Calculus

2020/2021

Content, progress and pedagogy of the module

Learning objectives

Knowledge

  • Real functions of two and more variables – definitions, results and techniques concerning partial derivatives.
     
  • Integration in plane and space wrt. various coordinate systems – including connections between such integrals.
  • Complex numbers as an extension of the real numbers – in a geometric as well as an algebraic setup. The connection between the complex exponential function and trigonometric functions.

  • The structure of the set of solutions to different types of first and second order differential equations.

Skills

  • Differentiation of functions of several variables (including composite functions) as well as a geometric understanding of this.
  • Extrema for functions of two and three variables.
  • Maxima and minima for functions of two variables.
  • Set up and evaluate simple integrals in plane and space wrt. various coordinate systems.
  • Add, multiply and divide complex numbers. Transform between polar and Cartesian form.
  • Solve and plot various types of first- and second order differential equations.

Competences

Can apply methods and concepts from calculus, including integration, complex numbers and differential equations to given problems relevant to the study programme.

Type of instruction

Lectures, exercises, videos, quiz, digitalised self-study, workshops on calculus problems relevant to the study programme.

Extent and expected workload

Since it is a 5 ECTS course, the work load is expected to be 137,5 hours for the student.

Exam

Exams

Name of examCalculus
Type of exam
Written or oral exam
ECTS5
Permitted aidsA four hour written exam without use of electronic aid. Notes, copies, books etc. are allowed.
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 codeMAT1CALC1345
Module typeCourse
Duration1 semester
SemesterSpring and Autumn
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 Mathematical Sciences
DepartmentDepartment of Mathematical Sciences
FacultyFaculty of Engineering and Science