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Title
Here come the title and subtitle as in the assignment
Supervisor
Here comes the name of the supervisor / reviewer as in the assignment
Author(s)
For each student in the group, give the name, identity number and e-mail address
Hand-in date
This is the date of submitting the zip-file with the report to the reviewer
Number of Attachments / Appendices
This includes any optional software scripts. Ensure proper documentation of your software; assume that your supervisor will only read the comments in your scripts. Unclear or incomplete comments are not being reviewed; this may affect your mark.
Table of Contents
Each item in the table of contents receives a separate heading (these are the numbered items in this template); each item is included in the table of contents.
The report plus attachments are always submitted electronically as a zipped PDF-file. Make sure that your supervisor can run any optional software without additional effort; that is: if necessary, add any additionally required files such as libraries or script files to your zip file, and make sure that everything is tested before submitting to the supervisor. Your supervisor will not debug your code. If your supervisor cannot run your software due to technical shortcomings for which you are responsible, your assignment will be marked as insufficient.
Summary
A summary of no more than A4 contains the essential message of the report. Although it cannot contain any details, the text of this summary should be readable without prior knowledge, for instance by one of your fellow-students from another group (same year, but other assignment).
Description of the Modeling Process
This is the main part of the report. It contains the construction, execution and evaluation of the actual model. The modeling process, as described in week 1 of the lectures defines the structure of the report.
You write three versions of the report. These will be called v1, v2, and v3. In version v1 you write about parts 6 9; in version v2 about 6 15; in version v3 about 6 30. In a next version you will, in general, revise parts that you wrote in the previous version(s). Notice: it may happen that not all parts 6 22 below will occur. If you are very sure that, for a particular item in your report, nothing meaningful can be contributed, you merely give the heading of the item, and leave the body empty. Dont change the numbering scheme of the items.
Definition phase: context ( problem definition and purpose
Context
This is a concise description of the context in your own words. This context optionally includes theory that you use. Used theory is briefly summarized in your own words. The summarized theory may contain text fragments from external sources, provided you give an adequate reference. Make sure your supervisor can check all external sources. The link below contains a detailed description of the appropriate way to include bibliographical references..
HYPERLINK "http://drcwww.uvt.nl/its/voorlichting/handleidingen/bibliotheek/apa.pdf" http://drcwww.uvt.nl/its/voorlichting/handleidingen/bibliotheek/apa.pdf
Problem Definition and Purpose
The problem statements in the assignments are deliberately formulated vaguely. You will need to obtain a more precise formulation of the problem. The item Problem Definition contains the re-formulation of the problem in your own words. Which of the purposes, discussed in week 1 of the lectures, applies to your problem?
Sub-questions
Very often, the central question can only be answered after answering one or more sub-questions. In this item, you formulate the sub-questions. A (sub-)question is only a valid (sub-)question when you can assess if it is correctly answered. For instance: we want to find out if we can understand X is not a valid question, as you cannot simply assess if you have understood X. A good (sub-) question could be: we want to find if X can be explained by Y. This question will have an answer of the form yes or no (or yes, provided that or no, unless ). In answering any (sub-) question, obviously you have to indicate how you arrive at the answer.
Conceptualization: initial problem ( conceptual model
Concepts, properties, values and relations
A conceptual model describes the entities, represented by concepts, occurring in the model. It also describes their properties, and their relations. Some entities are standard objects you are familiar with. In that case, you can immediately identify quantities for their properties. For any quantity, you give the name, the unit and the type, that is: the collection of values the quantity can take. For instance, for a (linear) spring, the force is proportional to the elongation, and the associated property is the spring constant (with unit N/m, and type, for instance, R+ if you dont know its exact value during the conceptualization phase), and its rest length (in m; the type is for instance {95 105} mm in case the spring is given). More often, however, things are less simple, and some introduction is necessary to explain how the concept is described in terms of properties (for instance: the mercury in the thermometer in terms of density, volume and thermal expansion coefficient; a patient in hospital in terms of age, gender, symptoms and medication, and a streetlamp in terms of height, location near the road, energy consumption and light production, ) In any case, your conceptual model contains all quantities (names, units, types), arranged in a well-organized list.
The choice to incorporate certain concepts, and to omit others, will often relate to assumptions or approximations. In the street illumination example, elaborated in PowerPoint presentation Studio Lecture 12, the choice to leave out trees in the conceptual model is an example of an assumption (we assume that the light of the street lanterns is not obstructed by foliage of trees). The choice to omit the moon is an example of an approximation (we ignore the light of the moon in comparison to the light of the street lanterns). In section 9 of your report, you will also mention some of the crucial assumptions and approximations of your conceptual model.
