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Cursus: 202001231
202001231
Vector Calculus
Cursus informatie
Cursus202001231
Studiepunten (ECTS)3
CursustypeOnderwijseenheid
VoertaalEngels
Contactpersoondr. T.S. Craig
E-mailt.s.craig@utwente.nl
Docenten
VorigeVolgende 2
Examinator
dr. T. Akkaya
Examinator
dr.ir. A. Braaksma
Examinator
dr. T.S. Craig
Contactpersoon van de cursus
dr. T.S. Craig
Examinator
prof.dr. J.L. Hurink
Collegejaar2021
Aanvangsblok
2A
AanmeldingsprocedureZelf aanmelden via OSIRIS Student
Inschrijven via OSIRISJa
Cursusdoelen
1.  Sketch and describe regions in R^2 and R^3 in Cartesian, polar, cylindrical and spherical coordinates as applicable
 
2. Calculate integrals of multivariable functions
  • determine whether a given vector field is conservative and if so identify its potential
  • parametrise curves and compute line integrals, including in the applications of work and mass
  • compute double, surface and triple integrals, including in the applications of mass, area, volume and flux
 
3. apply the theorems of Gauss (Divergence), Green and Stokes
  • compute the divergence and curl of a vector field and explain their physical meanings
  • decide which type of integral is relevant for each application
Inhoud
Vector Calculus extends the single variable calculus of Calculus 1 and 2 into multivariable and vector calculus. The course deals extensively with integration; we shall cover double, triple, surface and line integrals. In the contexts of double and triple integrals we shall carry out coordinate changes, While our major focus is on shifts between Cartesian and polar/cylindrical/spherical coordinates, we shall also look at special one-off cases of coordinate changes. A key feature of this section of the course is the Jacobian. Applications we shall look at include area (double, surface), mass (line, double, surface, triple), work done (line) and flux (surface). We shall look at vector fields and line integrals of vector fields where path independence is an important concept. Using the concepts of div and curl, we shall close the course off with the powerful vector calculus theorems: Green’s, Stokes’ and Divergence, which extend the Fundamental Theorem of Calculus into higher dimensional spaces.
 
Voorkennis
Recommended: Calculus 1 for AT&EE and Calculus 2 for AT&EE, or similar courses up to and including and introduction to multivariable functions.
Participating study
Bachelor Electrical Engineering
Module
Module 3
Verplicht materiaal
Book
Adams, R.A., Essex, C. (2018).Calculus: a Complete Course (Ninth or Tenth edition). Pearson. ISBN: 9780134154367
Aanbevolen materiaal
-
Werkvormen
Assessment
AanwezigheidsplichtJa

Hoorcollege

Werkcollege

Zelfstudie met begeleiding

Toetsen
Written test

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