Propagation of Error

Propagation of Error

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 and Uncertainty

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 vs Systematic Error

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. 

Basic Error Propagation

This is the standard equation for error propagation:

Propagation of Error

This represents the uncertainty in the measurement of some value x. Suppose you are measuring this value based on this equation:

Propagation of Error

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:

Propagation of Error
Propagation of Error
Propagation of Error
Propagation of Error

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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4 years ago

GETTING A JOB CHEAT SHEET!!

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4 years ago

math help bc i can’t watch ya’ll suffer anymore

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. 

4 years ago
8 / 1 / 2018 //

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:(


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1 year ago

girl im bored lets browse academic articles


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4 years ago

From Beginner to Intermediate: an intense plan for advancing in language

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.***

1 year ago
My Morning Coffee / Jupiter
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3 years ago

Colleagues AUs

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


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1 year ago

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.

1 year ago

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?

4 years ago

School, Studying, and Learning Masterpost!!!

School, Studying, And Learning Masterpost!!!

[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!

a divider containing a graphic of the top view of a pen and pencil on top of a notebook, with a phone to its right and a beverage to its upper right corner.

Tips for school in general

General school tips, dealing with online class, strategies for school in general, etc

Attention and Concentration

How to pay better attention in online classes | another

Strategies to improve concentration

How to stick to your plans

Schoolwork and Tasks

Review Tips and Presentation Advice

Dealing with executive dysfunction masterpost

How to use google search like a unicorn

How to annotate a text

General Tips

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

Grad school advice

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Studying

Study Strategies and other study advice things

Studying general

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

Study Breaks

On productive breaks

Types of study breaks

How to deal with mental fatigue

Note taking

Hybrid note taking nethod

Note taking guide

Upgrade your notes resources masterpost

Using google docs to take notes

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Resources

Resources that could be useful for school and academics

Self study

Self study resources (masterpost)

Learn things for free (masterpost)

Textbooks | more textbooks

Sites to download literature masterpost

Free online courses

Technology and Apps

Asmr ambiences (masterpost)

Productivity apps and extensions (masterpost)

Wallpapers screensavers and apps

Productivity apps masterpost

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American Sign Language

Mandarin learning resources

Classical language learning

Arts

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IB Psychology Study Tips

How to study for mathematics

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Black History Library

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Other Studyblr and Academic Stuff

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Journaling/Bujo

Journal prompts

How to fill your empty notebooks (masterpost)

Studyblr

Dividers graphics for posts

How to start a studyblr | another post

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Master the art of napping

Job interview tips + masterpost

Use firefox instead of chrome

Actual frugal recipes (lots of helpful websites and links)


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