Content, progress and pedagogy of the
module
The module is based on knowledge achieved in the modules
Calculus and Linear algebra or similar.
Learning objectives
Knowledge
- Have knowledge about fundamental methods in vector analysis in
the 2 and 3 dimensional space, and have knowledge about
applications of the theory to engineering
- Have knowledge about the Laplace transform and how to apply it
to solve differential equations exemplified by problems from e.g.
mechanics, electronics or heat transfer
- Have knowledge about complex analytic functions
- Have an understanding of power series and Taylor series
- Have an understanding of how complex analytic functions and
power series can be applied to study physical systems
Skills
- Be able to use vector calculus, within the topics:
- Inner product (dot product)
- Vector product (cross-product)
- Vector and scalar functions and vector fields
- Space curves, tangents and arc length
- Vector differential calculation: Gradient, divergence,
curl
- Vector integral calculation: Line integrals, path independence
of line integrals, double integrals, Green's theorem in the
plane, and surface integrals
- Be able to apply the theory of Fourier series, within the
topics:
- Fourier series and trigonometric series
- Periodic functions
- Even and odd functions
- Complex Fourier Series
- Be able to apply the theory of Laplace transformations, within
the topics:
- Definition of the Laplace transformation. Inverse
transformation. Linearity and s-translation
- Transformation of elementary functions, including periodic,
impulse and step functions
- Transformation of derivatives and integrals
- Solution of differential equations
- Convolution and integral equations
- Differentiation and integration of transformed systems of
ordinary differential equations
- Be able to apply complex analytical functions to conformal
mapping and complex integrals within the topics:
- Complex numbers and the complex plane
- Polar form of complex numbers
- Exponential functions
- Trigonometric and hyperbolic functions
- Logarithmic functions and general power functions
- Complex integration: Line integrals in the complex plane
- Cauchy's integral theorem
Competences
- Be able to use vector calculus, series, Laplace transforms and
complex analytic functions to solve fundamental engineering
problems.
Type of instruction
The programme is based on a combination of academic, problem
oriented and interdisciplinary approaches and organised based on
the following types of instruction that combine skills and
re-flection:
- lectures
- class teaching
- project work
- workshops
- exercises (individually and in groups)
- teacher feedback
- professional reflection
- portfolio work
- laboratory work
- e-learning
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 | Applied Engineering Mathematics |
Type of exam | Written exam
4-hour examination. |
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 |