| Language of instruction : English |
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| Degree programme | | Study hours | Credits | P2 SBU | P2 SP | 2nd Chance Exam1 | Tolerance2 | Final grade3 | |
 | 3rd year Bachelor of Mathematics option Biomathematics | Compulsory | 135 | 5,0 | 135 | 5,0 | Yes | Yes | Numerical |  |
| 3rd year Bachelor of Mathematics option Computational Mathematics | Compulsory | 135 | 5,0 | 135 | 5,0 | Yes | Yes | Numerical | |
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| | | Learning outcomes |
- 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. | - 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. | - 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. | - 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. | - EC
| EC 8: A graduate of the Bachelor of Mathematics programme had some skills in modelling.
| - EC
| EC 10: A graduate of the Bachelor of Mathematics programme has knowledge of a number of applications of mathematics | - EC
| EC 12: A graduate of the Bachelor of Mathematics programme has a basic knowledge of programming and is able to use common mathematical software (e.g.. Maple, Matlab). | - EC
| EC 13: A graduate of the Bachelor of Mathematics programme is familiar with English professional literature.
| - EC
| EC 14: A graduate of the Bachelor of Mathematics programme has a critical attitude and a research attitude.
| - 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. |
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| | EC = learning outcomes DC = partial outcomes BC = evaluation criteria |
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Content: This course is an introduction to numerical methods for partial differential equations (PDEs). For each of the three important categories of PDEs (elliptic, parabolic, hyperbolic), we study basic properties and analyze suitable numerical methods (finite differences, finite volumes, finite elements). The student will use these methods to approximate the solution to a partial differential equation in order to simulate a process from the sciences (could be physics, biology, chemistry or engineering). Next to methodologies, mathematical issues regarding the reliability of the obtained approximations will be treated. These mathematical issues involve error analysis, consistency, stability and convergence.
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Lecture ✔
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Response lecture ✔
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Period 2 Credits 5,00
| Evaluation method | |
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| Written evaluaton during teaching periode | 70 % |
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| Additional information | A student has to take part in all the subexams. In case the student does not take part in one or more of the subexams, he/she will get a grade "N" ("examenonderdeel niet volledig afgelegd: ongewettigd afwezig voor onderde(e)len van de evaluatie") |
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Second examination period
| Evaluation second examination opportunity different from first examination opprt | |
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| Explanation (English) | 100% oral exam |
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| Prerequisites |
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The student is able to perform elementary algebraic operations on matrices, such as addition, multiplication and solution of systems of equations (LU, Choleski, Gauss etc).
The student is able to use Numerical Integration, Interpolation, Iterative methods for nonlinear equations (such Newton-Raphson, Picard's Fixed Method).
The student is able to use numerical time-integration for initial value problems, and (s)he is able to assess mathematical issues like convergence, consistence and stability.
The student is able to compute eigenvalues, eigenvectors, eigenfunctions for matrices and elementary differential operators.
The student is able to apply Riesz' Representation Theorem and Lax Milgram's Theorem (though these concepts will be recapitulated).
The student is able to integrate over curves, surfaces and volumes, and (s)he is able to apply Gauss' Divergence and Stokes' Circulation Theorems. |
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| Compulsory coursebooks (printed by bookshop) |
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[foutschatting eindige elementenmethode],[This document describes an introduction to the error analysis of finite element methods.] |
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| Compulsory course material |
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1. Book: J van Kan, A Segal, FJ Vermolen. Numerical Methods in Scientific Computing. Delft Academic Press, second edition, 2014, ISBN 9789065623645
2. Lecture notes: J Schuetz and FJ Vermolen. Still in development |
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| 3rd year Bachelor of Mathematics option free choice addition | Optional | 135 | 5,0 | 135 | 5,0 | Yes | Yes | Numerical | |
| Exchange Programme Mathematics | Optional | 135 | 5,0 | 135 | 5,0 | Yes | Yes | Numerical | |
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| | | Learning outcomes |
- 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. | - 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. | - 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. | - 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. | - EC
| EC 8: A graduate of the Bachelor of Mathematics programme had some skills in modelling.
| - EC
| EC 10: A graduate of the Bachelor of Mathematics programme has knowledge of a number of applications of mathematics | - EC
| EC 12: A graduate of the Bachelor of Mathematics programme has a basic knowledge of programming and is able to use common mathematical software (e.g.. Maple, Matlab). | - EC
| EC 13: A graduate of the Bachelor of Mathematics programme is familiar with English professional literature.
| - EC
| EC 14: A graduate of the Bachelor of Mathematics programme has a critical attitude and a research attitude.
| - 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. |
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| | EC = learning outcomes DC = partial outcomes BC = evaluation criteria |
|
|
Content: This course is an introduction to numerical methods for partial differential equations (PDEs). For each of the three important categories of PDEs (elliptic, parabolic, hyperbolic), we study basic properties and analyze suitable numerical methods (finite differences, finite volumes, finite elements). The student will use these methods to approximate the solution to a partial differential equation in order to simulate a process from the sciences (could be physics, biology, chemistry or engineering). Next to methodologies, mathematical issues regarding the reliability of the obtained approximations will be treated. These mathematical issues involve error analysis, consistency, stability and convergence.
