Partial Differential Equations
Faculteit  Science and Engineering 
Jaar  2022/23 
Vakcode  WBMA00805 
Vaknaam  Partial Differential Equations 
Niveau(s)  bachelor 
Voertaal  Engels 
Periode  semester II b 
ECTS  5 
Rooster  rooster.rug.nl 
Uitgebreide vaknaam  Partial Differential Equations  
Leerdoelen  At the end of the course, the student is able to: 1. The student is able to prove existence, uniqueness, stability and wellposedness of initial and boundary value problems for linear (up to fourth order) order PDE. They are also able to classify PDEs as linear, nonlinear, hyperbolic, parabolic, and elliptic. They are also able to use the maximum principles for elliptic and parabolic PDE to characterize solutions to these equations on domains. 2. The student can reproduce and apply analytical methods to solve PDEs such as using the method of characteristics, change of variables and very importantly separation of variables. They can compute Fourier series and Fourier integrals as well as reproduce some standard Green's functions. 3. The student should be able to reproduce the main theorems from the textbook and to be able to apply them. To be able to modify the proofs of the main results and to be able to apply them with necessary changes to similar situations. 4. solve (elementary) problems which are directly or closely related to the material taught in the course having applications in physics and applied mathematics. 

Omschrijving  Problems in physics are in general modelled in terms of PDEs such as the wave equation, the diffusion equation, and the Laplace equation. In this course the basic notions for PDEs will be treated, including classification of PDEs, uniqueness of solutions, and wellposedness. The course will focus on analytical methods to solve PDEs, including the method of characteristics, separation of variables, GreenÂ’s functions, and Fourier series.  
Uren per week  
Onderwijsvorm 
Hoorcollege (LC), Werkcollege (T)
(Mandatory presence in class. Several homework quizzes will be given in class and they can count towards the homework score of the grade.) 

Toetsvorm 
Opdracht (AST), Schriftelijk tentamen (WE), Tussentoets (IT)
(The final grade is F if F=<5.0 and max(F, 0.75F+0.25M, 0.85F+0.15H, 0.6F+0.3M+0.1H) otherwise. Here H is the average of the best 4 out of 5 homework assignments, including possible homework quizzes, M is the grade of the midterm exam, and F is the grade of the final exam. ME and H do not count for the reexam.) 

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


Entreevoorwaarden  Background knowledge from Ordinary Differential Equations is assumed  
Opmerkingen  
Opgenomen in 
