# Mathematics 1

## Code

ME-MAT1

## Version

2.0

## Offered by

Mechanical Engineering

## ECTS

5### Prerequisites

Calculus corresponding to A-level in the Danish gymnasium. For GBE-MATX

### Main purpose

The

course will strengthen and expand the student’s basic abilities in mathematics,

in particular in calculus.

### Knowledge

After completing the course, the student can:

- Explain limits of simple expressions
- Describe the meaning of a functions derivative
- Reproduce rules for derivatives, including the chain rule
- Explain the meaning of partial derivatives
- Explain the connection between definite integrals and areas under and between graphs
- Identify order and type of ordinary differential equations
- Explain the use of polar coordinates
- Explain how the complex numbers is an extension of the reals

### Skills

After completing the course, the student can:

- Find limits
- Calculate derivatives using standard differentiation rules
- Calculate partial derivatives
- Determine characteristics of curves, including tangent vector, normal vector and curvature
- Calculate indefinite integrals, using substitution and integration by parts when appropriate
- Determine definite integrals
- Convert between Cartesian and polar coordinates
- Apply complex numbers, including conversion between different representations

### Competences

After completing the course, the student must be able to:

Use the covered methods in other courses when appropriate. Read texts that use the notation and concepts covered.

### Topics

### Teaching methods and study activities

The course runs for approximately 13 weeks with 4 lessons per week. The total work load for the student is 138 hours.

The teaching will consist of class room teaching with theory lectures combined with problem solving. The students are expected to prepare by reading and problem solving between classes.

### Resources

Hass,

Heil, and Weir, Thomas’ Calculus, Pearson, latest global edition

### Evaluation

### Examination

Prerequisites for exam:

None

Exam type:

Written exam

Duration is 4 hours

Grade is exclusively based on the exam

Internal co-examiner

Tools allowed:

All usual, but no communication and no use of the web during the exam

Re-exam:

Same as ordinary

### Grading criteria

7-point scale

### Additional information

### Responsible

Uffe Vestergaard Poulsen

### Valid from

2/1/2022 12:00:00 AM

### Course type

Compulsory Course for Mechanical Engineering

2. semester

### Keywords

<div class="ExternalClassDDB37F41D32742BD9949A6AE2E90114D"><p>Limits, Differentiation, Integration, Ordinary differential equations, Vector functions and curves, Functions of several variables, Polar coordinates, Complex numbers</p></div>