of installing software on a PC or an equivalent operating system. General internet abilities.

### 2. Learning outcomes *

- You can read and write mathematical formulas correctly.
- You know the terminology involving linear algebra in R^n.
- You can solve problems anout differentiation and integration, differential equations, Taylor and fourier series.
- You can present your results in an orderly fashion, in acceptable Dutch.

### 3. Course contents *

In this course, the most important subjects regarding linear algebra of a finite number of variables are treated. The purpose is to make the students acquainted with techniques in linear algebra that can be useful in a broader (applied) scientific context. Much attention will be given to recognising problems and applying correct mathematical techniques for solving, or at least a correct formulation of the problem in order to be able to solve it (by e.g. using computers). The students have to acquire the formal language of mathematics. The correct mathematical expression of certain concepts will be regarded as important.

Participating in the college will require active contribution by the students, e.g. in turns they will have to present the solution of their exercises on the blackboard; the end goal being that the students are considered to be able to present their results in an orderly fashion before their peers.

I. Introduction: Vectors, real vector spaces, lineare (in)dependence and span, bases, coördinates

II. Matrices: addition, scalar multiplication, internal multiplication,, regular and singular matrices

III. Determinants, main determinant, rank

IV. Solving systems of equations by means of the methods of Gauss-Jordan and Cramer

V. Vector geometry in the plane and the space, lines and planes and their relative position, collinearity en coplanarity

VI. Euclidean spaces, scalar and vector product, length, angle, orthogonality

VII. Linear transformations, kernel, image, original, eigenvectors en eigenvalues

Introduction to Maple

### 4 International dimension*

### 5. Teaching method and planned learning activities

### 6. Assessment method and criteria

Written assignment

### 7. Study material *

#### 7.1 Required reading

The students will be provided with a Dutch course, where the stress will be put on the demonstration of examples with the theory, which can also be used as a reference work for further self study. A major portion is taken up by (unsolved) exercises, some of which are treated in the course, others are the subject of self study.

• W. Peeters. Wiskunde - Toegepaste Lineaire Algebra

**7.2 Optional reading**

The following study material can be studied voluntarily :As prior knowledge the following book is being used:

• S. Verwulgen en E. Soetens. Wiskunde voor de beginnende bachelor. Academia Press

To bridge the gap with other courses, the following work is sometimes used:

Erich Steiner, The Chemistry Maths Book (Oxford)

### 8. Contact information *

dr Werner Peeters

Dept. Mathematics and Computer Science

Middelheimlaan 1 gebouw G 3.14

werner.peeters@uantwerpen.be

Exercises are being taught by:

- Nick Schenkels (for biochemistry): nick.schenkels@uantwerpen.be

- Jens Hemelaer (for chemistry): jens.hemelaer@uantwerpen.be

Study monitor:

Valerie De Witte

valerie.dewitte@uantwerpen.be