# 2018/2019

Linear algebra

## 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 of definitions, results and techniques within the theory of differentiation and integration of functions of two or more variables
• Must have knowledge of the trigonometric functions and their inverse functions
• Must have knowledge of complex numbers, including rules for computation and their representations
• Must have knowledge of factorization of polynomials over the complex numbers
• 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 parameterizations, tangent vectors and curvatures of such curves
• Must have knowledge of the theory of second order linear differential equations with constant coefficients

#### Skills

• Must be able to visualize functions of two and three variables using graphs, level curves and level surfaces
• Must be able to determine local and global extreme for functions of two and three variables
• Must be able to determine area, volume, moment of inertia etc. using integration theory
• Must be able to approximate functions of one variable using Taylor's formula, and use linear approximations for functions of two or more variables
• Must be able to perform arithmetic computations with complex numbers
• Must be able to find the roots in the complex quadratic equation and perform factorization of simple polynomials
• Must be able to solve linear second order differential equations with constant coefficients, in general, and with initial conditions
• Must be able to use the concepts, findings and theories introduced in the course to make mathematical deductions in the context of simple and concrete abstract problems

#### Competences

• Shall demonstrate development of his/her knowledge of, understanding of, and ability to make use of, mathematical theories and methods within relevant technical fields
• Shall, given certain pre-conditions, be able to make mathematical deductions and arguments based  on concepts from multi-variable calculus

### Type of instruction

The programme is based on a combination of academic, problem-oriented and interdisciplinary approaches and organised based on the following work and evaluation methods that combine skills and reflection: • Lectures • Classroom instruction • Project work • Workshops • Exercises (individually and in groups) • Teacher feedback • Reflection • Portfolio work

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

## Exam

### Exams

 Name of exam Calculus Type of exam Written or oral examination ECTS 5 Permitted aids With certain aids: Unless otherwise stated in the course description in Moodle, it is permitted to bring all kinds of (engineering) aids including books, notes and advanced calculators. If the student brings a computer, it is not permitted to have access to the Internet and the teaching materials from Moodle must therefore be down loaded in advance on the computer. It is emphasized that no form of electronic communication must take place. Assessment 7-point grading scale Type of grading Internal examination Criteria of assessment As stated in the Joint Programme Regulations. http:/​/​www.engineering.aau.dk/​uddannelse/​studieadministration/​