 COURSE SYLLABUS

Functions of Several Variables and Computer Tools 7.5 credits

Flervariabelanalys och datorverktyg
First cycle, M0032M
Version
Course syllabus valid: Autumn 2020 Sp 1 - Present
The version indicates the term and period for which this course syllabus is valid. The most recent version of the course syllabus is shown first.

Syllabus established
The syllabus is approved by the Department of Mathematics and is valid from August 2007.

Last revised
by Niklas Lehto 08 Nov 2019

 Education level First cycle Grade scale G U 3 4 5 Subject Mathematics Subject group (SCB) Mathematics

Entry requirements

In order to meet the general entry requirements for first cycle studies you must have successfully completed upper secondary education and documented skills in English language and Linear Algebra and Differential Equations M0031M or equivalent.

Selection

The selection is based on 1-165 credits.

Course Aim
To pass the course the student should be able to

• Give an account of the concepts of limit, continuity, partial derivatives, chain rule, directional derivatives, gradient and Taylor polynomial.
• Find stationary points and classify them; determine extreme values for continuous functions defined on closed bounded domains; apply the method of Lagrange multipliers in simple cases.
• Interpret and calculate multiple integrals by iterated integration and perform change of variables.
• Interpret and calculate line integrals and curve integrals.
• Interpret and apply important concepts and results from vector analysis: vector fields, divergence, rotation, Green’s theorem, Stokes’ theorem and Gauss’ theorem.
• Use the software Matlab to solve systems of linear equations, solve ordinary differential equations, solve optimization problems, curve fitting and write scripts that perform complex tasks.
• Show ability to identify and solve problems by the methods that are taught in the course.

These skills and abilities are practiced through problem solving, hand-in assignments and computer laborations.

Contents
Functions of several variables, limits, partial derivatives, differentiability, Taylor expansions, optimisation with or without constraints, multiple integrals, line integrals and vector calculus. Solving problems using mathematical software.

Realization
Lectures, problem solving.

Examination
Written examination on the calculus part and written reports concerning mathematical software.

Examiner
John Fabricius

Transition terms
The course M0032M is equal to MAM284

Literature. Valid from Autumn 2014 Sp 1 (May change until 10 weeks before course start)
R. A. Adams, Calculus: A complete course, Addison-Wesley, Toronto (the latest edition).
MATLAB, An Introduction With Applications, fourth edition, förlag: John Wiley & Sons, Inc.

Course offered by
Department of Engineering Sciences and Mathematics

Modules