Calculus 2 (for IEM)
Faculteit  Science and Engineering 
Jaar  2019/20 
Vakcode  WPMA18004 
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 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. 4) 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. 5) knows the Implicit Function Theorem and is able to apply it. 6) understand change of coordinates Cartesian, polar, spherical and cylindrical coordinates. 7) accurately depict and compute the dot product and the cross product of vectors, and understand what a vector field is. 8) compute the curl and the divergence of a vector field and has an idea of the geometric meaning. The student is able to determine whether a vector field is conservative, and compute a potential function for a conservative vector field. 

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 and directional derivatives and vector fields. The course culminates with the solution of optimization problems by the method of Lagrange multipliers. 

Uren per week  
Onderwijsvorm  Hoorcollege (LC), Opdracht (ASM), Werkcollege (T)  
Toetsvorm 
Schriftelijk tentamen (WE)
(If the mark for the final exam is 4.5 or higher then the grade for the course will be determined by max(FE, 0.2ME2 + 0.2 ME1 + 0.6 FE) where FE is the mark for the final exam, and ME1 and ME2 are the marks for the midterm exams. If the mark for the final exam is lower than 4.5 then the grade for the course will be the mark for the final exam.) 

Vaksoort  propedeuse  
Coördinator  A.M.S. Waters, PhD.  
Docent(en)  A.M.S. Waters, PhD.  
Verplichte literatuur 


Entreevoorwaarden  The course unit assumes prior knowledge acquired from Calculus 1 and Linear Algebra 1.  
Opmerkingen  
Opgenomen in 
