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Kies de Nederlandse taal
Course module: 202001227
202001227
Vector Calculus
Course info
Course module202001227
Credits (ECTS)2
Course typeStudy Unit
Language of instructionEnglish
Contact persondr. M. Schlottbom
E-mailm.schlottbom@utwente.nl
Lecturer(s)
Lecturer
ir. F.A. de Kogel
Contactperson for the course
dr. M. Schlottbom
Lecturer
dr. M. Schlottbom
Lecturer
dr.ir. G. Zwier
Academic year2020
Starting block
1A
Application procedureYou apply via OSIRIS Student
Registration using OSIRISYes
Aims
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
Content
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 Calculus2. Surface integration allows us to calculate the area of curved surfaces, and also 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.
 
Assumed previous knowledge
Calculus 1
Calculus 2
Module
Module 5
Participating study
Bachelor Chemical Science & Engineering
Required materials
Book
Thomas’ Calculus, Early Transcendentals, 12th edition
Recommended materials
-
Instructional modes
Assessment

Lecture

Q&A

Self study with assistance

Tutorial

Tests
Exam

Remark
Test in the 5th week of the module

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Kies de Nederlandse taal