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 Cursus: 202200147
 202200147Calculus 2
 Cursus informatie
Cursus202200147
Studiepunten (ECTS)4
CursustypeOnderwijseenheid
VoertaalEngels
Contactpersoondr. T.S. Craig
E-mailt.s.craig@utwente.nl
Docenten
 Vorige 1-5 van 66-6 van 6 Volgende 1
 Docent M. Carioni Examinator dr. T.S. Craig Contactpersoon van de cursus dr. T.S. Craig Docent dr. T.S. Craig Docent dr.ir. P. van 't Hof
Collegejaar2023
Aanvangsblok
 1B
OpmerkingPart of module 2 EE.
Minor students: register for the minor!
AanmeldingsprocedureZelf aanmelden via OSIRIS Student
Inschrijven via OSIRISJa
 Cursusdoelen
 body { font-size: 9pt; font-family: Arial } table { font-size: 9pt; font-family: Arial } The student will: be proficient in techniques of solving integrals including improper integrals as well as be familiar with the Fundamental Theorem of Calculus. Have a thorough understanding of infinite series and tests for convergence, in particular power and Taylor series. Be able to parametrise space curves and find arc lengths and tangent lines. Be able to work effectively with functions of two variables including sketching, assessing for differentiability, determining directional derivatives and tangent planes, and finding extrema using methods including Lagrange multipliers. Sketch and describe regions in R2 and R3 in Cartesian, polar, cylindrical and spherical coordinates as applicable Compute double, surface and triple integrals, including in the applications of mass, area, volume and flux
 Inhoud
 body { font-size: 9pt; font-family: Arial } table { font-size: 9pt; font-family: Arial } Sequences, series and summation: We shall define sequences and series and consider the convergence of infinite sequences and series. To do this we use a variety of different tests for convergence and also look at approximation errors. Series of particular interest are the p-series, geometric series, and Taylor and Maclaurin expansions. We shall consider summation techniques with particular interest in the relationship with Riemann sums. Integration, single variable: We define integration in the context of areas under curves and use Riemann sums to determine definite integrals from first principles. We study the Fundamental Theorem of Calculus and use some integration techniques such as integration by substitution and integration by parts. Integration, multivariable: Also starting from the concept of Riemann sums, we define and compute double and triple integrals in two- and three-dimensional space. Three-dimensional geometry: Our primary interest here is in space curves and surfaces. We parametrise space curves, find arc lengths, and determine the intersection of surfaces as curves. We see the graphs of functions of two variables as surfaces and consider what it means for limits of such functions to exist and how to define continuity. In the context of surfaces we consider families of level curves, tangent planes, directional derivatives and optima. We close off this section with Taylor series in two variables and using Lagrange multipliers to determine optima.
Voorkennis
 Secondary school mathematics up to and including an introduction to calculus. Calculus 1 for AT, TN, and EE is preferred but not required.
 Participating study
 Bachelor Electrical Engineering
 Module
 Module 2
Verplicht materiaal
Book
 Adams, R.A. and Essex, C. (2018).Calculus: A Complete Course, 9th Edition. Pearson. ISBN: 9780134154367
Aanbevolen materiaal
-
Werkvormen
Assessment
 Aanwezigheidsplicht Ja

Lecture
 Aanwezigheidsplicht Ja

Self study with assistance
 Aanwezigheidsplicht Ja

Self study without assistance

Tutorial
 Aanwezigheidsplicht Ja

Toetsen
 Calculus 2OpmerkingClosed book, written test
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