Calculus - Blog Posts
equations are so freaky man... like wdym I can do whatever I want to you as long as I do it to both sides... freaky ahh numbers....
I had.... the weirdest nightmare(????) I've ever had??????
Ok so like
I was in a sophomore/junior high school class
And we were learning math (I FUCKING LOVE NUMBERS)
And the teacher was all like Today!! We're learning a new topic!!!! Cross Multiplication!!!! And everyone was so confused all like
What's multiplication?????? And so I, being the massive fucking buzzkill nerd I am, ask the teacher Oh! When do we learn Calculus? (In my school ppl usually start pre-calc junior/senior year) And everyone in the class stared at me like I was some kind of extraplanar freak
And then the teacher kinda softly whispered In college.... And then I started crying
And I woke up right after I started crying
Math 😔
Sir Isaac Newton Hareket Yasaları
1666 yılında daha 23 yaşındayken Galileo ve Kepler’in çalışmalarında da faydalanarak “Hareket Yasaları” ve “Kütle Çekim Yasalarını” geliştirdi. Kalkülüs ve Cebir’in kurucuları arasındadır. 1687 yılında klasik fiziğin temeli olan hareket yasalarını 3 ciltlik “Principia” isimli kitabında anlatmıştır.
Newton, Galileo, Descartes hareketle ilgili fikirlerde bulunmuştur. 1600’lü yıllardan önce cisim hep durma eğilimi gösterir mantığı varken bu üç adam her şeyi değiştirdi. Cisimlerin aslında durmaya karşı bir direnç gösterdiğini savundu. Ve klasik fizik Newton’un ellerinde doğdu.
1.Yasa Eylemsizlik:
Eylemsizlikten ilk olarak Galileo bahsetmiştir. Newton kitabında eylemsizlik için “her cisim eğer üzerine etkiyen bir kuvvet tarafından durumu bozulmaya zorlanmazsa düzgün doğrusal hareketini ya da durma halini korumaya direnir” açıklamasını yapmıştır.
Sabit bir kuvvet uygulanan cismin kütlesi arttıkça, eyleme karşı direnci artar. Burada Newton 2.yasayla bir bağlantı kurmuştur. Zaten bu yüzden Descartes ve Galileo’dan hareket yasalarında çok daha önemli bir yerde görülür.
2.Yasa:
F=mxa formülünden de anlayacağımız gibi; cisim kütlesiyle ters , uygulanan kuvvetle doğru orantılı olarak ivmelenir. İvme gibi kavramları açıklamak için şuan da diferansiyel işlemler kullanırız. Aslında Newton’da bunların doğruluğunu kanıtlamak için Kalkülüs ve Cebir’i geliştirerek kullanmıştır.
3.Yasa Etki-Tepki:
Eğer bir cisme bir kuvvet uygulanırsa aynı şekilde cisimde bir tepki kuvveti doğurur. Kuvvetlerin çift olduğunu kabul ederiz bu yasayla birlikte.
Newton Hareket Yasalarını doğru kabul edebilmemiz için referansımız 1.Yasa olarak almamız lazım bu referans sistemine “eylemsiz referans” deriz. Newton’a göre mutlak uzay ve mutlak zaman göreli değildir. Bunun sebebi Newton’da bir sınırımız vardır. Einstein İzafiyet Teorisinde zaman ve uzayın tek bütün kabul edildiği ve göreceli olduğunu ortaya koymuştur. Sınırları bildiğimiz sürece Newton mantıklıdır.
Y’ever read something and have understanding that has eluded you interminably suddenly stop, curl up, and snuggle neatly into a fold in your brain because a new way way opened to it?
It's 10:52 and I just woke up from a nap. Why am I napping at night, you may ask? It's cuz I'm a HEATHEN.
But no I been thinking. What the fuck is up with people going the Egyptians couldn't build the pyramids, they didn't know calculus. That's a thing right? Tell me if I'm wrong.
But I'm be operating under the presumptions that it is. HOW THE FUCK DO YOU KNOW IT'S NOT A THING. MOTHERFUCKING AUGUSTUS CAESER BURNT DOWN THE GREAT LIBRARY OF ALEXANDRIA. Also, like, if Isaac Newton discovered calculus in the 1600s, some 600 years after the dark ages, how come the Egpytians couldn't do it? They got together in 3100 BCE and production started in like 2500 BCE. Good timing to figure out what calculus is.
These are my thoughts in this fine evening. I must study now and hope to find sleep in a few hours. Good night.
I have an intuition the chain rule was used here but I don’t have sufficient knowledge of differential equations to understand fully how it works
okay so for anyone that got an A in physical chemistry … HOW? i was originally pre health but i want to go into research now, so my physics is only algebra based bleh but so far have gotten A in my calculus classes (will be taking calculus 3 spring)
techinally they are my last major class excluding physics 2 and an elective, i have seen the math of physical chemistry it looks interesting but very daunting . SOS send help please with any advice !!!
