# 2024/2025

## Content, progress and pedagogy of the module

### Learning objectives

#### Knowledge

• Real functions of two and more variables – definitions, results and techniques concerning partial derivatives.

• Integration in plane and space wrt. various coordinate systems – including connections between such integrals.
• Complex numbers as an extension of the real numbers – in a geometric as well as an algebraic setup. The connection between the complex exponential function and trigonometric functions.

• The structure of the set of solutions to different types of first and second order differential equations.

#### Skills

• Differentiation of functions of several variables (including composite functions) as well as a geometric understanding of this.
• Extrema for functions of two and three variables.
• Maxima and minima for functions of two variables.
• Set up and evaluate simple integrals in plane and space wrt. various coordinate systems.
• Add, multiply and divide complex numbers. Transform between polar and Cartesian form.
• Solve and plot various types of first- and second order differential equations.

#### Competences

Can apply methods and concepts from calculus, including integration, complex numbers and differential equations to given problems relevant to the study programme.

### Type of instruction

Lectures, exercises, videos, quiz, digitalised self-study, workshops on calculus problems relevant to the study programme.

### Extent and expected workload

Since it is a 5 ECTS course, the work load is expected to be 150 hours for the student.

## Exam

### Exams

 Name of exam Calculus Type of exam Written or oral exam ECTS 5 Permitted aids Please see the semester description / module description Assessment 7-point grading scale Type of grading Internal examination Criteria of assessment The criteria of assessment are stated in the Examination Policies and Procedures

## Facts about the module

 Danish title Calculus Module code MAT1CALC1345 Module type Course Duration 1 semester Semester Spring and Autumn ECTS 5 Language of instruction Danish and English Empty-place Scheme Yes Location of the lecture Campus Aalborg, Campus Esbjerg, Campus Copenhagen Responsible for the module Morten Grud Rasmussen

## Organisation

 Study Board Study Board of Mathematical Sciences Department Department of Mathematical Sciences Faculty The Faculty of Engineering and Science