# 2019/2020

## Content, progress and pedagogy of the module

### Learning objectives

#### Knowledge

• Have knowledge about definitions, results and techniques within the theory of differentiation and integration of functions of two or more variables
• Have knowledge about the trigonometric functions and their inverse functions
• Have knowledge of the description of simple surfaces in orthogonal, polar and cylindrical coordinates
• Have knowledge about complex numbers, including computation rules and their representations
• Have knowledge about factorisation of polynomials over the complex numbers
• Have knowledge about the complex exponential function, its characteristics and its connection with trigonometric functions
• Have knowledge about curves in the plane (in both rectangular and polar coordinates) and space, and  parameterisations, tangent vectors and curvatures of such curves
• Have knowledge about the theory of second order linear differential equations with constant coefficients

#### Skills

• Be able to visualize functions of two and three variables using graphs, level curves and level surfaces
• Be able to determine local and global extrema for functions of two and three variables
• Be able to determine surface area, volume, moment of inertia, etc. using integration theory
• Be able to approximate functions of one variable using Taylor's formula, and to use linear approximations for functions of two or more variables
• Be able to perform arithmetic computations with complex numbers
• Be able to find the roots in the complex quadratic equation and perform factorisation of  polynomials in simple cases
• Be able to solve linear second order differential equations with constant coefficients, in general, and with initial conditions
• Be able to reason through the use the concepts, results and theories in simple concrete and abstract problems

#### Competences

• Be able to develop and strengthen knowledge, comprehension and application of mathematical theories and methods in other subject areas
• Be able to reason and argue on the basis of the given conditions using mathematical consepts fra calculus

### Type of instruction

Lectures with exercises.

### 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 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 F-MAT-B1-3 Module type Course Duration 1 semester Semester 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 Mathematics, Physics and Nanotechnology Department Department of Mathematical Sciences Faculty Faculty of Engineering and Science