Integration in PYTHON (Symbolic AND Numeric)
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- čas přidán 15. 07. 2024
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In this video I show how to evaluate integrals symbolically and numerically in python. The main packages used here are sympy for symbolic evaluation and scipy for numeric evaluation.
Code:
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Discord:
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0:00 Intro
1:18 Symbolic Integration
6:30 Numerical Integration (Functions)
11:14 Numerical Integration (Data) - Věda a technologie
Most underrated science channel imo
You’re the real MVP!!!
Thank you for making those videos!!
Can’t wait to see some mechanics focused videos!!
Best of luck!
Awesome! I learned something new that integrating a dataset using the cumulative_trapezoid function removes the noise and actually produces a smooth curve! Very nice ❤️❤️❤️
Awesome content dude, hope your channel subscribers boom!!! Thank god i found this channel!
All the best!
Fantastic videos! Don't ever stop doing them!! Very underrated, but already most of my group know of you :) Hope more join!
You have literally saved my life, my guy! I needed to integrate the flux values for my target star, but I didn't know how... Thanks a lot!
I came back here to comment again. i rarely do this but this is sooo helpful to me as a math major. THANK YOU MAN!
Jeez, the algorithm is getting good. I needed this today for a real world data set. I think I arrived at an OK answer but in an incredibly roundabout way. Integration of real world time series data is so useful in my line of work. Thank you so much.
Honestly, I'm sooo grateful for those videos! Thanks a million!
I love watching your tutorials.
Now, two years later and python3.11 and whatever is the newest version of sympy, one can get a solution involving the gamma function for the first example of an "unsolvable" integral at 6:49. I'm getting a solution.
OMG, you are so underrated! These videos are amazing. You have just earned one new subscriber.
cool stuff, just watched the whole vid, I do more machine learning with python but integrals are always important. Thanks!
Brilliant stuff mate, helping me a lot! Keep up the good work!
Nice one dude, i'm probably not gonna understand any of this since i'm still learning. but it's sounds very awesome and interesting!!
Good stuff mate. I can remember integrating some beasts by hand, so this is awesome.
Thank you brother, I was working on problem regoriously last 5 days continuously . I was stuck . I just needed one command which i understand from you video. Thamnks a lot, man.
I just found this video. Thanks so much! You're an excellent teacher.😀
Thank you so much! I did Physics at University quite a few years ago now so things brings back some fond memories! :)
All I can say is: "WOW, just wow!" This Is Truly An Informative Teaching Session. Thank you for sharing your experience. 🙏
I'll really try and work with this. Thank you!!
Are you going for the streamer/gamer video stile? I like that :)
The camera looks good, allow me to suggest you to get a condenser microphone if you crave that clean and deep studio voice and it would probably remove a little bit of keyboard noise too.
The sound is almost always more important than the video, especially for headphones users and especially if you talk a lot in your videos, wich you do. I would remove that thick black outline in the camera overlay, i think it would look sharper and more modern, and i would also reframe it in a 16:9 ratio in but that's my personal taste. As for the location of the overlay on the screen, try to see which one works best for your type of videos. I've been watching your videos all week, you are a talent, i've never coded in my life but i'm installing jupyter right now, have a good day :)
This is the thing that I needed..... Thank you, sir !
Thank you so much,,you have no idea how much you are helping
Mr. P Solver, you are the best!
Saved my life, thnx awesome content
Thank you so much for this video. You are lifesaver
Very epic. Nice.
Your content is the best from youtube congrats 🎉 and thank you
Thanks for you video. My problem is solved right after I watched this video
Man this helped so much, thank you bro!!
Today i understood the real taste of integration and ,for removing integration fear thanks sir😊
Thank you very much for this video! Really helpful!
This is amazing!!! Thank you
Truly Amazing
will you do digital signal processing and some control system with python? Great videos!
Oh my goodness, thank you for this video!!!
Excellent video; thank you.
Very nice presentation and thank you so much. This is the best way to teach programming i think.
One should not just spell out the correct syntax. The learner needs to understand the errors as well.
Surely with chatGPT, now it is easier to identify the errors.
Still this was helpful.
@Mr. P Solver Great video, very helpful! I was wondering how you are able to automatically display your output as formal equations rather than code? Also, is there somewhere I can find the sample data you used in this tutorial?
Great vid dude
Great video. Cheers m8.
Muy bueno , muchas gracias!
