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HVAC in Buildings (5020)
HW/SW co-design (3468)
Hybrid materials and functional interfaces (4895)
Hydrodynamics (1416)
ICT tools for Chemical Engineers (4033)
Image Processing (2169)
Imagination 1A (3066)
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Immunity (3620)
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Implementing systems and process innovation - basics (4797)
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Improvement science (4838)
In depth crash investigation (2222)
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Industrial (4918)
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Infection and immunity (3922)
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Inference for Statistics and Data Science (4564)
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Information management (4999)
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Innovation in building (4226)
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Insolvency Law (2154)
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Instrumental, technical and communication skills (3973)
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Integratie en lezingen (3252)
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Introduction in research and design methodology (2387)
Introduction in the History of Architecture and Arts I (2384)
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Introduction into Chemical Process Technology (0620)
Introduction of Bayesian Inference (3562)
Introduction physiotherapy competency profile and workfield (3942)
Introduction to Accounting, Finance and Governance (3909)
Introduction to algorithms for quantum communication and computing (4902)
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Introduction to Psychology (4738)
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Introduction to Semiparametric Regression (4004)
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Investment Analysis (3756)
IoT (4482)
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Kidney and digestion (4603)
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Learning and development (4159)
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Lifestyle and environment (4705)
Linear algebra (3983)
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Linear Models (3560)
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Lipids in Health and Disease (4566)
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Live Project (4134)
Logic and model theory (1602)
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Machine components (2660)
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Management 4 (2343)
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Management accounting (1770)
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Marine traineeship and fieldwork (3124)
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Materials design and synthesis (4678)
Materials for advanced health care (4898)
Materials for organic electronics (4906)
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Materials Science (1950)
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Media and Communication Studies I (4734)
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Past, present and future healthcare (4758)
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Programming and algorithmic thinking (3725)
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Language of instruction : English

Sequentiality
Advising sequentiality bound on the level of programme components
Group 1
Following programme components are advised to also be included in your study programme up till now.
Calculus 1 (3376)
4.0 stptn
Calculus 2 (3323)
4.0 stptn
Computer Labs for Mathematics (4550)
5.0 stptn
Linear algebra (3983)
4.0 stptn
Numerical methods 1 (1805)
4.0 stptn
Numerical methods 2 (3238)
4.0 stptn
Programming and algorithmic thinking (3725)
5.0 stptn
Or group 2
Following programme components are advised to also be included in your study programme up till now.
Calculus 1 (4543)
4.0 stptn
Calculus 2 (3323)
4.0 stptn
Computer Labs for Mathematics (4550)
5.0 stptn
Linear algebra (3983)
4.0 stptn
Numerical methods 1 (1805)
4.0 stptn
Numerical methods 2 (3238)
4.0 stptn
Programming and algorithmic thinking (3725)
5.0 stptn

Degree programme Study hours Credits P2 SBU P2 SP 2^{nd} Chance Exam^{1} Tolerance^{2} Final grade^{3}
Bachelor of Mathematics year 3 - pakket toegepaste wiskunde Optional 135 5,0 135 5,0 Yes Yes Numerical
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.

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 3.4: 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 4.3: A graduate of the Bachelor of Mathematics programme can recognize a gap (hole) or redundant step in a calculation or proof

DC 4.4: A graduate of the Bachelor of Mathematics programme can improve a proof or calculation by removing redundant steps and errors, and/or by filling in gaps

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 6.2: A graduate of the Bachelor of Mathematics programme can take a bird''s eye view of various mathematical topics and subfields

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

DC 6.4: A graduate of the Bachelor of Mathematics programme can integrate principles learned in one topic into another, new topic

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

DC 8.2: De bachelor wiskunde begrijpt eenvoudige natuurkundige beginselen en modellen

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 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).

