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Cursus: 202001218
202001218
Calculus 2
Cursus informatie
Cursus202001218
Studiepunten (ECTS)3
CursustypeOnderwijseenheid
VoertaalEngels
Contactpersoonprof.dr. A.A. Stoorvogel
E-maila.a.stoorvogel@utwente.nl
Docenten
VorigeVolgende 2
Examinator
M. Carioni
Examinator
ir. F.A. de Kogel
Examinator
dr. L. Pehlivan
Docent
dr. C.A. Pérez Arancibia
Examinator
dr. V. Ramirez Garcia Luna
Collegejaar2021
Aanvangsblok
2A
OpmerkingPart of module 3 B-ME
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 Mechanical Engineering
Module
Module 3
Verplicht materiaal
Book
Thomas’ Calculus (12th edition) ISBN 9781783991587
Aanbevolen materiaal
-
Werkvormen
Lecture

Self study with assistance

Tutorial

Workshop
AanwezigheidsplichtJa

Opmerking
Case
Toetsen
Calculus 2

Participation

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