Prerequisite/Recommended prerequisite for
participation in the module
Linear algebra, Calculus.
Content, progress and pedagogy of the
module
Purpose
The dynamical behaviour of systems is typically described by
differential equations. This course supports the semester theme by
providing mathematical tools for analysing such systems in
detail.
Learning objectives
Knowledge
- Must have knowledge of important results within vector analysis
in 2 and 3 dimensions
- Shall be able to understand Laplace transformation and use it
to solve differential equations.Must have knowledge of complex
analytic functions
- Must have an understanding of power series and Taylor
series
- Must have knowledge of Laurent series and the method of
residues integration
Skills
- Must be able to use vector analysis, including inner product,
vector product, vector functions, scalar functions and fields, as
well as elements of vector differential and integral calculus
- Must have understanding of Fourier series, including concepts
such as trigonometric series, periodic functions, even and odd
functions, complex Fourier series and forced oscillations resulting
from non-sinusoidal input
- Shall be able to understand and utilize the Laplace transform
for analysis of differential equations; specific subjects include:
- The definition of the Laplace transforms.
- Inverse transformation.
- Linearity and s-shift.
- Transformation of common functions, including regular, impulse
and step functions.
- Transformation of derivatives and integrals.
- Solving Differential Equations
- Folding and integral equations
- Differentiation and integration of transformed systems of
ordinary differential equations
- Using Tables
- Shall be able to use complex analytical functions within the
contexts of conformal mappings and complex integrals; specific
subjects include:
- Complex numbers and complex plane
- Polar form of complex numbers
- Exponential, trigonometric and hyperbolic functions
- Logarithmic functions and general power functions
- Complex Integration: Line integrals in the complex plane
- The Cauchy integral theorem
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 be able to identify their own learning requirements and
structure their own learning within the context of fundamental
mathematics.
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 | Advanced 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/ |