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Me when I look at the sheer amount of content in my degree + the fact that I've been asked to transfer into second year engineering so I need to teach myself all of first year

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maybe we were the virus all along

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My mom just sent me this video without any context??

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From Aristotle’s Nicomachean Ethics

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some scenery drawings of pride and prejudice

twitter / ig / prints

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Hmmm

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I take further maths and I don't think this thought ever once crossed my mind. Humbled.

But it's really easy to see why: 2% of 50 = 0.02×50 = 0.01x50x2 = 0.5x2

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MATLAB speaks the truth

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A short note on how to interpret Fourier Series animations

When one searches for Fourier series animations online, these amazing gifs are what they stumble upon.

They are absolutely remarkable to look at. But what are the circles actually doing here?

Vector Addition

Your objective is to represent a square wave by combining many sine waves. As you know, the trajectory traced by a particle moving along a circle is a sinusoid:

This kind of looks like a square wave but we can do better by adding another harmonic.

We note that the position of the particle in the two harmonics can be represented as a vector that constantly changes with time like so:

And being vector quantities, instead of representing them separately, we can add them by the rules of vector addition and represent them a single entity i.e:

                                                  Source

The trajectory traced by the resultant of these vectors gives us our waveform. 

And as promised by the Fourier series, adding in more and more harmonics reduces the error in the waveform obtained.

        Have a good one!

**More amazing Fourier series gifs can be found here.

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Tag urself I'm e^x

The signs as different-order derivatives of e^x

Leo: e^x

Libra: e^x

Cancer: e^x

Virgo: e^x

Aries: e^x

Sagittarius: e^x

Aquarius: e^x

Gemini: e^x

Scorpio: e^x

Taurus: e^x

Capricorn: e^x

Pisces: e^x

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+c can go drown; it's such a pain for solving differential equations

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Grandi would say that only half a person is killed if the train went back and forth in time, to kill 1-1+1-1+1-1+1... people

Edit I know this isn't how sums of series actually works

wat u do??

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problem solving tips that actually worked for me

Hey there!

If you have a math, or science related subject (like I always do), you’ll find that you really can’t escape analysis and problem solving, especially if you’re majoring in something science or maths related. So I am here to share some tips that actually made studying technical subjects a little bit easier and manageable for me in college:

Practice solving. If you have a subject that requires you to solve, you really have to practice solving, there is no easy way out of this one. This allows you to develop your own technique in solving the problem. You can start by doing the problems you did in class, then venture out to some examples in textbooks, then further into the problems in the textbooks until you get the hang of how the concepts and theories are applied. 

Listen during class. I know, it’s boring. But you have to do this. This way, you’ll be able to understand the topic once it is presented to you. In my opinion, it’s better if you let an expert explain it because they know the important bits in the lesson. Then study it afterwards on your own to develop your own techniques.

Ask your professors. Don’t be afraid to ask questions in class. Or if you’re shy, you can ask them after the class. However, it’s important that you ask them about the lesson when you already did your part; meaning: you already studied the material/solution over and over again but there’s just something that you can’t seem to grasp. 

Study before the class. Studying the lesson in advance doesn’t hurt. Plus, it works because you already have an idea about it. However, I don’t do it usually. What I do is that prior the discussion, I study the lessons that are going to be essential to the next topic. Example: Say that our topic later will be about introduction to thermodynamics (which includes derivation of various thermodynamic formulas); what I’m going to study instead is the different integration and derivation techniques, and different basic thermodynamics concepts like laws of thermodynamics. This ensures me that I know the prerequisite lessons of the next topic in class.

Absorb the conceptual parts of the topic first. Before diving into the problems itself, try to digest the concepts or theories behind it first. This way, you can understand which information is important and easily think of a solution because you know the problem’s framework. Even when your professor gives you a problem that seems different from your other sample problems, the concepts will still be the same throughout.

Reverse engineer the solution. Reverse engineering is reading and understanding your solution from bottom to top. I do this to make connections while going through the solution. I usually ask myself “‘where did this come from?’, ‘why did this happen?’, or ‘why is the answer like this?’” It allows me to look into the parts that I missed which are usually concepts or theories that I forgot to apply in solving the problem.

