# Mathematics 1 (2021)

#### Course manager

Christian Møller Pedersen

#### Semester schedule

Autumn (13-week period)

#### ECTS

10

#### Language of instruction

English

#### Course type

Compulsory

#### Qualifications

Admission requirements for the Bachelor of Engineering in Biotechnology programme

#### Objectives

In combination with Statistics, the purpose of the course is to provide the students with the basic mathematical and statistical foundation that is required for the Bachelor of Engineering in Biotechnology programme. Thus, focus is on such mathematical theories and methods as are applicable in connection with other courses under the programme, and associated project work. The purpose of the course is to provide the students with a general understanding of how mathematical concepts, theories and techniques can be applied in connection with the description and analysis of conditions and problems of relevance to the education, as well as the engineering profession.

#### Content

- Complex numbers
- Linear algebra
- Functions of two variables
- Differential equations

#### Learning targets

On completion of the course, the student is expected to be able to:

**Knowledge**

- The real and complex coordinate space
- Elementary complex functions
- Vector spaces
- Matrix algebra
- Systems of linear equations
- Linear dependence
- The eigenvalue problem
- Gradient field and contours
- Stationary points and extreme values
- Taylor expansion
- 1st and 2nd order differential equations

**Skills**

Complex numbers

- Carry out basic manipulations with complex numbers
- Solve linear and quadratic equations in complex space

Linear algebra

- Do basic matrix operations e.g. addition, subtraction, multiplication, and inversion
- Solve systems of linear equations using matrix methods
- Compute determinants, eigenvalues, and eigenvectors of matrices

Functions of two variables

- Compute partial derivatives
- Compute directional derivatives
- Find stationary points
- Classify extreme points
- Calculate approximating polynomial

Differential equations

- Classify a differential equation
- Solve inhomogenous 1st and homogeneous 2nd order differential equations analytically

#### Teaching method

Teaching in class, podcasts and problem solution

#### Qualifications for examination participation

- Approval of all written assignments.

Each assignment will be performed and submitted subject to guidelines set out by the course manager.

#### Examination and aids

- Written examination. Duration of the examination: 4 hours.

__ Permitted aids__: Textbooks, notes and mathematical program/spreadsheet. No access to the internet

- Oral examination. Duration of examination: 30 min.

__Permitted aids__: Own notes. No access to the internet

In the final assessment shall comprise the written and the oral examination equally (50:50).

The form of examination at a 3rd attempt may vary from the above.

#### Marking

External: Written examination

Internal: Oral examination

#### Grading

The 7-point grading scale