## Calculus 2 (for IEM)

 Faculteit Science and Engineering Jaar 2022/23 Vakcode WBIE017-05 Vaknaam Calculus 2 (for IEM) Niveau(s) propedeuse Voertaal Engels Periode semester II a ECTS 5 Rooster rooster.rug.nl

Uitgebreide vaknaam Calculus 2 (for IEM)
Leerdoelen At the end of the course, the student is able to:
1. compute the lengths of parametric curves, reparametrize curves by arclength and compute the scalar curvature of a curve.
2. knows the definition of continuity for vector valued and multivariable functions, and is able to check continuity for such functions.
3. has a firm understanding of differentiability for vector valued and multivariable functions including partial and directional
4. derivatives and is able to compute partial and directional derivatives from the definition, linear approximations, and determine the tangent plane of the graph of a multivariable function. He/she is able to apply the chain rule.
5. determine extrema of multivariable functions. This also includes extrema under a constraint by applying the method of a Lagrange multiplier. For functions of two variables, the students can use the Hessian to distinguish between minima, maxima and saddle points.
6. knows the Implicit Function Theorem and is able to apply it.
7. understand change of coordinates Cartesian, polar, spherical and cylindrical coordinates.
8. accurately depict and compute the dot product and the cross product of vectors, and understand what a vector field is.
9. knows and is able to apply the integral theorems of Green, Stokes, and Gauss.
10. is able to compute double and triple integrals representing surface and volumes of shapes, respectively.
Omschrijving Calculus II is a multivariable calculus course sequence for engineers, and physical scientists, and business management.

The course treats topics related to differential calculus in more than one variable. Topics will include curves in the plane, curves and
surfaces in space, coordinate systems, partial differentiation, tangent planes to surfaces, directional derivatives, vector
fields and optimization problems by the method of Lagrange multipliers.
Uren per week
Onderwijsvorm Hoorcollege (LC), Opdracht (ASM), Werkcollege (T)
Toetsvorm Opdracht (AST), Schriftelijk tentamen (WE), Tussentoets (IT)
(If the mark of the final exam is 4.5 or higher then the grade for the course will be max (FE, 0.6 FE + 0.2 ME1 + 0.2 ME2, 0.8 FE + 0.2 HW), where FE is the mark for the final exam, ME1 and ME2 are the marks for the midterm exams, and HW is the average mark of the homework assignments. If the mark of the final exam is lower than 4.5 then the grade for the course will be the mark of the final exam.)
Vaksoort propedeuse
Coördinator P.M.J. Tibboel, PhD.
Docent(en) P.M.J. Tibboel, PhD.
Verplichte literatuur
Titel Auteur ISBN Prijs
Calculus. Early transcendentals. Newest (9th) Edition (International Metric Edition). Cengage Learning (2020) James Stewart et al. 9780357113516
Div, Grad, Curl, and All That: An Informal Text on Vector Calculus (Fourth Edition) H.M. Schey 9780393925166
Entreevoorwaarden The course unit assumes prior knowledge acquired from Calculus 1 and Linear Algebra 1.
Opmerkingen This course was previously registered with course code WPMA18004
Opgenomen in
Opleiding Jaar Periode Type
BSc Courses for Exchange Students: Engineering: Biomedical-Industrial-Mechanical - semester II a verplicht
BSc Industrial Engineering and Management 1 semester II a verplicht
Pre-master/Fast-track for MSc Engineering: BME – IEM - ME  (Pre-Master ME Applied University) - semester II a verplicht
Pre-master/Fast-track for MSc Engineering: BME – IEM - ME  (Pre-Master IEM & ME Custom courses) - semester II a verplicht
Pre-master/Fast-track for MSc Engineering: BME – IEM - ME  (Pre-Master IEM Applied University PTL) - semester II a verplicht