When I first started in physics, I was utterly clueless about propagating error. After three years of college, I have a better grasp of it and feel more comfortable using it in the lab. Have a look if you’re having trouble with error propagation!
Error: an unknown quantity in the realm of the state of nature
Uncertainty: a parameter in the realm of our state of knowledge about nature
Type A uncertainty: statistical in nature (an example of this would be if you were launching an object 15 times and recorded each distance)
Type B uncertainty: not statistical in nature (an example of this would be a digital reading on a scale - no matter how many times you put the same object on the scale, you will get the same reading)
Random Error
environmental fluctuations
equipment noise
natural processes
Systematic Error
environment: fixed beyond a relevant parameter
measurement technique: assumptions, experimenter bias
equipment with an offset or using equipment beyond its limits
uninformed choices
You can reduce random error by taking more measurements.
You can reduce systematic error through thoroughness, properly calibrating equipment, reading manuals, and ensuring reproducibility.
This is the standard equation for error propagation:
This represents the uncertainty in the measurement of some value x. Suppose you are measuring this value based on this equation:
You took three measurements, a, b, and c, and plugged them into this equation to get x. However, there is some uncertainty associated with each of these three values. Let’s say you measured a on a scale, b on an oscilloscope, and c with a ruler. There is uncertainty associated with all of those measurements. When you’re reading the scale, you read it as 15.45g. Let’s assume there is an uncertainty of 0.01g in that reading. Similarly, you read your oscilloscope to be 3V, and there is an uncertainty of 0.05V. You read your ruler to be 3.45cm, and there is an uncertainty of 0.05cm. We now have our uncertainties for the three values:
a = 15.45g +/- 0.01g
b = 3V +/- 0.05V
c = 3.45cm +/- 0.05cm
The other aspect of the uncertainty equation is taking the partial derivative. Those are the dx/da and dx/db parts of the equation. We will take the partial with respect of each term.
The partial derivative of the equation for x with respect to a is 2a2
The partial derivative of the equation for x with respect to b is 2
The partial derivative of the equation for x with respect to c is 4.5
Now, we can plug into our equation:
Your uncertainty in your measurement for x is +/- 22.86.
I hoped this helped you if you’re struggling with uncertainty!
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I’m in my fourth year of engineering school and I didn’t get here without lots of outside help bc assigned math textbooks are lame and confusing and professors/teachers are more worried about feeling superior to bunch of groggy teenagers than actually teaching.
I have personally used all of these websites without receiving any security warnings from Bitdefender TrafficLight or AdGuard AdBlocker. They are all either completely free or have a free version that isn’t shit.
Wolfram Demonstrations (animated graphics)
Khan Academy (arithmetic through differential equations)
She Loves Math (arithmetic through differential equations)
math24 (calculus & differential equations)
Paul’s Online Math Notes (algebra through differential equations)
MIT OpenCourseWare (calculus through graduate-level mathmatics)
OpenStax Math (precalculus, trigonometry, & calculus)
Wolfram Alpha Examples
Desmos (online calculators)
GeoGebra (online calculators)
SparkNotes Math Study Guides (pre-algebra through calculus)
eMathHelp (calculators, but more specific)
Software for your TI calculator
ticalc (programs for your TI calculator)
Wikibooks Math Department (all the math)
Andy’s Cheat Sheets (calculus)
Cheatography (find free cheat sheets)
Open Access Math Textbooks
Engineer4Free (Calc, DiffyQ, & Linear Algebra tutorials)
Flammable Maths on YouTube (general high school/college level problems and derivations)
3Blue1Brown on Youtube (very, very good for understanding spacial concepts in calculus and beyond)
Vihart on Youtube (explaining math with doodles)
Bonus: Stay hydrated, take vitamin c, study next to a window during the day if possible, and remember not to let people base your worth on your aptitude for math.
8 / 1 / 2018 //
Tomorrow I start my finals month and let’s just say physics midterm isn’t really the thing I want to start off with. but this is my life/desk situation right now, flooded with tons of formulas that just won’t go in my head easily:(
Introduction
I studied Spanish at school for 3 years and now I'm at a low B1 level. I can actually understand pretty well while listening or reading but I can't communicate fluently.
This plan will include vocabulary build up, some grammar revision, a lot of listening, reading and writing. And could be used for the most languages, not only Spanish.
