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 150 hours for the student.

Exam

Exams