DC 12.3: A graduate of the Bachelor of Mathematics programme can work with mathematical software such as Matlab

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

DC 13.2: A graduate of the Bachelor of Mathematics programme comes into contact with international professional literature from various fields of mathematics

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 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

DC 16.2: A graduate of the Bachelor of Mathematics programme has insight into his/her learning process through self-evaluation

DC 16.3: A graduate of the Bachelor of Mathematics programme can adjust his/her learning process if needed

EC = learning outcomes DC = partial outcomes BC = evaluation criteria

General Knowledge: Elementary numerical techniques like numerical quadrature, Lagrangian Interpolation, Root finding. Elementary linear algebra like matrix addition - multiplication, eigenvectors, eigenvalues. Vector algebra like Stokes' Circulation Theorem, Gauss' Divergence Theorem. Elementary knowledge of ordinary differential equations, numerical integration, stability, consistence, convergence.

Behavior:

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 (Quadrature), 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 integrate over curves, surfaces and volumes, and (s)he is able to apply Gauss' Divergence and Stokes' Circulation Theorems.

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.

Lecture ✔
Response lecture ✔

Period 2 Credits 5,00

Evaluation method
Written evaluaton during teaching periode 50 %

Oral evaluation during teaching period 0 %

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

Compulsory coursebooks (printed by bookshop)
foutschatting eindige elementenmethode,This document describes an introduction to the error analysis of finite element methods. Numerical Methods in Scientific Computing,cursusboek

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: F.J. Vermolen. Introduction into error analysis of finite element methods

Master of Teaching in Sciences and Technology - Engineering and Technology choice for subject didactics math Optional 135 5,0 135 5,0 Yes Yes Numerical
Learning outcomes

EC 5.4. The master of education is a domain expert SCIENCES: the EM has advanced knowledge and understanding of the domain disciplines relevant to the specific subject doctrine(s).

EC = learning outcomes DC = partial outcomes BC = evaluation criteria

General Knowledge: Elementary numerical techniques like numerical quadrature, Lagrangian Interpolation, Root finding. Elementary linear algebra like matrix addition - multiplication, eigenvectors, eigenvalues. Vector algebra like Stokes' Circulation Theorem, Gauss' Divergence Theorem. Elementary knowledge of ordinary differential equations, numerical integration, stability, consistence, convergence.

Behavior:

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 (Quadrature), 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 integrate over curves, surfaces and volumes, and (s)he is able to apply Gauss' Divergence and Stokes' Circulation Theorems.

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.

Lecture ✔
Response lecture ✔

Period 2 Credits 5,00

Evaluation method
Written evaluaton during teaching periode 50 %

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")

Compulsory coursebooks (printed by bookshop)
foutschatting eindige elementenmethode,This document describes an introduction to the error analysis of finite element methods. Numerical Methods in Scientific Computing,cursusboek

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: F.J. Vermolen. Introduction into error analysis of finite element methods

Exchange Programme Mathematics Optional 135 5,0 135 5,0 Yes Yes Numerical
General Knowledge: Elementary numerical techniques like numerical quadrature, Lagrangian Interpolation, Root finding. Elementary linear algebra like matrix addition - multiplication, eigenvectors, eigenvalues. Vector algebra like Stokes' Circulation Theorem, Gauss' Divergence Theorem. Elementary knowledge of ordinary differential equations, numerical integration, stability, consistence, convergence.

Behavior:

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 (Quadrature), 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 integrate over curves, surfaces and volumes, and (s)he is able to apply Gauss' Divergence and Stokes' Circulation Theorems.

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.

Lecture ✔
Response lecture ✔

Period 2 Credits 5,00

Evaluation method
Written evaluaton during teaching periode 50 %

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")

Compulsory coursebooks (printed by bookshop)
foutschatting eindige elementenmethode,This document describes an introduction to the error analysis of finite element methods. Numerical Methods in Scientific Computing,cursusboek

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: F.J. Vermolen. Introduction into error analysis of finite element methods

^{1} Education, Examination and Legal Position Regulations art.12.2, section 2.
^{2} Education, Examination and Legal Position Regulations art.16.9, section 2.
^{3} Education, Examination and Legal Position Regulations art.15.1, section 3.

Legend
SBU : course load SP : ECTS N : Dutch E : English