# 2018/2019

## Content, progress and pedagogy of the module

Purpose:
Calculus is the branch of mathematics that studies differential equations and operations such as integration. Differential equations, in turn, describe (among other things) how signals in electric circuits behave

### Learning objectives

#### Knowledge

• Must have knowledge on real functions of two or more variables.
• Must have knowledge of the trigonometric functions and their inverse functions
• Most have knowledge of Taylors formula and Taylor series
• Must have knowledge of complex numbers and roots in polynomials
• Must have knowledge of the complex exponential function, its characteristics and its connection with trigonometric functions
• Must have knowledge of curves in the plane (both rectangular and polar coordinates) and spatial parameterisations, tangent vectors and curvatures of such curves
• Must have knowledge of the Laplace transform and its use in relation to solving differential equations.

#### Skills

• Must be able to approximate functions via Taylor series
• Must be able to carry out differentiation of functions of more variables, and have a geometric understanding that allows solution of inhomogeneous second order linear differential equations.

#### Competences

• Must be able to solve linear differential equations with constant parameters
• Must be able to solve coupled first order linear differential equations and inhomogeneous second order linear differential equations
• Must be able to give a geometric description of real functions in 2 and 3 variables

### Type of instruction

See the general description of the types of instruction described in the introduction to Chapter 3.

## 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 As stated in the Joint Programme Regulations http:/​/​www.en.tech.aau.dk/​education-programmes/​Education+and+Programmes/​