# Calculus II

• ECTS credits10
• Teaching semesterSpring
• Course codeMAT112
• Number of semesters1
• LanguageNorwegian
• Resources

Spring

## Objectives and Content

Objectives:

The objective of the course is to give an introduction to the central ideas and results from real analysis

Content:

An introduction to real analysis with an emphasis on the Riemann integral, basic properties of curves and surfaces, convergence of sequences and series, and also vectors and functions of several variables.

## Learning Outcomes

On completion of the course the student should have the following learning outcomes defined in terms of knowledge, skills and general competence:

Knowledge

The student

• knows the basic properties of continuous functions, including the notion of uniform continuity.
• knows the theory of the Riemann integral for bounded functions.
• knows the basic concepts in the theory of sequences and series.
• knows the basic theory of plane curves.
• knows the theory of functions of several variables, including the notions of continuity and differentiability.
• knows the theory of extreme values for functions of several variables.

Skills

The student

• can determine if a bounded function is integrable.
• can use a variety of tests to check convergence of sequences and series.
• can compute the length of a curve and the area bounded by a closed course.
• can compute the partial derivates of functions of several variables and use this to solve various problems, including extreme value problems.

General Competence

The student

• has gained a basic understanding of central ideas and results from calculus that enables the student to apply these methods in an independent fashion in relevant situations

MAT111

M101: 9 ECTS

Excercises

## Forms of Assessment

Written examination: 4 hours

Examination support materials: Non- programmable calculator, according to model listed in faculty regulations