De elektronische studiegids voor het academiejaar 2025 - 2026 is onder voorbehoud.





Partial differential equations (3341)
  
Coordinating lecturer :Prof. dr. Sorin POP 
  
Member of the teaching team :Mevrouw Ayesha JAVED 
 Prof. dr. Fred VERMOLEN 
 Prof. dr. Jochen SCHÜTZ 

Language of instruction : English
Credits: 5,0
  
Period: semester 2 (5sp)
  
2nd Chance Exam1: Yes
  
Final grade2: Numerical
 
Sequentiality
 
   No sequentiality
   Advising sequentiality bound on the level of programme components
 
 

Prerequisites

1. The student is familiar with open and closed sets in Rn.

2. The student can differentiate, and can apply the chain rule.

3. The student knows the meaning of (and can compute) the gradient, divergence, can apply partial integration, or the Green/Gauss theorem.

4. The student has basic knowledge in ordinary differential equations (first and second order linear equations with constant coefficients, separable equations, qualitative methods: phase line, phase plane)

5. The student is familiar with Fourier series (orthogonality of functions, calculating the coefficients, Parseval’s identity, convergence results)

6. The student has general knowledge of the series of functions (convergence criteria, differentiation/integration).

Some of the points above are presented briefly in the study material, in particular for the ordinary differential equations and for the series of functions.


Content

This course is an introduction to the theory of partial differential equations and includes several important applications.

The general study goal is to provide a basic understanding of the three major types of partial differential equations (elliptic, parabolic and hyperbolic) and the related initial and boundary value problems. In particular, basic methods for for finding solutions explicitly will be discussed.

Contents (subject to adjustement): first order equations, method of characteristics, second order linear equations, the diffusion equation (energy estimates,uniqueness, similarity solutions, fundamental solutions, initial and boundary value problems, separation of variables), the Laplace equation (uniqueness, boundary value problems, separation of variables), wave equation (energy estimates, uniqueness, boundary value problems, initial value problems, separation of variables), nonlinear equations (travelling waves)


Organisational and teaching methods
Organisational methods  
Lecture ✔  
Response lecture ✔  


Evaluation

Period 2    Credits 5,00

Evaluation method
Written evaluaton during teaching periode30 %
Transfer of partial marks within the academic year✔
Conditions transfer of partial marks within the academic yearSee additional information
Homework✔
Written exam70 %
Closed-book ✔
Additional information

The weighting 30% assignments 70% written exam is only valid if the grade for the written exam is greater or equal to 8. If the grade for the written exam is less than 8 then this grade will count for 100%, so the assignments have the weight 0%. This rule also applies to the second session (resit). For the resit, the grade for the assignments remains valid. 

De verdeling 30% huiswerktaken 70% schriftelijk examen geldt alleen als het cijfer voor het schriftelijk examen groter of gelijk is aan 8. Als het cijfer voor het schriftelijk examen minder is dan 8 is dan telt het cijfer van het schriftelijk examen voor 100%. De regel geldt voor beide zittingen, het cijfer voor de huiswerktaken blijft geldig ook voor de tweede examenkans.

Second examination period

Evaluation second examination opportunity different from first examination opprt
No
 

Compulsory course material
 

Study material & Study guide (available on Blackboard)
 

Recommended reading
 

W.A. Strauss, Partial Differential Equations: an Introduction, John Wiley and Sons, 139780470054567

C.J. van Duijn, M.J. de Neef, Analyse van Differentiaalvergelijkingen, 9789040712654
 

Remarks
 

The students are advised to complete the following course before following 'Partial Differential Equations': 'Vector Calculus and Differential Equations' (4708).

Following 'Functional and Fourier analysis' (3985) is not necessarily required, but Fourier series are assumed to be known.

'Analysis 2' (3190) and 'Dynamical Systems' (3195) are useful but not necessarily required.


Learning outcomes
Bachelor of Mathematics
  •  EC 

    • EC 1: A graduate of the Bachelor of Mathematics programme has a thorough basic knowledge and insight in various disciplines of Mathematics including algebra, geometry, analysis, numerical mathematics, probability theory, statistics, aspects of discrete mathematics and logic.

     
  •  DC 

    • 1.3: A graduate of the Bachelor of Mathematics programme has a thorough basic knowledge and understanding of analysis

     
  •  DC 

    • 1.7: A graduate of the Bachelor of Mathematics programme hasa thorough basic knowledge and understanding of differential equations

  •  EC 

    • EC 2: A graduate of the Bachelor of Mathematics programme has an advanced knowledge and insight into the main branches of Mathematics (pure mathematics, applied mathematics,...).

     
  •  DC 

    • 2.2: A graduate of the Bachelor of Mathematics programme possesses advanced knowledge and understanding of applied mathematics

     
  •  DC 

    • 2.1: A graduate of the Bachelor of Mathematics programme possesses advanced knowledge and understanding of pure mathematics

  •  EC 

    • EC 3: A graduate of the Bachelor of Mathematics programme has mastered the formal mathematical language and methodology. He/she is able to work at a sufficiently high level of abstraction.

