FIN.

The topic that made an impact to me in class is vector. It was such a simple concept when I was introduced to it on my Physics classes but this course made me appreciate it more that vector is not just simply a Physics-Mathematics lesson and applied in Physics-related concepts such as force, weight, etc. Vectors are basically everywhere and the journal entries of my classmates somewhat prove that with various interesting real life applications of vectors. I liked Gaussian Elimination and Gauss-Jordan too although the experience solving it on the second exam was … UGH.

If I can summarize this course in one word, it would be eigen. Because the course (and the professor too (: ) is a class of its own.

Thank you sa mga naging groupmates ko sa quizzes! Thank you Sir for making each of your class session light and enjoyable. Good luck sa future endeavors.

Does Laplace Have Le Place in Economics?

You may have only heard (and applied) Laplace Transform perhaps in your Mathematics subject or maybe in your Computer Networks subject, but did you know that it could be possible to apply this theory on certain stochastic and deterministic economic problems?

“In a deterministic economic process the value of each function under consideration is known in advance at every future point of time.” These functions can be the cost per unit time period, the number of demanded units per unit time period, etc. For example, the maximized discounted value of a future cash flow existing during a given time interval, finite or infinite, would take a very simple form in Laplace terms[1]. The Laplace expression would be more involved if we are only to study the discounted value from a finite time interval [0, T] . The derived equations using the Laplace transform such as this one:

[1]

would be of great use to variety of problems such as feedback controlled-production problems, inventory problems, etc.

“In a stochastic economic process, the functions studied possess some property of giving uncertain outcomes.” This uncertainty stems from stochastic variables which have values that are unknown in advance. We also take note here the probability of these stochastic variables taking values within a certain interval which is the probability density function. If this probability function is time invariant, the process is stationary. After series of derivation and under the assumption that “using the expected value as suitable measure of the process result”, stochastic economic processes can be treated like deterministic processes.”[1] An example of a problem would be computing the expected present value of a season’s variational revenue flow using this derived equation:

[1]

For the a detailed derivation and usage of Laplace transform in equation form, the source material is provided.

Source:

Web Design|nǫiƨɘᗡ dɘW

When we talk about symmetry, another word that comes to mind is balance. And when we talk about balance, it is about various elements properly arranged together and contribute to a bigger,harmonious picture wherein no individual element is dominant over the others.

Design, when it comes to art, is a very broad area. And we cannot really say that when a form of art appeals to an individual, everyone will also like it. “Beauty is in the eye of the beholder” is what they usually say. Still, symmetry is widely regarded as something beautiful because maybe it appeals to our instincts that everything should be in the right order and it annoys most of us when something is off, out of place or simply just asymmetric.

One useful application of symmetry that I could think of and is also at least related to a career path is web development which also involves web design. Using symmetry for user interface provides stability between the elements and components of design. Overall, it enhances the user experience as it makes it easy for the viewers to understand what’s going on and to follow along. The visitors will be able to focus more on what your website brings with added comfort. There should at least be one instance where we visited a website and closed it immediately because of how non uniform it was in presenting its contents. And that is an example of a website that does not bring comfort.

There are many examples of symmetric design in web development. Here are some examples:

• Reflection Symmetry (Horizontal and Vertical) – It is when there is a mirror reflection of an element, either when you draw an imaginary line from top to bottom or right to left. A more “relax” type of horizontal symmetry is approximate horizontal symmetry which is when “items do not have to half perfectly”.
• Color Symmetry – Apart from shapes, colors can also be symmetric. This means that somewhere in the color wheel, every color has its opposite wherein if paired together, they create a balance and harmony considering symmetric design. (Just like how we have someone that is destined for us except only when you vow not to be in a relationship.)

In conclusion, however, symmetric design does not always fit a certain concept or theme for web design. They say that it is hard to emphasize a single element when everything is symmetric. In fact, most of the websites we use such as social media sites are not symmetric, they are asymmetric. Principles and guidelines in symmetric web design are just there to help designers create a layout that is balance between aesthetically-pleasing and easy to the eyes. In the end, if you’re designing something that you own, what matters is whatever floats your boat.