Look for key terms or phrases. There are some problems that put in information that may seem unimportant, but actually is really important. Examples such as the phrases constant velocity, constant acceleration, starting from rest, accelerate uniformly, reversible isothermal, adiabatic conditions, isobaric/isochoric compression/expansion, etc., are easy to miss but actually gives you vital information especially when solving a problem.

Try to ask yourself how or why it happened in every step of the solution. You can do this to gauge your mastery of the lesson. If you can answer yourself confidently, then you’ve studied well enough. But, if you can’t or if you feel that it’s not enough, then you better get your pen, paper, and calculator to practice some more.

If you have to draw it, draw it. Some problems need the use of your imagination, and these problems are the ones that get tricky most of the time. It’s easier to draw each of the time frames that are important so you get the sense of what’s going on between these pictures. This way, you’ll know which information you’re missing and which ones are you failing to take into account.

It’s okay to be messy and slow while practicing. Not all of time you can solve in a tumblr-esque manner because, dude, tumblr notes or solutions are soooo pretty to look at, BUT, what’s more important is that you understand each step of the solution and how the answer came to be 8.0658 m/s directed 32° south of west. So it’s okay to have dashes, strikethroughs, and crosses on your scratch paper, as long as you’re learning, a messy solution on a paper you’re not going to submit to your professor is fine.

IF YOU’VE REALLY GOTTEN THE HANG OF SOLVING IT, try to solve a fresh set of problems as fast and accurately as you can. Try to solve as if you’re in an exam. This is also to gauge how well you’re prepared for it, but you need to do this accurately. I repeat, accurately. It doesn’t work if you’ve finished it in less than an hour but all of your answers are wrong.

Rest. If you know that you’ve done a good job, then take your mind off of everything first and let it wander to wherever it wants to wander. You deserve it ✨

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So this is so beautiful. It's not quite a maxim (although could be reduced to 'earn your dreams') but damn it's basically my life philosophy. I hate people who emptily say 'you don't know until you try' - how about 'try because you won't accept any other alternative'?

“The simple fact is that people who achieve excellence in their fields didn’t just have a dream. They got up at 4:00 am to practice on parallel bars or had to forgo other desirable activities and paths in order to get in six hours of violin practice a day, or stayed off several million absurd writing advice blogs with their overheated little cliques that dispense useless regurgitated maxims and empty praise and decide to actually confront their own thoughts on a page. Or they read Beowulf and Dante carefully and deeply when they didn’t see any point, since all they were interested in was Sylvia Plath, because someone of more experience and wisdom told them to do so. I don’t know whether we’re overly lazy, stupid, or childish these days. But the idea of preparing oneself for excellence has somehow disappeared. So – my advice to dreamers: Don’t just follow your dreams. Earn them. Do what it takes to achieve it. Work for it. Don’t just sit there and dream because if you do, it will never, ever be yours.”

— Harrison Solow, Don’t Follow Your Dream (via crimsun)

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When you swirl wine, you create a rotating wave that travels in the direction that you’re moving the glass. You would expect that anything floating atop that fluid would travel in the same direction of rotation. But it turns out, for a large, thin raft floating atop the rotating fluid, that’s not the case. 

Above you can see a swirling container, rotating counter-clockwise, with a raft of foam. This is from a timelapse where only one photo is taken per rotation, so that it’s easier to see how the foam is rotating relative to the container. And, once enough foam covers the surface, it starts rotating in a clockwise direction – opposite the container! It works for more than foam, too. The researchers show that the same holds for powders or beads. The key to the counter-rotation is that the raft needs to be coherent; it has to be able to transmit friction and internal stress among its constituents. Otherwise, the raft will just drift along with the swirling wave. (Image and research credit: F. Moisy et al., source, arXiv; via Improbable Research; submitted by David H. and Kam-Yung Soh)

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When u finally figure out the solution to a physics question

“I’m living at a peak of clarity and beauty I never knew existed. Every part of me is attuned to the work. I soak it up into my pores during the day, and at night—in the moments before I pass off into sleep—ideas explode into my head like fireworks. There is no greater joy than the burst of solution to a problem. Incredible that anything could happen to take away this bubbling energy, the zest that fills everything I do. It’s as if all the knowledge I’ve soaked in during the past months has coalesced and lifted me to a peak of light and understanding. This is beauty, love, and truth all rolled into one. This is joy.”

— Daniel Keyes, Flowers for Algernon (via quotespile)