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Cursus: 202001226
202001226
Vector Calculus
Cursus informatie
Cursus202001226
Studiepunten (ECTS)2
CursustypeOnderwijseenheid
VoertaalEngels
Contactpersoondr. M. Schlottbom
E-mailm.schlottbom@utwente.nl
Docenten
VorigeVolgende 1
Docent
V. Bosboom
Docent
dr. F. Kula
Docent
S. Piceghello
Examinator
dr. M. Schlottbom
Contactpersoon van de cursus
dr. M. Schlottbom
Collegejaar2022
Aanvangsblok
1A
OpmerkingPart of module 5 B-CE
AanmeldingsprocedureZelf aanmelden via OSIRIS Student
Inschrijven via OSIRISJa
Cursusdoelen
The student is able to:
  1. calculate line integrals and surface integrals
    • sketch the curve or surface
    • choose a suitable parametrization
    • define mass, charge, work, area, circulation, or flux as an integral
    • determine whether a given vector field is conservative and, should that be the case,
    • identify and use the corresponding potential
  2. apply the theorems of Gauss, Green, and Stokes
    • compute the divergence and curl of a vector field and explain their physical meaning
    • decide which type of integral each relevant application calls for
Inhoud
The course covers integral calculus over curves and surfaces and, as such, extends Calculus 2 where double and triple integrals for multivariate functions have been treated. In this course, we will define several new types of integrals meant to deal with various situations arising in applications. The first new type will be the line integral, which generalizes the ordinary integral introduced in Calculus 1, and which, for example, allows to calculate the length of bent curves. Accordingly, we will be able to find the total mass or charge held by such regions in applied settings. The vector variant of the line integral will lead us to the concept of work done by a force, which is a handy way of calculating the energy exchange between two systems. Next, we will introduce surface integrals, which generalize the double integrals introduced in Calculus 2. Surface integration allows us to calculate the area of curved surfaces, and the total mass or charge held by such surfaces in applications. The vector variant of surface integrals will allow us to introduce the notion of flux, a quantity which measures flow through a given surface and thus quantifies material exchange between two regions in space. The concepts of flow and flux are related to the divergence and curl of a vector field and will lead us to the theorems of Gauss and Green/Stokes connecting surface and line integrals to the multiple integrals of Calculus 2.
Voorkennis
Calculus 1
Calculus 2
Participating study
Bachelor Civil Engineering
Module
Module 5
Verplicht materiaal
Book
G.B. Thomas, M.D. Weir, J.R. Hass, Thomas’ Calculus, Early Transcendentals, 12th edition. Pearson Education Limited, ISBN 978-0-321-63632-4
Aanbevolen materiaal
-
Werkvormen
Assessment

Lecture

Q&A

Self study with assistance

Tutorial

Toetsen
Exam Vector Calculus

Opmerking
Test in the 5th week of the module

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