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Cursus: 202001221
202001221
Calculus 2
Cursus informatie
Cursus202001221
Studiepunten (ECTS)3
CursustypeOnderwijseenheid
VoertaalEngels
Contactpersoonprof.dr. A.A. Stoorvogel
E-maila.a.stoorvogel@utwente.nl
Docenten
VorigeVolgende 5
Docent
dr. T. Akkaya
Examinator
dr.ir. A. Braaksma
Docent
prof.dr. J.G.E. Gardeniers
Examinator
prof.dr. J.L. Hurink
Docent
dr. J. de Jong
Collegejaar2021
Aanvangsblok
2B
AanmeldingsprocedureZelf aanmelden via OSIRIS Student
Inschrijven via OSIRISJa
Cursusdoelen
The student is able to (especially w.r.t. functions of two or three variables):
  1. work with partial derivatives and applications.
  2. define and evaluate double and triple integrals over bounded regions
Inhoud
This course introduces the mathematics needed for disciplines such as classical mechanics, thermodynamics, fluid dynamics, and probability theory.
This course directly follows up on the courses Calculus 1A and 1B. The aim is to introduce differential calculus for functions of more than one variable. Applications of this theory include the chain rule, linearizations, differentials, and extreme values (both with and without constraints).

In the spirit of univariate functions, integrals of multivariate functions will be defined as limits of Riemann sums. In this case, the domain of integration becomes, for example, a rectangle, a disc, or a spherical region. This leads to double and triple integrals which can be used to compute areas, volumes, probabilities, charges, forces, masses, and moments of inertia.

Sometimes integrals of multivariate functions are easier to compute when the usual Cartesian coordinates are replaced by polar, cylindrical, or spherical coordinates. Determinants, which will also be a topic in the course Linear Algebra, play an important role in these coordinate transformations.

The follow-up course Vector Calculus (BMT,CE,CSE,ME) will cover line and surface integrals. By parameterising the domain of integration these integrals can be reduced to single or double integrals. The theorems of Gauss, Green, and Stokes provide a deep connection between all these integrals.
 
Participating study
Bachelor Scheikundige Technologie
Module
Module 4
Verplicht materiaal
Book
Thomas’ Calculus (12th edition) ISBN 9781783991587
Aanbevolen materiaal
-
Werkvormen
Lecture

Self study with assistance
AanwezigheidsplichtJa

Tutorial
AanwezigheidsplichtJa

Workshop
AanwezigheidsplichtJa

Toetsen
Final exam

Participation

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