     
  •  DC 

    • 3.1: A graduate of the Bachelor of Mathematics programme masters mathematical notation

     
  •  DC 

    • 3.2: A graduate of the Bachelor of Mathematics programme can understand abstract reasoning and its message

     
  •  DC 

    • 3.3: A graduate of the Bachelor of Mathematics programme can formulate and express abstract reasoning mathematically in accordance with axiomatic structure and logic

     
  •  DC 

    • 3.4: A graduate of the Bachelor of Mathematics programme can understand the consequences (implications) of abstract reasoning

  •  EC 

    • EC 4: A graduate of the Bachelor of Mathematics programme is able to understand a mathematical proof, he/she is able to judge whether an argument is correct and is able to understand which properties are used (in the context of the acquired knowledge). He/she can identify a gap or a redundant step in a proof or a calculation.

     
  •  DC 

    • 4.1: A graduate of the Bachelor of Mathematics programme can understand and assess the correctness of a mathematical proof or argument

     
  •  DC 

    • 4.2: A graduate of the Bachelor of Mathematics programme can recognize and understand which (axiomatic) properties are used and needed in a mathematical argument or proof

  •  EC 

    • EC 5: A graduate of the Bachelor of Mathematics programme can apply the theories and methods to relatively simple mathematical problems (theoretical as well as computational). He/she can make and write down a mathematical line of reasoning by him/herself.

     
  •  DC 

    • 5.1: A graduate of the Bachelor of Mathematics programme can apply computational methods (e.g., integration, derivation of functions, variation of parameters, hypothesis testing, etc.) to solve simple mathematical problems

     
  •  DC 

    • 5.2: A graduate of the Bachelor of Mathematics programme can apply mathematical theories to analyze simple mathematical problems

     
  •  DC 

    • 5.3: A graduate of the Bachelor of Mathematics programme can, by using various proof techniques (e.g., direct/axiomatic proof, induction, incongruity, contraposition, counterexample, infinite descent), independently formulate and write a proof and mathematically correct argument within the material learned

  •  EC 

    • EC 6: A graduate of the Bachelor of Mathematics programme is able to integrate the acquired knowledge in new mathematical topics.  He/she understands the connection between subjects. 

     
  •  DC 

    • 6.1: A graduate of the Bachelor of Mathematics programme can recognize common mathematical and logical principles in various mathematical subfields

     
  •  DC 

    • 6.3: A graduate of the Bachelor of Mathematics programme understands the relationship between various topics

  •  EC 

    • EC 7: A graduate of the Bachelor of Mathematics programme is able to autonomously comprehend new mathematical basic texts.

     
  •  DC 

    • 7.2: A graduate of the Bachelor of Mathematics programme can independently read new mathematical English basic texts comprehensively

  •  EC 

    • EC 8: A graduate of the Bachelor of Mathematics programme had some skills in modelling.

     
  •  DC 

    • 8.2: A graduate of the Bachelor of Mathematics programme understands simple physics principles and models

  •  EC 

    • EC 9: A graduate of the Bachelor of Mathematics programme is able to function as a member of a team.

     
  •  DC 

    • 9.1: A graduate of the Bachelor of Mathematics programme can interact and collaborate respectfully with team members

     
  •  DC 

    • 9.3: A graduate of the Bachelor of Mathematics programme can meet imposed deadlines

  •  EC 

    • EC 10: A graduate of the Bachelor of Mathematics programme has knowledge of a number of applications of mathematics.

     
  •  DC 

    • 10.1: A graduate of the Bachelor of Mathematics programme has knowledge of applications from the natural sciences

  •  EC 

    • EC 13: A graduate of the Bachelor of Mathematics programme is familiar with English professional literature.

     
  •  DC 

    • 13.1: A graduate of the Bachelor of Mathematics programme knows English names for various mathematical concepts in addition to Dutch

  •  EC 

    • EC 14: A graduate of the Bachelor of Mathematics programme has a critical attitude and a research attitude.

     
  •  DC 

    • 14.1: A graduate of the Bachelor of Mathematics programme thinks critically about acquired information

  •  EC 

    • EC 15: A graduate of the Bachelor of Mathematics programme is able to carry out by him/herself (or in group) a limited study on a mathematical topic, i.e. to use scientific sources in a critical manner, to carry out, report (in LaTex as well) and present the study.

     
  •  DC 

    • 15.1: A graduate of the Bachelor of Mathematics programme can conduct a limited study of a mathematical topic on their own or in groups

  •  EC 

    • EC 16: A graduate of the Bachelor of Mathematics programme is able to work and plan independently, he/she is able to evaluate him/herself and is able to adjust his or her behaviour accordingly.

     
  •  DC 

    • 16.1: A graduate of the Bachelor of Mathematics programme can plan his/her studies and activities

 
Bachelor of Physics
  •  EC 

    • EC 7: A graduate of the Bachelor of Physics programme is able to apply the mathematical methods which are used in physics and possesses good numerical skills, including computational techniques and programming skills.

 
  EC = learning outcomes      DC = partial outcomes      BC = evaluation criteria  
Offered inTolerance3
3rd year Bachelor of Mathematics J
3th year Bachelor of Physics option free choice addition J
3th year Bachelor of Physics option twin J
Exchange Programme Mathematics J



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