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Valid for year : 2008
 
TATA61 Multivariable and vector calculus, 6 ECTS credits.
/Flervariabel- och vektoranalys/

For:   D  

 

Prel. scheduled hours: 56
Rec. self-study hours: 104

  Area of Education: Science

Subject area: Mathematics
  Advancement level (G1, G2, A): G1

Aim:
The student should acquire the proficiency in multivariable and vector calculus required for subsequent studies. After completing the course the student should be able to:
  • define and explain the central concepts of the course e.g., basic topological notions, function, limit, continuity, functional determinant, volume, area mass, potential and the different kinds of derivatives and integrals that are used in the course.
  • quote, explain, use and in occurring cases prove the central theorems of the course e.g., the theorem of global extrema, differentiability implies existence of partial derivatives, the chain rule, variable substitution in multiple integrals, the connection between gradients and directional derivatives, Gauss' and Stokes' theorems and theorems on existence of potentials.
  • verify that results and partial results are correct or reasonable.
  • solve partial differential equations by using the chain rule.
  • calculate directional derivatives and equations for tangents, normals and tangent planes as well as explain the geometric interpretations of these objects.
  • find the global maximum and minimum of functions defined on compact sets.
  • calculate double integrals, triple integrals, improper multiple integrals, surface integrals, flux integrals and curve integrals by means of iterated integration, variable substitutions (e.g., polar, spherical and linear substitutions), Gauss' theorem, Stokes' theorem and potentials.


Prerequisites: (valid for students admitted to programmes within which the course is offered)
Linear Algebra, Calculus, one variable

Note: Admission requirements for non-programme students usually also include admission requirements for the programme and threshhold requirements for progression within the programme, or corresponding.
Organisation:
Lectures and lessons.

Course contents:
The space R^n. Fundamental notions from topology. Functions from R^n to R^p. Function graphs, level surfaces and level curves. Definitions of limit and continuity. Partial derivatives. Differentiability and differential. The chain rule. Gradient, normal, tangent and tangent plane. Directional derivative. Global extrema on compact sets. Multiple integrals. Iterated integration. Variable substitution. Area, volume and mass. Improper multiple integrals. Area elements and surface integrals. Vector fields and scalar fields. Divergence and curl. Flux integrals. Gauss' theorem. Curve integrals. Stokes' theorem. Potentials.
Course literature:
Persson, A, Böiers, L-C: Analys i flera variabler, Studentlitteratur, Lund 1988.
Additional material published by the Department of Mathematics.
Examination:
Written examination
 6 ECTS
 


Course language is Swedish.
Department offering the course: MAI.
Director of Studies: Göran Forsling
Examiner:

Course Syllabus in Swedish

Linköping Institute of Technology
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Contact: TFK , val@tfk.liu.se
Last updated: 12/05/2007