Content, progress and pedagogy of the module

Learning objectives


  • Have knowledge about definitions, results and techniques within the theory of differentiation and integration of functions of two or more variables
  • Have knowledge about the trigonometric functions and their inverse functions
  • Have knowledge of the description of simple surfaces in orthogonal, polar and cylindrical coordinates
  • Have knowledge about complex numbers, including computation rules and their representations
  • Have knowledge about factorisation of polynomials over the complex numbers
  • Have knowledge about the complex exponential function, its characteristics and its connection with trigonometric functions
  • Have knowledge about curves in the plane (in both rectangular and polar coordinates) and space, and  parameterisations, tangent vectors and curvatures of such curves
  • Have knowledge about the theory of second order linear differential equations with constant coefficients


  • Be able to visualize functions of two and three variables using graphs, level curves and level surfaces
  • Be able to determine local and global extrema for functions of two and three variables
  • Be able to determine surface area, volume, moment of inertia, etc. using integration theory
  • Be able to approximate functions of one variable using Taylor's formula, and to use linear approximations for functions of two or more variables
  • Be able to perform arithmetic computations with complex numbers
  • Be able to find the roots in the complex quadratic equation and perform factorisation of  polynomials in simple cases
  • Be able to solve linear second order differential equations with constant coefficients, in general, and with initial conditions
  • Be able to reason through the use the concepts, results and theories in simple concrete and abstract problems


  • Be able to develop and strengthen knowledge, comprehension and application of mathematical theories and methods in other subject areas
  • Be able to reason and argue on the basis of the given conditions using mathematical consepts fra calculus

Type of instruction

Lectures with exercises.

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 examCalculus
Type of exam
Written or oral exam
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 titleCalculus
Module codeF-MAT-B1-3
Module typeCourse
Duration1 semester
Language of instructionDanish and English
Empty-place SchemeYes
Location of the lectureCampus Aalborg, Campus Esbjerg, Campus Copenhagen
Responsible for the module


Study BoardStudy Board of Mathematical Sciences
DepartmentDepartment of Mathematical Sciences
FacultyFaculty of Engineering and Science