Thoughts for the Future

Having taken the Linear test, I feel great. I thought it was straight forward, although I messed up on a few parts but mistakes are kind of natural to me by now. It's been a while since I have even gotten a perfect score on my tests. Of course seeing the test makes me happy since it wasn't anything horrible like my other classes where the test average for the class is failing. There will be places to improve and one of those places is reading the questions thoroughly. I read one of the questions as what is the general formula for the governing equations instead of what is the general formula for a mathematical model. Maybe I'll take my time next time instead of rushing it seeing that I had at least 15min left to take the test. The individual project however, seems like it could end up being very complicated. Although it depends on each person's system and model and how they approach it. Mine being a normal truss and comparing it to bridges seems like it could be difficult but rather very easy. Since I can create my own loading for the bridge such as a car's weight. Then if I find how much a average car weighs per unit length and multiply that by the bridge's length then I can find a uniform distribution across the bridge. That would be for when the bridge has traffic and average max loading would occur across the bridge. Then for even more weight I could think of a truck or something that weighs even more than a average car and test that. I think testing the loading at certain points might help also. I'm taking away that the bridge could suffer from climate and just looking at the forces, also taking away fatigue on the bridge. Although fatigue is very important when picking the material and it's dimensions I think if I'm only focusing on the forces and how much force is needed to keep the bridge from deforming the best option is to simplify my system.

Pre-Midterm Feelings

As I head into my first Linear Systems midterm I feel prepared and that my grasp of the concepts are concrete. Although, the creating differential equations or defining systems homework had me stressed for a long while the other homework was particularly straight forward. I believe that I can obtain a good grade if I am able to complete the review homework for this week without any trouble. I have learned how to define a system, the steps that one needs to take in solving problems (physicists, mathematician, engineer), matrices, and coding in MatLab. I have learned more such as laws being not laws but don't need to state all of them. What ended up surprising me was the amount of work load I have this semester, not just from Linear Systems class but from my other classes. However the other bigger surprise was how well I have been keeping up with the work load. The challenging part is to come, since we are only half way into the semester. Finals will be something I will and won't look forward to since most finals are cumulative, but will end up being the last thing I have to do until I can go on a summer vacation. My favorite topic by far is the matrix math, although I have seen some people struggle to learn it, after a while you seem to understand what steps are needed in order to reduce a matrix, or multiply them.

Conservation Laws and Defining a System

My previous post being about conservation of population, I wanted to actually get into detail in how I would design my system and conservation law. First I would define my system to be an open system since mass (people) would be allowed to travel in and out of the system. The boundary would be of a small city or town. I could to a whole country but a city would work since it would have much higher mass flow rates considering traveling through cities are more common than countries. This conservation of population would be based off the conservation of mass flow since it's basically how people travel through cities. This can be observed by tolls, having a toll whenever someone would cross to another city and then tallying them up to see how much people travel in and then out. An example could be Philadelphia. Many people come from New Jersey, Washington DC, New York, and Baltimore go to Philadelphia. Even on holidays people visit their families and it could be in any of those locations outside Philadelphia. I've met some people that come from other areas that have to take the train of drive in order to get to Temple University. They end up going back home and I think that is a perfect example of conservation principles. However, if I couldn't use toll booths as a way to measure the amount of people coming in and out of the city then I would create a matrix to solve for those variables. I would set up how much people travel through trains, cars, and maybe even planes. How many times does a train maybe even a train from New York to Philadelphia arrive each day. Then by setting up the car, train and plane equations then I could find how much people can fit in a train or car or plane then set it up in a matrix of 3x3 and solve. the answer would come out in a 3x1 showing how much people would actually travel per year or month and add them up to find the amount coming in. Do the same for the amount of people coming out and hopefully finding out they are very similar.

Conservation Laws

             Almost anything can be governed by a linear systems of equations. One example could be monitoring the population of a city/state/country, like how much people come to visit or how much are being born. It would be difficult to put a conservation law on the general population but if we can try to use a conservation law on a smaller portion such as the amount of people that travel then we could simplify our calculations. This can be similar to another system in the way that we have to start with a conservation law, and design or model the system to fit what we need. After defining our system we can use a conservation law that applies and try to get a differential equation or a linear equation to obtain our solutions. Systems have the same ideal process in obtaining information but the equations could be different. Such as a volumetric problem may differ from our population problem. The volumetric problem could deal with air, or water being inserted or distributed which would create a mass flow rate equation. Although the mathematics behind it might be the same, where we could eliminate the differential part if there is no change. Either way we start by playing physicists, then mathematician, and then engineer to figure out the solution(s). The steps are similar but the details of the solution may differ.