Multivariable Calculus, 4 credits

Main field of study

Course level

Advancement level

Course offered for

• Computer Science and Engineering, M Sc in Engineering
• Information Technology, M Sc in Engineering

Entry requirements

Note: Admission requirements for non-programme students usually also include admission requirements for the programme and threshold requirements for progression within the programme, or corresponding.

Prerequisites

Intended learning outcomes

The student should acquire the proficiency in multivariable calculus required for subsequent studies. After completing the course the student should be able to:

• define and explain the central concepts of the course e.g., basic topological notions, function, limit, continuity, functional determinant, volume, area, mass, potential and the different kinds of derivatives and integrals that are used in the course.
• quote, explain, use and in occurring cases prove the central theorems of the course e.g., the theorem of global extrema, differentiability implies existence of partial derivatives, the chain rule, variable substitution in multiple integrals and the connection between gradients and directional derivatives.
• verify that results and partial results are correct or reasonable.
• calculate limits for functions of several variables
• solve partial differential equations by using the chain rule.
• calculate directional derivatives and equations for tangents, normals and tangent planes as well as explain and use the geometric interpretations of these objects and use them to solve problems.
• calculate multiple integrals by means of iterated integration and variable substitutions (e.g., polar, spherical and linear substitutions).

Course content

The space R^n. Fundamental notions from topology. Functions from R^n to R^p. Function graphs, level surfaces and level curves. Definitions of limit and continuity. Partial derivatives. Differentiability and differential. The chain rule. Gradient, normal, tangent and tangent plane. Directional derivative. Multiple integrals. Iterated integration. Variable substitution. Area, volume and mass.

Teaching and working methods

Lectures and lessons.

Examination

Grades

Department

Director of Studies or equivalent

Examiner

Education components

Course literature