Your conceptual model also addresses the relations between concepts. The conceptual model follows the structure of week 2 of the lectures. Apart from a textual version, you will also give a diagram, where the same information has been put together in an orderly fashion. You use the notation discussed in the lectures (entity-relationship diagram) or, if you are familiar with UML, you can give a UML diagram.
Formalization phase: conceptual model( formal model
Quantities and their Relationships
Which quantities occur in your model (presumably, these are properties of your concepts)? You will base yourself on the conceptual model, the sub-questions, and the theory you use. For each quantity, apart from its type and its unit, give its role: is the quantity for you to decide, is it asked, is it a constant, or is it an intermediate quantity? (the 4 categories, discussed in week 5). Which relations among quantities do you assume? Name these relations (equation, inequality, function, constraint, definition, interpolation, educated guess,, ) For each relation, where meaningful, give the assumptions that need to hold for it to apply, and indicate if the assumptions indeed do hold..
Approximations and Assumptions
Most often, you dont know exactly how things relate, you only have ideas about approximate relationships. In this item, you list the most important estimates in your model. The choice to leave out a particular entity from the modeled system is also an example of an estimation. For instance: we decide to leave out the effect of moonlight in the street illumination model.
Derivations
Give the necessary mathematical derivations. Make sure your notation is clean and clear. Dont ever write a free term (x+3 sin y doesnt mean anything), but proceed from one meaningful expression to the next. An expression is essentially a mathematical sentence: just like in natural language, a mathematical text is composed of sentences. For instance: 3x+6y=9 and y=4x, so we have the equation 27x=9 with x=1/3 as a solution), and clarify non-trivial steps, including their intention (now we will differentiate left and right with respect to t since we want to know for which time p becomes stationary). Pay attention to when you use units and when you dont. You may be able to use the methods of week 4, including the chain of dependencies and the to-do-list.
Special Cases
Investigate the relations you find (= new formulas), and look for special cases. For instance: what is the interpretation of some quantities being 0, what happens if quantities go to infinity or if they are equal to each other? Choose your interesting cases with care. This includes ranges of applicability: for which interval of values is a particular expression meaningful, and when does it lose its meaning? Sometimes an assignment will contain hints to search for interesting special cases.
Estimates
Estimates are a particular case of assumptions. An estimate is an assumption about the value of a quantity. To evaluate expressions, quantities need values. Some values are given, for instance outcomes of measurements, to be found in a table or on the Internet. In other cases you may need to search for (numerical) values: what would be a reasonable estimation for the coefficient of expansion of plastic? How do you find the needed (numerical) values? As much as possible, try to find estimates using common sense. Starting from things that you know by heart or from daily practice, or that you can derive, without help, from your immediate environment that is: only look up values in books or in the Internet if you find no way to deduce them by yourself. Sometimes you may be able to use the wisdom of the crowds. For each estimate you use, either give an argument or at least three independent sources, plus an indication of the accuracy (see week 6).
Execution phase: formal model ( result
Rephrase the problem statement in formal terms
The purpose of the model was formulated in items 7 en 8. At that time, there were no mathematical expressions yet. Now that you have a formal model, you can rephrase the problem in mathematical terms, for instance: quantity h should be as small as possible, whereas p does not exceed q.
Calculations / Implementation / Simulation
This item contains the required calculations to achieve your model purposes. This may involve implementing one or more formulas in a computer program, or filling in expressions in a spreadsheet. It also may mean that you will be playing with a simulation where, of course, playing is directed at finding an answer to je modeling purpose. Document all non-trivial choices (for instance: since we cannot solve f(x)=0 in closed form, we use the bisection method according to ( HYPERLINK "http://en.wikipedia.org/wiki/Bisection_method" http://en.wikipedia.org/wiki/Bisection_method), see module SOLVE_IT, lines 23-28).
Validation and Verification; Accuracy and Precision
The outcomes of your calculations wont be exactly correct. Discuss the accuracy of your results, and assess if this accuracy is sufficient to solve the initial problem. What are the various sources for errors in your outcome? Think of effects that you ignore in the model, inaccuracies in the numbers you use, lack of precision in your calculation, populations that are too small for statistical relevance, etc.. To assess the accuracy in your model outcome, you may want to look at approximations (we ignore the thermal losses in the electric wires. But since their resistance is at most 1% of the lamps resistance, the difference in consumed power caused by this error is at most ). You can also slightly perturb the values of estimated values and assess the resulting change in the output (this is a sensitivity analysis: with 10% change in p, there is no more than 5% change in q. We can therefore ascertain that, despite the uncertainty in p, method I is always more efficient than method II). Use the things you learned in chapter 6!
