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## Syllabus for

MVE035 - Multivariable analysis

Owner: TKTFY
6,0 Credits
Grading: TH - Five, Four, Three, Not passed
Education cycle: First-cycle
Major subject: Mathematics, Engineering Physics
Department: 11 - MATHEMATICAL SCIENCES

Teaching language: Swedish

 Course module Credit distribution Examination dates Sp1 Sp2 Sp3 Sp4 Summer course No Sp 0105 Examination 6,0 c Grading: TH 6,0 c 14 Mar 2016 pm SB, 02 Apr 2016 pm SB, 23 Aug 2016 pm SB

#### In programs

TKTFY ENGINEERING PHYSICS, Year 1 (compulsory)
TKTEM ENGINEERING MATHEMATICS, Year 1 (compulsory)

#### Examiner:

Forskarassistent  Dennis Eriksson

#### Eligibility:

In order to be eligible for a first cycle course the applicant needs to fulfil the general and specific entry requirements of the programme(s) that has the course included in the study programme.

#### Course specific prerequisites

Linjär algebra och geometri motsvarande kursen TMA660 och Matematisk analys fortsättning (envariabelanalys) motsvarande kursen TMA976.

#### Aim

The course provides basic knowledge of the fundamental theories within mathematical analysis.

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

The goal is to provide the students with the necessary mathematical tools in analysis in several variables for forthcoming and following courses at the Engineering Physics programme.

#### Content

Functions of several variables. Partial derivatives, differentiability, the chain rule, directional derivative, gradient, level sets, tangent planes.
Taylor's formula for functions of several variables, characterization of stationary points.
Double integrals, iterated integration, change of variables, triple integrals, generalized integrals.
Space curves. Line integrals, Green's formula in the plane, potentials and exact differential forms.
Sufaces in R3, surface area, surface integrals, divergence and curl, Gauss' and Stokes' theorems.
Some physical problems leading to partial differential equations. Partial differential equations of the first order. Differentiating through the integral.
Functional determinants, inverse functions theorem, implicit functions. Extremal problems for functions of several variables, Lagrange's multiplier rule.

#### Organisation

Lectures and exercises. Computer exercises with Matlab and Mathematica.

#### Literature

A. Persson, L.-C. Böiers: Analys i flera variabler, Studentlitteratur, Lund.
Övningar till Analys i flera variabler, Institutionen för matematik, Lunds tekniska högskola.

OTHER LITERATURE
L. Råde, B. Westergren: BETA - Mathematics Handbook, Studentlitteratur, Lund.
E. Pärt-Enander, A. Sjöberg: Användarhandledning för Matlab, Uppsala universitet.

#### Examination

A written examination.

Page manager Published: Mon 28 Nov 2016.