Recommended prerequisite for participation in the module

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
• 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