## Calculus 2

 Faculteit University College Groningen Jaar 2019/20 Vakcode UCGAC211 Vaknaam Calculus 2 Niveau(s) bachelor Voertaal Engels Periode semester I a ECTS 5 Rooster rooster.rug.nl

Uitgebreide vaknaam Calculus 2
Leerdoelen 1.The student can compute the lengths of parametric curves, reparametrize curves by arclength and compute the scalar curvature of a curve.

2.The student knows the definition of continuity for vector valued and multivariable functions, and is able to check continuity for such functions.

3.The student knows the definitions of partial and directional derivatives and is able to compute partial and directional derivatives from the definition.

4.The student knows the definition of differentiability for multivariable functions, can compute linear approximations, and determine the tangent plane of the graph of a multivariable function.

5.The student knows and is able to apply the chain rule for multivariable functions.

6.The student is able to determine extrema of multivariable functions, and for functions of two variables, the students can use the Hessian to distinguish between minima, maxima and saddle points.

7.The student is able to determine extrema under a constraint using the method of Lagrange multipliers.

8.The student is able to compute double and triple integrals in Cartesian, polar, spherical and cylindrical coordinates.

9.The student can compute the curl and the divergence of a vector field and has an idea of the geometric meaning.

10.The student can compute line integrals of scalar functions and vector fields.

11.The student is able to determine whether a vector field is conservative, and compute a potential function for a conservative vector field.

12.The student is able to compute the flux of a vector field through a surface in R3 .

13.The student knows and is able to apply the integral theorems of Green, Stokes, and Gauss.
Omschrijving Calculus 2 is one of the modules of the Research and Methodology: Year 2 course. It is aimed
at those who are oriented towards major in Physics and Smart Technologies, but also Artificial Intelligence and ICT.

The course Calculus 2 gives a classical introduction to the field of multivariable calculus. The course proceeds the course Calculus 1 which mainly concerns the calculus of functions of a single variable, and generalizes many of its concepts like continuity, differentiability and integration to the case of multivariable functions. Apart from the background established in Calculus 1 many aspects from the course Linear Algebra 1 like vectors, linear maps, matrices and inner products are heavily used in Calculus 2. In Calculus 2 the means are developed to compute the work required to displace a body along a curve through a given force field or to compute the amount of fluid flowing through a surface in a period of time from the velocity field of the fluid.
The course culminates in the study of the integral theorems by Green, Stokes and Gauss which form, e.g., the basis for formulating Maxwell’s Equations of electrodynamics. The concepts developed in Calculus 2 are used in many advanced courses in mathematics and physics.

The topics addressed in Calculus 2 are spatial curves together with their parametrization by arclength and their curvature, continuity of vector valued functions and multivariable functions, partial and directional derivatives, the linear approximation of a multivariable function, the chain rule for multivariable functions, the tangent plane of the graph of a multivariable function, extrema of multivariable functions and of multivariable functions with constraints using the method of Lagrange multipliers, multiple integrals, the Jacobian, integration of vector fields along curves and over surfaces, conservative vector fields and potential functions, the curl and divergence of vector fields, and Green’s, Stokes', and Gauss' Theorems.

Requirements/ pre-requisites : Calculus 1, Linear Algebra
Uren per week 8
Onderwijsvorm Seminar
Toetsvorm Assignments, Written exam
Vaksoort bachelor
Coördinator dr. O. Kavatsyuk
Docent(en) dr. O. Kavatsyuk
Verplichte literatuur
Titel Auteur ISBN Prijs
Calculus Early transcendentals. 8th edition, (International metric edition) James Stewart 9781305272378 ca. €  75,00
Entreevoorwaarden Calculus 1, Linear Algebra
Opmerkingen
Opgenomen in
Opleiding Jaar Periode Type
Academic Core - semester I a verplicht
Health and Life Sciences  (Electives Year 2) - semester I a verplicht
Liberal Arts and Sciences  (Year 2) - semester I a keuzegroep
Mind Machines and Morality  (Compulsory) - semester I a verplicht
Smart Technologies  (Compulsory) - semester I a verplicht