Multivariable calculus, Course, - Luleå University of Technology

COURSE SYLLABUS

Multivariable calculus 7.5 credits

Flervariabelanalys

First cycle, M0055M

Version

Course syllabus valid: Autumn 2021 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.

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 the course Linear Algebra and Differential Equations (M0049M) or equivalent.

More information about English language requirements

Selection

The selection is based on 1-165 credits.

Course Aim

This course covers differential, integral and vector calculus for functions of several variables. Emphasis is placed on problem solving with and without computational tools.

Contents

Functions of several variables: partial derivatives, differentiablity, chain rule, gradient, directional derivatives.
Taylor polynomials, quadratic forms, critical points.
Extreme value problems on restricted domains, Lagrange multipliers.
Multiple integrals, iterated integration, general coordinate systems, Jacobian.
Parametric curves and surfaces, tangent plane, arc length, surface area.
Line integrals in two and three dimensions. Green’s theorem with application.
Surface integrals, vector fields and flux integrals. Divergence and curl. Gauss’ theorem and Stokes’ theorem.
Visualization, computations and basic programming in Matlab.

Examination

If there is a decision on special educational support, in accordance with the Guideline Student's rights and obligations at Luleå University of Technology, an adapted or alternative form of examination can be provided.

A written exam is given at the end of the course that includes both theory and problems. The Matlab content is examined through hand-in assignments. The final grade is based solely on the result of the written exam.

Transition terms

The course replaces M0032M.

Examiner

John Fabricius

Literature. Valid from Autumn 2020 Sp 1 (May change until 10 weeks before course start)

• Robert A. Adams, Calculus: A Complete Course, Pearson Canada, senaste upplagan. ISBN: 9780134154367
• Per Jönsson, MATLAB – beräkningar inom teknik och naturvetenskap, 3:e upplagan. ISBN: 9789144069265

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Course offered by

Department of Engineering Sciences and Mathematics

Modules

Code	Description	Grade scale	HP	Status	From period	Title
0002	Assignment report	U G#	1.50	Mandatory	A19
0003	Written exam	G U 3 4 5	6.00	Mandatory	A21

Study guidance

Study guidance for the course is to be found in our learning platform Canvas before the course starts. Students applying for single subject courses get more information in the Welcome letter. You will find the learning platform via My LTU.

Syllabus established

by Niklas Lehto 15 Feb 2019

Last revised

by Head Faculty Programme Director Niklas Lehto 17 Feb 2021

Published:3 January 2019

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