# 2020/2021

## Prerequisite/Recommended prerequisite for participation in the module

A-level mathematics from a Danish high school or equivalent.

## Content, progress and pedagogy of the module

### Learning objectives

#### Knowledge

Students who have passed the module should be able to explain

• Real functions of two and more variables – definitions, results and techniques concerning partial derivatives.
• Curvature and torsion determine curves in space.
• Integration in plane and space wrt. various coordinate systems – including connections between such integrals.
• 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.
• Calculation of  curvature and torsion, arc length, velocity, acceleration and interpretation of these in a geometric setting.
• Set up and evaluate simple integrals in plane and space wrt. various coordinate systems.
• Solve and plot various types of first- and second order differential equations.

#### Competences

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

### Type of instruction

• Lectures
• Exercises
• Videos
• Quiz
• Digitalized self-study,
• Workshops on calculus problems relevant to the study programme.

150 hours

## Exam

### Exams

 Name of exam Calculus Type of exam Written or oral exam ECTS 5 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