Prerequisite/Recommended prerequisite for
participation in the module
The module is based on knowledge achieved in the modules Calculus
and Linear algebra or similar.
Content, progress and pedagogy of the
module
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
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 | Advanced calculus |
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 |