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 fx82 (all varieties: ES, ES Plus, EX, Solar etc.)
More about examination support material