
The student is able to:
1. calculate line integrals and surface integrals
 sketch the curve or surface
 choose a suitable parametrization
 define mass, charge, work, area, circulation or flux as an integral
 determine whether a given vector field is conservative and, should that
 be the case, identify and use the corresponding potential
2. apply the theorems of Gauss, Green and Stokes
 compute the divergence and curl of a vector field and explain their physical meaning
 decide which type of integral each relevant application calls for


The course covers integral calculus over curves and surfaces and, as such, extends Calculus 2 where double and triple integrals for multivariate functions have been treated. In this course we will define several new types of integrals meant to deal with various situations arising in applications. The first new type will be the line integral, which generalizes the ordinary integral introduced in Calculus 1, and which, for example, allows to calculate the length of bent curves. Accordingly, we will be able to find the total mass or charge held by such regions in applied settings. The vector variant of the line integral will lead us to the concept of work done by a force, which is a handy way of calculating the energy exchange between two systems. Next, we will introduce surface integrals, which generalize the double integrals introduced in Calculus 2. Surface integration allows us to calculate the area of curved surfaces, and also the total mass or charge held by such surfaces in applications. The vector variant of surface integrals will allow us to introduce the notion of flux, a quantity which measures flow through a given surface and thus quantifies material exchange between two regions in space. The concepts of flow and flux are related to the divergence and curl of a vector field and will lead us to the theorems of Gauss and Green/Stokes connecting surface and line integrals to the multiple integrals of Calculus 2.




 Assumed previous knowledgeBachelor Biomedical Engineering 
  Required materialsBookThomas’ Calculus, Early Transcendentals, 12th edition 

 Recommended materialsInstructional modesAssessment
 Lecture
 Q&A
 Self study with assistance
 Tutorial

 TestsExam RemarkTest in the 5th week of the module


 