Coevaluations

Solid Works and 3D printing

Well it was very obvious that this project was a challenge for us. Starting from the way of arranging the formulas, to integrating and adapting for 3D printing. We realized that it is not very clever to use scales specially when you’re using formulas with constant change (such as sine), it is better to work with real scales rather than proportions. We lived the complications of translating math to practical means but also realized how important it is the design for the materials and how practical it is to work with functions to understand dimensions or maybe even optimization with a different use. Overall, we tried to work together and help each other in what we could do best or maybe help the others understand the work better with its applications. Personally I think that this project made very obvious the way calculus contributes to industry, I can only imagine making a piece for a machine or product without the use of math, it would be a disaster! Math helps us define and control what we do, and I think this is of uttermost importance when applying it to industry or creation or planning or design or engineering or in other words, daily life. I think this is the answer to the question… ¿So when are we applying this in real life?

Volume calculations

The formula we used in order to calculate the aproximate volume of the piece printed was the one we saw on module 4 "volume by disks for rotation about the x-axis". Since it was an addition of three functions we treated them separately and integrated each one in the corresponding formula. 

So when calculating the first volume we encountered our first complication which was a natural logarithm squared but with a diferent argument as the ones seen in class. There were several ways to solve this problem, the first one was by "u" substitution and integration by parts, but also you could solve it by using integration by parts, then improper and proper fraction, these were topics seen in modules 5 and 6 in which we discussed integration techniques. The rest of the integrals were quite easy and almost made by an automatic process, by using trigonometry integration techiniques and "u" substitution. These complications were the same presented on the other process so you could take these in count for that process too. 

Geogebra and functions (design)

The geogebra first design 

 

Our idea was to try to keep it simple, we made a scale model of what we wanted to make (a jar). We decided to include some curves to make it resamble as most as posible to a jar. So you could say that we first made the image and then made the math fit in. Due to the extension and shape of the sine we decided that would be our middle function or the "body" of the jar. Then we realized that the logarithm could connect with a softer curve in order to create the base. Finally we added the polynomial to make the top, almost cup like to finish the vase. This looked very beautiful in scale but had many problems when we tried to adapt it to solidworks, speacially because the shape of the sine changes depending on the period. So even though we planned we had to change it all over again. 

The geogebra second design 

Taking as base the first design we modificated the original functions instead of thinking "scale-like". The first and very obvious change was the sine's period, and from that by trial and error fitted again the other functions. That meant that we had to re-do the whole integral process and calculus but it was easier to translate it to solid works and then to rotate it. 

New semester (Final)

Division

Module 3

Use of technological resources

Thanks to the use of online homework as well as the explanation offered by my math lab I've been able to clear a lot of my doubts, specially talking about the solving problems. Also it has helped me to see the things that I must review. In this case is more about the solving problems and rounding up decimals. But as you can see in the evidence of grades, I recovered after the 83 in the solving problems (mostly my mistakes were about decimals). Also it helped me practice for the mid-term quiz and partial. I actually like working with online homework because it's a very good practice to see what I do wrong and how I can make it right. 

 

Capacity to work with others

Part of our learning process is to understand the applications of all the theory we study. Therefore we gathered in teams and made some calculations (using all what we had been taught) in order to find some measures. I find this to be very useful and entertaining. It also taught me how to accept other points of view about how to solve. Sometimes I wanted to do very complicated things when they could've been solved rather in a much simpler way. 

Module 2

Capacity to work with others

The most important learnings we had this module were about the Basic and Reciprocal trigonometric ratios, and the special angles. Without the knowledge of those basic concepts, solving the next problems and understanding the other modules would be very difficult if not kind of impossible. 

I dedicated a lot of time to understand those concepts and to clear al my doubts about them so that when I had to work along my classmates I could properly contribute in teamwork to analyze problems and solve them. We helped each other and even though we solved the problems by ourselves we shared with the team how in order for everyone to understand. 

Autonomous learning

I know that we learn from mistakes and also that exams help us not only see our areas of opportunity but also how we overcame mistakes. I had a particular problem last semester with a problem of application of knowledge regarding angles and arc length, so by myself I dedicated to understand it and in the next exam I could solve it properly.