12 March (Calc 3 Pain)
I normally try not to post in color, but today I feel that it’s warranted. I just finished my last lecture with my calc 3 professor and I couldn’t help but be a bit sad.
We all have that teacher whom we don’t expect to make a difference in our lives, but upon getting to know them you come to find that they are a giant breath of fresh air.
With the toxicity of school leeching itself into every orifice, nook, and cranny it was nice having that one class I could count on to be invigorating.
This one is for you Mr. Lewis. I can’t begin to repay you for your teaching service, but the least I can do is show my genuine appreciation for you.
8 March (Calc 3: Test Day)
You know, taking notes by asking questions really has improved my memory retention. I find myself getting the problems correct because I actually understand the process of what is happening not just the system that gets me to where I need to be.
If you haven’t feed yourself or hydrated please do that, every bit helps
Stay up ✌🏿
🎧 Trappin in paradise 80 by Smooth s o u n d s
***Taking a test***
**Chapter I'm struggling with**
*5 points each;10 questions*
Me: I did OK... Maybe I can make up points in the other chapters.
**Chapter I'm good at**
Me: :)
*1 point each;3 questions*
Me: :(
Repost @dark_____sky___ ---------------------------------------------------- ❤️ Like! 🍎 Follow @_space___lover_ 📜 Share with math lovers! 🔊 Turn on post notifications! ---------------------------------------------------- #isaacnewton #newton #principiamathematica #physics #math #science #engineering #scientist #theoretical #applied #theoreticalphysics #quantumphysics #meme #memes #physicsmemes #mathmemes #sciencememes #dankmemes #mathjokes #physicsjokes #physicsfun #sciencehumor #facts #astro #cosmology #reddit #scifi #pi #numbers #calculus https://www.instagram.com/p/CSWw5L7DeZh/?utm_medium=tumblr
Metal People
Why aren't the metal people melting in this heat
Why am I still out here? It's because I can smell sand and salt
And the heat reminds me of summer
Although
I am questioning what in the world am I doing The birds chirping
The traffic
The anxiety It feels like a good day
For the beach and nothing else To get your feet burned in the sand
And the sharp feel of shark water But I'm here on an uncomfortable park bench
Made to look like a place to sit
Made to be uncomfortable So much for the brick and concrete, cars and calc I could have drove home and be arriving there now
But why would I want to be there Have I become one of the metal people
Just here watching the other people I guess not quite yet
Because I can feel the human slowly dripping from the pits
This Cannot Be Natural
I want to stay
Cradled in between
Sweetly smooth melodies
Where I let my fingers go wandering freely
Humming the notes
That I did not take during calculus class
The reason was that I was busy dreaming of an impossible life
That’s what happens to me
When I feel stuck in between the bars without a single key
My signature move of not paying attention,
To the epsilon-delta definition of a limit
And honestly, I might have just found my mathematical limit of brain power
The tone of my voice has gotten beaten down
I cannot learn at this fast tempo
For the next bunch of weeks, I'm stuck with the strings attached
I try to simply count it out but it doesn’t add up
I don’t know how to measure
The slope of my own tangents
I put my signature on a piece of paper that says
This summer class requires a ton of deadication or it could easily result in failure
And now I feel
The sharp pain
That makes me fall flat
On my back
I can feel the anxious vibrato
Building up in my hands
Maybe I need a rest
This cannot be natural
calculus?
more like calculost. please don’t ask me what the derivative of a log base is because i might (i will) combust into ashes of weeb culture & self deprication
The topologist’s sine curve.
Limts: f(x)=sin(1/x) is a rare example of a function with a non-existent one-sided limit. More technically, f(x)=sin(1/x) is defined for all numbers greater than zero, yet the limit as x approaches zero from the right of f(x)=sin(1/x) does not exist. This can be reasoned by considering the value of f at x-values near zero. Informally, f(near zero) could be 1 f(just a bit closer to zero) could be -1 so f(numbers near zero) does not seem to settle on a single y-value.
Continuity: Note that f is continuous for all numbers greater than zero but not continuous at x=0 since f is undefined there. Even if we were to “fill in the bad point” and let f(0)=0, the function would still not be continuous at zero! (note this is the natural choice as sin(0)=0). We can see that the adjusted f is still not continuous at zero since the sequence x_n=1/(pi/2+npi) converges but f(1/x_n) is the sequence (-1)^n which does not converge. This is similar to the argument above. In other words, closing in on x=0, we can keep finding x values such that f(x)=-1 and f(x)=1.
