Search programme

​Use the search function to search amongst programmes at Chalmers. The programme overview and the programme syllabus relating to your studies are generally from the academic year you began your studies.

​​​

Syllabus for

Academic year
MVE085 - Mathematical analysis in several variables V
 
Owner: TKVOV
5,0 Credits (ECTS 7,5)
Grading: TH - Five, Four, Three, Not passed
Level: A
Department: 11 - MATHEMATICAL SCIENCES


Teaching language: Swedish

Course module   Credit distribution   Examination dates
Sp1 Sp2 Sp3 Sp4 No Sp
0105 Examination 5,0 c Grading: TH   5,0 c   26 Oct 2006 am V,  19 Jan 2007 am V,  31 Aug 2007 pm V

In programs

TKVOV CIVIL ENGINEERING, Year 2 (compulsory)
TDATA COMPUTER SCIENCE AND ENGINEERING, Year 3 (elective)
TKDAT COMPUTER SCIENCE AND ENGINEERING, Year 3 (elective)

Examiner:

Professor  Håkan Andreasson



Eligibility:

For single subject courses within Chalmers programmes the same eligibility requirements apply, as to the programme(s) that the course is part of.

Course specific prerequisites

Pre knowledge Analysis in one variable, Linear algebra

Aim

Purpose The purpose of the course is to give a general mathematical
knowledge which is as useful as possible for further studies as well as
for an engineer.

Goal

The students who have passed the course
- should have a good understanding of the fundamental concepts of
mathematical analysis in several variables and numerical analysis
- should have obtained an understanding of the relations between
the different concepts
- should be able to use the concepts to solve mathematical problems
- should have improved their knowledge of how to use Matlab for problem
solving

Content

The space Rn, open/closed/compact sets,
Functions from Rn to Rm, curves and surfaces,
Limits, continuity, differentiability, the chain rule,
Partial derivatives, gradient and tangent plane,
differentials,
Functional matrices, functional determinant,
Numerical solution of non-linear systems of equations,

Extremal values, optimization on compact domains, optimization with
constraints. Applications for V-engineers.
Numerical optimization.

Double and tripple integrals, generalized double integrals,
Polar and spherical coordinates, substitution of variables,
Computations of volumes and areas of curved surfaces,
Curve integrals and Greens formula.

System of ODE, numerical solutions with V-applications.

General comments on PDE: The Laplace and the Poisson equations,
numerical solutions. Applications of Matlab.

Organisation

The teaching consists of lectures and tutorial sessions for smaller groups and numerical laborations. More information is given on the course website before the start of the course.

Literature

TA. Persson och L.C. Böijers: Analys i flera variabler. Belonging exercise book. Material on numerics that will be handed out.

Examination

The examination consists of a written exam at the end of the course and approvednumerical laborations.

More details about the examination can be found on the course website before the start of the course.


Page manager Published: Thu 03 Nov 2022.