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, 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/​