Source:

“What Is Symmetry In Web Design And How It Can Be Achieved?” : https://tympanus.net/codrops/2012/09/04/perfectly-paired-using-symmetry-in-web-design/

“Perfectly Paired: Using Symmetry in Web Design”: http://www.devtechnosys.com/2015/03/what-is-symmetry-in-web-design-and-how-it-can-be-achieved/

Rocket Science

To fly a rocket, there are many factors to consider and one of them is force. As we or some of us know, force is a vector quantity as it has both a magnitude and a direction and there are four types of forces to which rocket flight is subjected to such as weight, thrust as well as lift and drag which are aerodynamic forces. Weight is a gravitational forces while thrust and aerodynamics forces are mechanical force. The main difference between these two types of forces acting on the rocket is the latter requires physical contact with the medium that generates the force.

The magnitude of the gravitational force or the weight depends on the mass of the parts of the rocket, the amount of fuel and payloads such as satellites or space crafts. Have you seen a full scale rocket launch already, may it be on videos or in real life? Sometimes we see a rocket gets broken down into smaller rockets or staged where a smaller rocket rides a bigger rocket. I’ve researched that its actually engineers way to increase the rocket’s performance as the weight of the rocket changes when it exhausts fuel therefore having a constantly changing mass.

The thrust is the force responsible for moving the rocket through air and space. An application of Newton’s Law of Motion, particular the third law which is “For every action, there is an equal and opposite reaction”, which manifests through a propulsion system. This propulsion system accelerates a “working fluid” which is either a liquid or gas and expels this in one direction. The reaction to this expulsion is that it produces a thrust force which is then applied to the opposite direction to which the working fluid is expelled. The simplest rocket engine uses air as working fluid. There are many more factors to consider in thrust force but we’re not going to delve into that.

Lastly, the aerodynamics force which is broken down into two components: lift and drag, acts and is generated as rocket flies through the air. Drag is considered as aerodynamic friction and as we know friction opposes the direction of motion, therefore a source of drag is when solid surface of moving rockets comes in contact with the molecules of the air. Lift, on the other hand, is another application of Newton’s third law wherein the flow of gas is steered or turned by a solid object such as the nose cone or fins of a rocket in one direction, and the lift is generated in the opposite direction which is inclined to the flight direction. Aerodynamics force, however, is pretty negligible when it comes to full scale rockets but are very important in model rockets.

As they say, the only thing that is constant is change and this applies to rockets too. Magnitude of the four forces constantly changes as it flies through the air and sometimes the direction too. Adding up these forces, we gain a net external force and the resulting motion which is also a vector quantity in terms of displacement, velocity and acceleration, is explained by Newton’s laws of motion

https://spaceflightsystems.grc.nasa.gov/education/rocket/rktfor.html

I'm Levi.

Week 1: Introduce Yourself

Hi there. My name is Levi Joshua De Guia.

I didn’t really think much about the course and what to expect from it when I enlisted it during the first batch run. One thing’s for sure in my mind that time. It’s 13x, therefore it’s hard.

I was pretty comfortable with Mathematics during my high school days, permitting me to study the night just by browsing notes before the examination and still get a decent grade. Then, college happened. Institute of Mathematics’ exam difficulty happened. I absolutely hate solving sample problems as a way to review (except when there is an answer key) so when professors and instructors kept reminding us to practice to do well, I knew I’m done for. It also began in college where I “legit” didn’t understand what was happening on some lessons even though I was paying attention. So reflecting on the question now, I’m slightly not comfortable with Math anymore. But maybe I haven’t found my inspiration yet to truly appreciate and devote a part of myself to Mathematics.

I’m stressed already just by hearing the requirements I have to do this semester and it’s not even a week yet.

• Paul Rossener 3:55 pm on February 22, 2017 Permalink | Reply

I agree, college math is way different to high school math. But I hope you’ll find inspiration in math in our course, Levi. If not through the lessons, maybe through your seat mate. Jk

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