Kies de Nederlandse taal
Course module: 202001220
Calculus 2
Course info
Course module202001220
Credits (ECTS)3
Course typeStudy Unit
Language of instructionEnglish
Contact persondr. F. Kula
PreviousNext 2
Examiner J.A.H. Alkemade
dr. T.S. Craig
Examiner P. van 't Hof
dr. F. Kula
Contactperson for the course
dr. F. Kula
Academic year2022
Starting block
RemarksPart of module 4 B-CE
Application procedureYou apply via OSIRIS Student
Registration using OSIRISYes
The student is able to (especially w.r.t. functions of two or three variables):
  1. work with partial derivatives and applications.
  2. define and evaluate double and triple integrals over bounded regions
This course introduces the mathematics needed for disciplines such as classical mechanics, thermodynamics, fluid dynamics, and probability theory.
This course directly follows up on the courses Calculus 1A and 1B. The aim is to introduce differential calculus for functions of more than one variable. Applications of this theory include the chain rule, linearizations, differentials, and extreme values (both with and without constraints).

In the spirit of univariate functions, integrals of multivariate functions will be defined as limits of Riemann sums. In this case, the domain of integration becomes, for example, a rectangle, a disc, or a spherical region. This leads to double and triple integrals which can be used to compute areas, volumes, probabilities, charges, forces, masses, and moments of inertia.

Sometimes integrals of multivariate functions are easier to compute when the usual Cartesian coordinates are replaced by polar, cylindrical, or spherical coordinates. Determinants, which will also be a topic in the course Linear Algebra, play an important role in these coordinate transformations.

The follow-up course Vector Calculus (BMT,CE,CSE,ME, IEM) will cover line and surface integrals. By parameterising the domain of integration these integrals can be reduced to single or double integrals. The theorems of Gauss, Green, and Stokes provide a deep connection between all these integrals.
Module 4
Participating study
Bachelor Civil Engineering
Required materials
G.B.Thomas, M.D. Weir, J.R. Hass: ‘Thomas’ Calculus, Early Transcendentals’, (special edition for UT). ISBN: 9781784498139
Recommended materials
Instructional modes
Presence dutyYes

Self study with assistance
Presence dutyYes

Presence dutyYes

Presence dutyYes

Final exam


Kies de Nederlandse taal