Prerequisite/Recommended prerequisite for
participation in the module
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
Extent and expected workload
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, see list below
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/ |