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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
Advice
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.

=============================================== De studenten worden geadviseerd om de volgende cursus af te ronden voordat ze 'Partial Differential Equations' volgen: 'Vector Calculus and Differential Equations' (4708).

Het volgen van 'Functionele en Fourieranalyse' (3985) is niet noodzakelijk vereist, maar Fourierreeksen worden bekend verondersteld. 'Analyse 2' (3190) en 'Dynamische Systemen' (3195) zijn nuttig maar niet noodzakelijk vereist.

Degree programme Study hours Credits P2 SBU P2 SP 2^{nd} Chance Exam^{1} Tolerance^{2} Final grade^{3}
3rd year Bachelor of Mathematics Compulsory 135 5,0 135 5,0 Yes Yes Numerical
Learning outcomes

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

DC 2.2: A graduate of the Bachelor of Mathematics programme possesses advanced knowledge and understanding of applied 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: De bachelor wiskunde begrijpt eenvoudige natuurkundige beginselen en modellen

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

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

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)

Lecture ✔
Response lecture ✔

Period 2 Credits 5,00

Evaluation method
Written evaluaton during teaching periode 30 %
Transfer of partial marks within the academic year ✔

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

Compulsory course material
Study material & Study guide (available on Blackboard)

Recommended reading
Partial Differential Equations: an Introduction,W.A. Strauss,2,John Wiley and Sons,139780470054567 Analyse van Differentiaalvergelijkingen,C.J. van Duijn, M.J. de Neef,9789040712654

Exchange Programme Mathematics Optional 135 5,0 135 5,0 Yes Yes Numerical
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)

Lecture ✔
Response lecture ✔

Period 2 Credits 5,00

Evaluation method
Written evaluaton during teaching periode 30 %
Transfer of partial marks within the academic year ✔

Additional information The weighting 30% assignments 70% written exam is only valid if the grade for the written exam greater or equal is to 8. If the grade for the written exam less is than 8 then this grade will count for 100%. This rule applies for the second session (resit) too and 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.

Second examination period

Evaluation second examination opportunity different from first examination opprt

Compulsory course material
Study material & Study guide (available on Blackboard)

Recommended reading
Partial Differential Equations: an Introduction,W.A. Strauss,2,John Wiley and Sons,139780470054567 Analyse van Differentiaalvergelijkingen,C.J. van Duijn, M.J. de Neef,9789040712654

3th year Bachelor of Physics option twin Broadening 135 5,0 135 5,0 Yes Yes Numerical
3th year Bachelor of Physics option free choice addition Broadening 135 5,0 135 5,0 Yes Yes Numerical
Learning outcomes

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

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)

Lecture ✔
Response lecture ✔

Period 2 Credits 5,00

Evaluation method
Written evaluaton during teaching periode 30 %
Transfer of partial marks within the academic year ✔

Additional information The weighting 30% assignments 70% written exam is only valid if the grade for the written exam greater or equal is to 8. If the grade for the written exam less is than 8 then this grade will count for 100%. This rule applies for the second session (resit) too and 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.

Second examination period

Evaluation second examination opportunity different from first examination opprt

Compulsory course material
Study material & Study guide (available on Blackboard)

Recommended reading
Partial Differential Equations: an Introduction,W.A. Strauss,2,John Wiley and Sons,139780470054567 Analyse van Differentiaalvergelijkingen,C.J. van Duijn, M.J. de Neef,9789040712654

^{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