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Syllabus for

Academic year
MVE270 - Multivariable calculus
Flervariabelanalys
 
Syllabus adopted 2021-02-05 by Head of Programme (or corresponding)
Owner: TKIEK
7,5 Credits
Grading: TH - Pass with distinction (5), Pass with credit (4), Pass (3), Fail
Education cycle: First-cycle
Major subject: Mathematics
Department: 11 - MATHEMATICAL SCIENCES


Teaching language: Swedish
Application code: 51121
Open for exchange students: No
Maximum participants: 220
Only students with the course round in the programme plan
Status, available places (updated regularly): Yes

Module   Credit distribution   Examination dates
Sp1 Sp2 Sp3 Sp4 Summer course No Sp
0108 Examination 7,5c Grading: TH   7,5c    

In programs

TKITE SOFTWARE ENGINEERING, Year 2 (elective)
TKITE SOFTWARE ENGINEERING, Year 3 (elective)
TIDAL COMPUTER ENGINEERING - Common branch of study, Year 3 (compulsory elective)
TKDAT COMPUTER SCIENCE AND ENGINEERING, Year 3 (elective)
TKIEK INDUSTRIAL ENGINEERING AND MANAGEMENT, Year 2 (compulsory)

Examiner:

Johan Berglind

  Go to Course Homepage


Eligibility

General entry requirements for bachelor's level (first cycle)
Applicants enrolled in a programme at Chalmers where the course is included in the study programme are exempted from fulfilling the requirements above.

Specific entry requirements

The same as for the programme that owns the course.
Applicants enrolled in a programme at Chalmers where the course is included in the study programme are exempted from fulfilling the requirements above.

Course specific prerequisites

Knowledge corresponding to the courses Single variable calculus and Linear algebra in the I-program is presupposed.

Aim

The multivariable calculus part gives together with the courses in single variable calculus and linear algebra the fundamentals in mathematics that are common for many programs of education both inside and outside Sweden. For a large variety of applications of mathematics it is necessary to have a background in multivariable calculus.

Learning outcomes (after completion of the course the student should be able to)

In all mathematics the terminology is a fundamental ingredient for making it possible to communicate. After the multivariable calculus part of the course one should master the fundamental terminology and the central concepts as well as be able to treat problems of optimising functions of several variables and apply integrals of multivariable functions. Such applications are natural in technical and statistical contexts.

Content

First we consider different types of graphical illustrations such as function surfaces and level curves/surfaces. Moreover the concepts of limit, continuity, derivative are generalised to functions of several variables. This leads to investigations of concepts such as gradient and directional derivative. The chain rule that is important not only theoretically but also for applications is generalised to the several variable situation. Taylor expansion is studied and used to perform investigations of critical points. Investigations of extreme values are important in different kinds of economic applications. In this course we do such investigations both without and with constraints. In the latter case the method of Lagrange multipliers is used. Multiple integrals are defined and methods of their evaluation are given including change of variables. Applications mainly physical and statistical are treated. Other concepts that also are treated are parameterised curves vector fields and line integrals including Green s theorem.

Organisation

Instruction is mostly given in lectures and classes. More detailed information will be given on the course web page before start of the course.

Literature

The literature will be announced on the webpage of the course.

Examination including compulsory elements

Written examinations



The course examiner may assess individual students in other ways than what is stated above if there are special reasons for doing so, for example if a student has a decision from Chalmers on educational support due to disability.


Page manager Published: Mon 28 Nov 2016.