ING1021 Series and functions of several variables

Course description for academic year 2018/2019

Contents and structure

The course contains the following subjects:

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 items above are further illustrated with appropriate examples.

Learning Outcome

- Knowledge:

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

- Skills:

• The student is able to use mathematical notation to define and manipulate functions of several variables, sequences, series, power series, and integral transforms.
• The student is able to solve 1. and 2. order homogeneous and inhomogeneous difference equations.
• The student is able to investigate properties of the objects in the items 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.

- General Qualifications:

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

Entry requirements

Mathematics (R1+R2) from upper secondary school or equivalent.

Recommended previous knowledge

Analysis and Linear Algebra

Teaching methods

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

Compulsory learning activities

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

Assessment

Written exam, 5 hours, accounts for 100 % of the final grade.

Grade:  A - E / passed;  F / failed.

Examination support material

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