Calculus

2019/2020

Content, progress and pedagogy of the module

Learning objectives

Knowledge

  • 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

Skills

  • 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

Competences

  • 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.

Exam

Exams

Name of examCalculus
Type of exam
Written or oral exam
ECTS5
Assessment7-point grading scale
Type of gradingInternal examination
Criteria of assessmentAs stated in the Joint Programme Regulations.
http:/​/​www.engineering.aau.dk/​uddannelse/​Studieadministration/​

Facts about the module

Danish titleCalculus
Module codeF-MAT-B1-3
Module typeCourse
Duration1 semester
SemesterAutumn
ECTS5
Language of instructionDanish and English
Empty-place SchemeYes
Location of the lectureCampus Aalborg, Campus Esbjerg, Campus Copenhagen
Responsible for the module

Organisation

Study BoardStudy Board of Mathematics, Physics and Nanotechnology
DepartmentDepartment of Mathematical Sciences
FacultyFaculty of Engineering and Science