Topology: In topology, the topologist’s sine curve is a classic example of a space that is connected but not path connected. This space is formed in R^2 by taking the graph of f(x)=sin(1/x) together with its limit points (the line segment on the y-axis [-1,1], the red line on the second image). The graph of f is connected to this line segment as f and the segment cannot be sepearted by an open disc (no matter how small). This can be informally reasoned by the zooming illustration in the second image. But the space is not path connected by the sequence argument above (there is no path to the point (0,0)).
Image credits: http://mathworld.wolfram.com/TopologistsSineCurve.html and https://simomaths.wordpress.com/2013/03/10/topology-locally-connected-and-locally-path-connected-spaces/
My Calculus teacher, picking up and shaking a desk: "YOU WANT TO SEE IF THE DESK IS INCREASING OR DECREASING? TAKE THE DERIVATIVE OF IT."
also if integrating is the same thing as antidifferentiating, can i call differentiating "disintegration"?
can i disintegrate a desk to see if it's increasing or decreasing.
[8.08 am] Just finished revising all the vector calculus that I have done so far. I will do 10 more pages of vector calculus today. Just praying to God that this day goes well.
***
[12.29] I studied vector calculus for an hour and so done with it for today. I will later check out Paul's online notes to see if I can use them for my next two chapters. But for now, I'll watch a movie.
***
[10.18] I completed three chapters of analysis 1.Omgggg.I was listening to some om chantings in the afternoon because I was getting stressed. It did help and made my day go so much better. I still haven't figured out how I will remember the proofs. I understand them and only vaguely reconstruct them. I just have to remember that I don't need to stress about it. I'll eventually get to know about it. If you guys know how to do it then please let me know <3
***
217 days left to go...
Will I make it ?
The Mayriit Project.Stay tuned on a Tumblr blog near you.
Calculus
Time Travel Mathematics
Math Tips
(Pictures are not mine)
Well, let me tell you, we all have this love-hate relationship with this subject, right? The worst part is that when you don't know what the heck is going on, so, as a girl who studied maths (2 Volumes/textbooks) on her own during the year she was homeschooled, here are some tips and tricks that I did to get an A+ in my math finals!
Get your syllabus together
In the beginning I had no damn idea what was going on and it was just confusing. I had to do the first thing I did was taken my index/table of contents and mark the chapters which i knew very well and the ones I had no clue about. And then i arranged them with the marking scheme, like which one carries the most marks etc etc and study accordingly.
Complete lessons/chapters that you already know
When you finish off the things you already know then that's gonna give you the confidence you need even if you know only 1-2 chapters, learn it throughout and make sure that you'll get the answer no matter how twisted the sum is. If you're doubtful about the whole textbook like any normal person.... Start with the easy ones. (I know there are literally really no "easy" chapters, spare me)
Harder chapters need hard work
Most chapters like Trigonometry proofs, Geometry proofs, Algebra, Graphs, Mensuration and Calculus etc need more than minimum effort but here's a trick, what is the common thing in this? Yes, they're all formulae and theorem based which goes to my next point. These chapters are completely based on how much you've understood your basics.
Formulae and theorem cheatsheets
Make a list of all formulae and the theorem used in the book, write them chapter wise and no printouts or digital notes. Take a paper and write it down, no excuses. It helps you while you're practicing, revising and in the last minute review, it helped me damn much. Remember, maths is a sport. The basic formulae must come to you like reflexes.
YouTube is your best friend.
For every single chapter, go and watch the basics and how a sum is done step by step. A recommendation for this is Organic Chemistry Tutor who literally is one of the reasons i passed. He has videos from basic geometry, trigonometry, statistics to calculus. Search for your own YouTubers and be clear with concepts.
Math is fully memorization
Memorize formulae and theorems with the back of your hand, you should be able to recall them within seconds. Be thorough.
Memorize basic math values (if calculator isn't allowed)
Do this if you have a majority of chapters like Statistics, Mensuration, Profit/loss calculation etc, where large numbers are concerned. Memorize the first 10 square, cube, decimal and multiplication values. It may be dry but there are literally songs available for these things, I'm serious, i learnt the first 10 cube roots by listening to Senorita xD Search for rhymes and they'll definitely be many!!
Work it out!!!!!!
Can't stress this enough, atleast 30-40 mins is the minimum for maths. I'm serious, work out each sum, don't ever think it's a waste, you'll see the results. Practice makes perfect. Work out every single sum, from examples to exercise ones cause let's be honest, our examiners love to take problems from every nook and cranny of the book.
Whiteboard method
So, I made this up and it actually works, if you have a whiteboard or anything else, once you completed a chapter, take a random page and whatever sums you have on those two pages, you need to complete within a given time limit. It helps you to identify your weak points and where the hell you're losing both time and effort and not to mention that it gives you confidence boost up.
Hope this helps :))