ING1105 Series and Functions of Several Variables

Contents and structure

Functions of several variables:

• Graphs and level sets (level graphs)
• Limits and continuity in several variables
• Partial derivation, linearization and extreme values

 

Sequences, series, and integral transforms:

• Sequences, difference equations, series, and convergences
• Power series representation and radius of convergence
• Taylor series
• Fourier series
• Laplace transform

 

In addition to understanding concepts and methods of calculation, emphasis is placed on logical reasoning, mathematical notation, and the written presentation of solutions. Numerical methods are particularly useful for investigating sequences and series, and their convergence.

 

The above subjects are further illustrated with appropriate examples.

Learning Outcome

The student:

• is able to describe and exemplify the concept of functions of several variables
• is able to describe and exemplify different representations of functions of one variable, such as Taylor series, Fourier series, and the Laplace transform
• is able to describe and exemplify sequences and series of numbers

 

The student:

• is able to use mathematical notation to define and manipulate functions of several variables, sequences, series, power series, and integral transforms
• is able to solve 1st and 2nd order homogeneous and inhomogeneous difference equations
• is able to investigate properties of the objects listed above, such as properties of convergence of sequences, series and power series, definition sets, continuity, linearization, extreme values, and graphs and level sets for functions of several variables

 

The student:

• is able to communicate both in writing and orally on mathematical issues

Entry requirements

None

Recommended previous knowledge

Analysis and linear algebra

Teaching methods

Lectures, workshop and/or work in the computer lab.

Regular lectures, exercises, laboratory work, and similar activities will be given every third week. During the two weeks where there is no regular teaching, the students are expected to work on the subject by themselves or in teams and to follow course material that is made available online.

In special cases instruction will be given by an English speaking lecturer/guest lecturer. The exam will still be given in Norwegian.

Parts of the course might be given in Haugesund.

Compulsory learning activities

Yes, will be specified in the course plan by semester start.

Valid for the semester that the Preliminary Examination is completed and the next semester.

Assessment

Written exam, 5 hours.

Graded scale: A - E / F (failed).

Examination support material

Simple calculator: Allowed calculator is Casio fx-82 (all varieties: ES, ES Plus, EX, Solar etc.)

More about examination support material