Conclusion phase: result ( solution of the initial problem
Presentation and Interpretation
Sometimes the execution of your model will yield a number. More often, there will be a graph, or even a complete simulation. Give a well-substantiated choice for the way you present the outcome of your model. For instance, does the model purpose require error intervals? Is your purpose best served with a graph, a scatter plot (see HYPERLINK "http://en.wikipedia.org/wiki/Scatter_plot" http://en.wikipedia.org/wiki/Scatter_plot ), a histogram, or perhaps even an animated graph?
Translate the mathematical (numerical) results of the model back towards the non-mathematical terminology of the initial problem, and interpret the solution in that context. It is possible that you havent been able to solve the entire problem, perhaps because the results lacked accuracy or precision. In most cases, though, you will be able to draw (some) conclusions even if you cant say more than that your method was not quite sufficient, because It is important to judge how far you can go with your conclusions: your result is stronger if you can make more potent statements, but you can only take responsibility for conclusions that are rigorously substantiated.
Reflections and Discussions
Discussion after the Conceptual Model
Give a justification, or a critical, a posteriori, review of the choices in your conceptual model. For instance: we chose to leave out the influence of wind (=a concept). In hindsight, this was the right choice, since the occurring forces due to X, even with 7 Beaufort, are at least 5 times larger than wind force. It is also possible that in hindsight you must admit to have made a less wise choice: in hindsight, the influence of the waiting time in the laboratory for the blood tests turned out to be so large that assumption X did not hold.
Discussion after the Formal Model
Give a justification, or a critical, a posteriori review of the choices in your formal model. For instance: our assumption to ignore the changes of p in comparison to q were valid, since variations in p turn out to be no more than 0.001 mm whereas, in the same time, q moves more than 5 cm. It is also possible that you must confess to have done a less fortunate move in developing your formal model: in the derivation of X we divided by z, whereas in the extreme case that t gets bigger than 12, z has been seen become zero.
Discussion after the Result
The result is the bare outcome of the model calculations. If you made no mathematical mistakes, the answer will be fine from a numerical point of view. Still, it could be useless, for instance because values you find violate the assumptions you made underway, because inaccuracies are too big, or because statistical significance is insufficient. In this discussion you assess if your results is indeed valid.
Discussion after the Solution of the Initial Problem
Here, for the last time, you look back to the initial problem (formulated at item 7). Did you actually solve this problem? Or perhaps only partially, or not at all? Give arguments for your ordeal!
This completes the actual modeling assignment, the report with items 6 22 is intended for a hypothetical problem owner.
Reflection on the Assignment
Extension
Even the best model is not 100%. Suppose that you could allow yourself another week to work on the assignment, what would you do to make your results (even) better, and why?
Necessity for Improvement
In chapter 7 of the lecture notes, we give 8 criteria that can be used to compare models. With respect to which of these criteria do you think that your model should be improved, given the purpose, and why?
Possibilities for improvement
In chapter 7 of the lecture notes, we give 8 criteria that can be used to compare models. For which of these criteria do you have concrete ideas of how your model should be improved? Give a concise descirption of these ideas.
What aspects of your work are you proud of?
There is no room for false modesty in this section. Describe what you think was the strongest part of your assignment.
What have you learned?
Give a brief summary of your work in terms of the (generic) lectures. That is to say: the assignment you worked on was an application of the generic topics from the lectures. Find out (=write down) which topics you applied, and explain to what extend applying these topics helped (or didnt help ) your understanding.
Appendices
Used Literature
Add a list of used literature, compliant with the APA standard.
List of Definitions
The quantities you used typically have abbreviated names; halfway through the report the reader may have forgotten that Prm signifies the price of raw materials. Therefore, it is convenient to list all quantities in alphabetical order, together with their meaning. This list also contains the definitions of any less-frequent terms in your report (irradiance: the light intensity, incident on a surface, per surface unit, in Watt/m2), similar to the glossary of the lecture notes.
List of Illustrations
For each of the images in your report, you describe what it depicts and (in case it comes from the literature) its source reference.
Here, we mean: relations following from the correspondence between the model and the modeled system, or relations taken from the theory as used in the derivation of your model. We dont mean the mathematical derivations you do yourself, in order to fulfil the purpose; these occur in item 12.
An example of a guess is: I assume that the relation between the price of this product and the number of sold copies is given by the logistic function ( HYPERLINK "http://en.wikipedia.org/wiki/Logistic_function" http://en.wikipedia.org/wiki/Logistic_function) with quantities because ... . For these guesses, you may want to use the Relation Wizard or the Function Selector.
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