Department of Mathematics

New course (MAT-ENVIR) in collaboration with Princeton University

This fall semester, Professor Michael A. Celia of Princeton University will be teaching a special topics course focused on standard analytical and numerical solution methods for partial differential equations, with an emphasis on equations that describe various kinds of environmental transport processes.

Mike is an outstanding lecturer, and this is a unique opportunity to experience him discussing the application of partial differential equations and their solution methods to practical real-world problems.

At the same time, I will lecture our regular course on the theory of partial differential equations.  Mike and I are trying to coordinate our courses so they will be complementary while still being independent.  Mike will teach his course in Princeton with real-time video and audio connection to Bergen, while I will teach my course here in Bergen with a similar connection to Princeton.  We have used this kind of connected teaching in the past and it has worked quite well.  Both courses have Bergen course numbers – Mike's course is MAT-ENVIR (“Analytiske og numeriske metodar for transportproblem i naturlege system”) and my course is MAT 234 (“Partielle differensialligninger”).  Similarly, both courses will have course numbers at Princeton University.   Students from both universities can enroll in either or both courses.  Because of the time difference between Princeton and Bergen, both courses will be offered in the evenings here in Bergen.  Mike's course will be Tuesdays and Thursdays from 14:30 to 15:50, and my course will be Wednesdays from 14:15 to 17:00.

I have attached a general list of topics to be covered in each of the courses.  Our semester starts this week, and the first lecture in MAT 234 is this evening, while Mike's course will start during the first week of classes in Princeton (three weeks later - first lecture on Thursday Sept 12).  All lectures will be in the videoconference room in the first floor of Realfagbygget, near the stairs to the cafeteria.

Please let me know if you have any questions or would like additional information about these courses.  Note that postdocs and other members of the university are also welcome to attend Mike's course. 

General List of Topics for

Princeton CEE 599b: Analytical and Numerical Methods for Environmental Transport Problems and Bergen MAT 234: Partial Differential Equations

Week #

CEE 599b

MAT 234 / CEE 550

34 (21 Aug)


Course overview & Intro to PDEs

35 (28 Aug)


Function spaces

36  (4 Sept)


Sobolov spaces


Physical models

Hyperbolic PDEs & characteristics


Method of characteristics

Non-uniqueness, shocks and Rankine-Hugoniot


Separation of variables

Entropy solutions & vanishing viscosity


Integral transforms

Elliptic PDEs & fundamental solutions


Integral transforms

Mean value theorems


Integral transforms

Properties of harmonic functions


Fall break

Energy methods


Finite volume & finite difference

Parabolic PDEs


Finite elements

Parabolic PDEs


Time integration methods

Weak form of second-order PDEs


Time integration methods



Stability of numerical methods



Non-linear equations





Jan Martin Nordbotten (Jan.Nordbotten@math.uib.no)