Course syllabus for Multivariable analysis

Course syllabus adopted 2021-02-17 by Head of Programme (or corresponding).

Overview

  • Swedish nameFlervariabelanalys
  • CodeMVE655
  • Credits7.5 Credits
  • OwnerTKGBS
  • Education cycleFirst-cycle
  • Main field of studyMathematics
  • DepartmentMATHEMATICAL SCIENCES
  • GradingTH - Pass with distinction (5), Pass with credit (4), Pass (3), Fail

Course round 1

  • Teaching language Swedish
  • Application code 74127
  • Maximum participants70
  • Open for exchange studentsNo

Credit distribution

0121 Examination 7.5 c
Grading: TH		 7.5 c
  • 12 Jan 2022 am J
  • 11 Apr 2022 pm J
  • 15 Aug 2022 pm J

In programmes

Examiner

Go to coursepage (Opens in new tab)

Eligibility

Information missing

Course specific prerequisites

Single variable calculus and linear algebra

Aim

The aim of the course is to, in combination with other mathematics courses, provide a mathematical common knowledge useful in continued studies and professional areas. The course will provide knowledge in multivariable analysis necessary for other courses within the Global systems programme.

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

- define and handle the concepts of continuity, partial derivatives, differentiable function, gradient and directional derivatives of functions of several variables 
- solve optimization problems with several variables in compact areas and with side conditions 
- calculate double and triple integrals with different choices of coordinates 
- calculate curve and surface integrals 
- combine knowledge of different concepts in practical problem solving.

Content

Functions from Rn to Rm, curves and surfaces, 
Limits, continuity, differentiability, chain rule, 
Partial derivatives, gradient and tangent plane, directional derivatives, differentials, 
Functional matrices, functional determinants. 
Extreme values, optimization in compact areas, optimization with side conditions. 
Something about numerical optimization. 
Double and triple integrals, generalized double integrals. 
Polar and spherical coordinates, variable substitution. 
Volume calculations, mass center, area of curved surface. 
Curve integrals and Green's formula. 
Surface integrals, Gauss' and Stokes' theorems.

Organisation

Lectures and exercises

Literature

Course literature will be advertised on the course web-page.

Examination including compulsory elements

Written exam. Voluntary exercises giving bonus points for the exam may be given.

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.