Self-assessment for: Some examples of functional modeling

The following are some recommended self-assessment questions for the lesson called Some examples of functional modeling:

Question 1:

Could you repeat (could you have solved for yourself) the Examples studied in this topic? I would encourage you to do this. Write them out from scratch, e.g. saying to yourself for Example 2: What is the situation and functional model for the distance between two points? And then sketching it and writing it out in full using good notation and the best practices we have seen.

Question 2:

We were only trying to derive the functional models and look at their general forms in these examples. But there are several reasons the problems described by our examples cannot be solved. What are they? (For example, even if we measured the azimuth 100 times in Example 3, we’d never be able to solve for the unknown parameters in that situation.)

Question 3:

Why am I so insistent on using the full notation that includes terms such as \mathbf{l}_{true}? What’s the importance of the true part of \mathbf{l} and \mathbf{x}?

Question 4:

In Example 2 of this lesson, we found the functional model for a distance. What if we learned that there was a single scale factor error present in our measurements, due to a calibration error in the instrument we’re using. Can you update the functional model we obtained to reflect this change? (In other words, what if the set of unknown parameters also included a scale factor s?)

We didn’t do this in class but we discussed it, e.g. we saw the general math model and we discussed how systematic errors can also be estimated. I’m asking it to see whether you can apply the functional modeling approaches yourself to a slightly different problem.

Question 5:

a) For each of the examples we saw in the lessons on functional modeling, determine whether the models are linear or nonlinear in their nature.

b) How can one know whether a model is linear? What rule(s) apply?

Question 6:

We referred to models of the type in Example 5 as condition models (based on condition equations). Can you clearly describe what is a condition model?

The following schedules are for Alex’s in-class students:

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