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Lecture ✔
|
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|
Response lecture ✔
|
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|
Period 2 Credits 5,00
| Evaluation method | |
|
| Written evaluaton during teaching periode | 70 % |
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|
|
|
|
| Additional information | A student has to take part in all the subexams. In case the student does not take part in one or more of the subexams, he/she will get a grade "N" ("examenonderdeel niet volledig afgelegd: ongewettigd afwezig voor onderde(e)len van de evaluatie") |
|
Second examination period
| Evaluation second examination opportunity different from first examination opprt | |
|
| Explanation (English) | 100% oral exam |
|
|
|
|
|
| Prerequisites |
| |
The student is able to perform elementary algebraic operations on matrices, such as addition, multiplication and solution of systems of equations (LU, Choleski, Gauss etc).
The student is able to use Numerical Integration, Interpolation, Iterative methods for nonlinear equations (such Newton-Raphson, Picard's Fixed Method).
The student is able to use numerical time-integration for initial value problems, and (s)he is able to assess mathematical issues like convergence, consistence and stability.
The student is able to compute eigenvalues, eigenvectors, eigenfunctions for matrices and elementary differential operators.
The student is able to apply Riesz' Representation Theorem and Lax Milgram's Theorem (though these concepts will be recapitulated).
The student is able to integrate over curves, surfaces and volumes, and (s)he is able to apply Gauss' Divergence and Stokes' Circulation Theorems. |
|
|
| Compulsory coursebooks (printed by bookshop) |
| |
[foutschatting eindige elementenmethode],[This document describes an introduction to the error analysis of finite element methods.] |
|
|
| Compulsory course material |
| |
1. Book: J van Kan, A Segal, FJ Vermolen. Numerical Methods in Scientific Computing. Delft Academic Press, second edition, 2014, ISBN 9789065623645
2. Lecture notes: J Schuetz and FJ Vermolen. Still in development |
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| Master of Teaching in Sciences and Technology - Engineering and Technology choice for subject didactics math | Optional | 108 | 4,0 | 108 | 4,0 | Yes | Yes | Numerical | |
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| | | Learning outcomes |
- EC
| WET 1. The newly graduated student has advanced knowledge, insight, skills and attitudes in the disciplines relevant to his/her specific subject didactics and is able to communicate these appropriately to his/her stakeholders. |
|
| | EC = learning outcomes DC = partial outcomes BC = evaluation criteria |
|
|
Content: This course is an introduction to numerical methods for partial differential equations (PDEs). For each of the three important categories of PDEs (elliptic, parabolic, hyperbolic), we study basic properties and analyze suitable numerical methods (finite differences, finite volumes, finite elements). The student will use these methods to approximate the solution to a partial differential equation in order to simulate a process from the sciences (could be physics, biology, chemistry or engineering). Next to methodologies, mathematical issues regarding the reliability of the obtained approximations will be treated. These mathematical issues involve error analysis, consistency, stability and convergence.
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|
Lecture ✔
|
|
|
|
Response lecture ✔
|
|
|
|
Period 2 Credits 4,00
| Evaluation method | |
|
| Written evaluaton during teaching periode | 70 % |
|
|
|
|
|
|
| Additional information | A student has to take part in all the subexams. In case the student does not take part in one or more of the subexams, he/she will get a grade "N" ("examenonderdeel niet volledig afgelegd: ongewettigd afwezig voor onderde(e)len van de evaluatie") |
|
|
|
| Prerequisites |
| |
The student is able to perform elementary algebraic operations on matrices, such as addition, multiplication and solution of systems of equations (LU, Choleski, Gauss etc).
The student is able to use Numerical Integration, Interpolation, Iterative methods for nonlinear equations (such Newton-Raphson, Picard's Fixed Method).
The student is able to use numerical time-integration for initial value problems, and (s)he is able to assess mathematical issues like convergence, consistence and stability.
The student is able to compute eigenvalues, eigenvectors, eigenfunctions for matrices and elementary differential operators.
The student is able to apply Riesz' Representation Theorem and Lax Milgram's Theorem (though these concepts will be recapitulated).
The student is able to integrate over curves, surfaces and volumes, and (s)he is able to apply Gauss' Divergence and Stokes' Circulation Theorems. |
|
|
| Compulsory coursebooks (printed by bookshop) |
| |
[foutschatting eindige elementenmethode],[This document describes an introduction to the error analysis of finite element methods.] |
|
|
| Compulsory course material |
| |
1. Book: J van Kan, A Segal, FJ Vermolen. Numerical Methods in Scientific Computing. Delft Academic Press, second edition, 2014, ISBN 9789065623645
2. Lecture notes: J Schuetz and FJ Vermolen. Still in development |
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1 examination regulations art.1.3, section 4. |
| 2 examination regulations art.4.7, section 2. |
3 examination regulations art.2.2, section 3.
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| Legend |
| SBU : course load | SP : ECTS | N : Dutch | E : English |
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