Plan
Every day:
Conjugate one verb in present, past and future tenses
Make a list about 10 - 30 words long
Create flashcards with them and start learning them (I use Quizlet for flashcards)
Revise yesterday's set of flashcards
2-3 times a week:
Read an article or a few pages from a book
Write a few sentences about anything in your target language
Listen to one episode of podcast (at least one)
Once a week or every two weeks:
Watch a movie in your target language, preferably animated movie as the language used there is easier. You can watch with subtitles
Grammar exercises
Translate some short text
Once a month:
Write something longer, like an essay or report, on chosen topic
Additionally:
Talk to yourself, to your friends, to your pets
Text with someone
Look at the transcription while listening to the podcast for second time
Repeat what you hear (in podcast or movie)
Check words you don't know from the listening and reading
Read out loud
Listen to music in your target language - you can even learn the text and sing along
Watch YouTube in your target language
Change your phone language to the one you're learning
Think in you target language!!!
***This is very intense plan for self-learners, you don't have to do all of these things in the given time. Adjust it to your own pace. I'll try to stick to this, if I have enough time.***
my morning coffee / jupiter
We have to do a project together and it’s like the group projects in school: one is doing the work and the other one’s only sitting around and comments on everything.
We’re sharing a small office and we always fight about the temperature.
There is only one copy room on our floor and we both have to copy something, but someone’s obviously having a good time in there, so we both stand there awkwardly and wait for them to finish.
You took the last bit of coffee and didn’t make a new one. That’s unacceptable.
Since you started working here you never stopped asking me out for lunch and it always seemed like a joke to you, so today I say yes and wait for your reaction.
The company is searching for a new slogan and made a competition out of it for their employees and we both want to win the car that the winner is getting.
I hear you swearing at your computer because it doesn’t open your mail account, move over, I’m going to fix it.
One of the colleagues is retiring and we were supposed to order a cake and forgot about it, the party starts in half an hour, we have to do something!!!
You can find more prompts on my sideblog: creativepromptsforwriting
literally though if you feel like your life is slipping through your fingers and every day goes too fast… try doing hard things, not just taking the easy route, like reading and making art and exercising and cooking a meal from scratch and journaling, doing these things without distraction, without being absorbed on a screen… the time will stretch and you’ll be reminded that life is long and beautiful if you make it so.
OKAY CAN SOMEBODY EXPLAIN TO ME HOW THE FUCK YOU SHIP A PACKAGE OF COOKIES TO A FRIEND WHO LIVES IN NEW JERSEY, ONLY TO HAVE IT NOT GET THERE ON TIME BECAUSE IT SOMEHOW ENDED UP IN GUAM?
I JUST
GUAM?
[id: an animated black and white gif of a person tapping a pencil on a blank sheet of notebook paper. /end id]
Dividers used are by @firefly-graphics and their IDs are in the alt text!
General school tips, dealing with online class, strategies for school in general, etc
How to pay better attention in online classes | another
Strategies to improve concentration
How to stick to your plans
Review Tips and Presentation Advice
Dealing with executive dysfunction masterpost
How to use google search like a unicorn
How to annotate a text
For the lazy night owl (masterpost)
University tips and advice
Avoiding burnout (tips + resources)
Dealing with impostor syndrome
Good emotional skills to know for college but also for life in general
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Study Strategies and other study advice things
For neurodiverse students (masterpost)
Studying with ADHD (the actual post is a joke about but check the notes - they have actual advice there)
How to study for an exam in a really short time (masterpost)
Scheduling studying + other productivity tips (masterpost)
Studying effectively
Lazy Study Tips
Study tips from a Psychology Prof
Studying with a study buddy
On productive breaks
Types of study breaks
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Hybrid note taking nethod
Note taking guide
Upgrade your notes resources masterpost
Using google docs to take notes
Resources that could be useful for school and academics
Self study resources (masterpost)
Learn things for free (masterpost)
Textbooks | more textbooks
Sites to download literature masterpost
Free online courses
Asmr ambiences (masterpost)
Productivity apps and extensions (masterpost)
Wallpapers screensavers and apps
Productivity apps masterpost
Resources and Tips on specific subjects
Languages and linguistics of africa
75 free language learning resources
American Sign Language
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Black History Library
Not much school related but I included because they could be useful
Journal prompts
How to fill your empty notebooks (masterpost)
Dividers graphics for posts
How to start a studyblr | another post
Master the art of napping
Job interview tips + masterpost
Use firefox instead of chrome
Actual frugal recipes (lots of helpful websites and links)