Thanks brother you care aabout aur time !
as your name, you are solver. great explanations make me understand all of this video. danke
Yes, your lectures are tremendously useful in terms of promoting accurate thinking.
Speaking of Pyhsics and all the struggle pertaining to an obsolescent energy source such as oil,
please forgive us for throwing this in,
I tend to think that Einstein's thinking led us into a blind alley;
restricting us to Light Speed with one's reasoning limited to the paradigm of space-time,
in light of the fact that Laplace had set out, and succeeded to transform all functions of time.
Where does this lead us philosophically?
A Hyperspace or S-Domain reality too abstract to get us across the galaxy in no time at all? 🤔
This, of course, brings us to the issue of Gravity and the utilization of its underpinning principles for the purpose of obtaining free Energy.
Given Newton's intuition that Gravity can't possibly be a quality of matter, but a force introduced into matter-matter interaction as the result of an external phenomenon,
described by Dr. Nieper in the 1970s, as a latent, omnipresent scalar field.
Rather than the Einsteinian space curvature caused by putting lecture room planets on the fabric of a dormitory bedsheet space.
Nieper goes on, that if disturbed correctly, let's say by way of a 3D in itself rotating magnetic field,
energy greater than the power needed to create that magnetic field was produced.
Allegedly, the measured efficiency of such a system was at least 300%.
I'm still trying to get my head around that part of electromagnetic theory.
Maybe you can do better. 😦
thank you. very useful videos.
I hope to use a graphic interface with Python code to make it exciting.
fantastic!!!
Thank you
How can i call bessel function because i want to calculate the symbolic integrale of J0(a*x)/(x^5)
How about integrating over matrix elements? So every matrix element is an f(x). Could you cover that or give some references, that would really help! (Without just looping over entries)
Which function should I use to calculate the area under the curve of a set of data which is not equally spaced? X is not the same.
Very nice. What about the constants after integration?
It's a disater for me, every expression I add gets summed up with the previous ones. How do I only run a specific series of cells?
is there any videos to show how to load sparse matrix from MMf file and carry out linear algebra on it ?
How to add assumptions, such as possible ranges for constants, whether a constant can be zero, if constants are necessarily real?
Хорошее видео, интересный канал!
Hi, I don't know if you ever answer this question in other videos but have you ever done the integral in an adaptive grid?
Thank you so much
How do you print those functions after you have integrated them like you have?
How do you integrate when the coefficient is decimal number
Hello!I need little bit help from you.I have a maths course "Time Scale Calculus", and I want to do coding in python of this course.When I import timescalecalculus as tsc, module not found error came,please help how I can get this tsc module in my python.please help 😭
Legend
Its showing ModuleNotFoundError : module named 'scipy.integrate ' ; 'scipy' is not a package.
Can anyone help please .!
Can you please help me to integrate f(x)=exp(a*x**2), a is an arbitrary constant.
You should upload these .ipynb files These are awesome templates !!
Awesome
thank u
I tried to duplicate your Covid example. I have a .csv file with two columns for date and total cases. The dates are formatted like this: 2023-03-14 When I run your example, np.loadtxt keeps giving the error: "could not convert string '2023-0314' to object at row 0, column 1" What's the solution to this problem? Thanks very much!
Can you do more fitting videos, please? Fitting the data based on a formula.
I shouldn’t ask this because I’m not worth it, but could you upload something related with fenics and python?
***********
Many thanks for all your videos, I really appreciate them!
Thanks! For some reason the examples that you showed that don't work, run for me and I do get an answer.
What IDE is that you have used I'm not getting the same result in pycharm
That's jupyter lab
2:05
d/dx[sin(x)] = cos(x)
I get the integral without being actually done as the output, does that mean it can’t be solved. (Mathematica solved it)
GREAT GREAT
I have a quick question. Why is cumulative_trapezoid(y) ten times larger than numpy.cumsum(y)*(x[1] - x[0])?
Probably because cumulative trapezoid on its own doesn't take into account the spacing in x (which is probably 0.1 in this case). Did I make this error in this video?
Thank god they didn't keep the Matlab function name for cumulative trapezoidal integration...
Hmm. Any expression I can write down. . . 🤔
$\int\limits_{-\infty}^{\infty} \frac{\log{\left(x^{4} + 1
ight)}}{x^{2} + 1}\, dx = \;ln\left(6+4\sqrt{2}
ight)^{\pi} \; = \;7.71542$
Haven't got many teeth left. