Applied Engineering Mathematics


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


  • 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


  • 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


  • 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.



Name of examApplied Engineering Mathematics
Type of exam
Written exam
4-hour examination.
Assessment7-point grading scale
Type of gradingInternal examination
Criteria of assessmentThe criteria of assessment are stated in the Examination Policies and Procedures

Facts about the module

Danish titleAnvendt ingeniørmatematik
Module codeN-EN-B3-3A
Module typeCourse
Duration1 semester
Language of instructionDanish
Empty-place SchemeYes
Location of the lectureCampus Aalborg, Campus Esbjerg
Responsible for the module


Study BoardStudy Board of Energy
DepartmentDepartment of Energy
FacultyThe Faculty of Engineering and Science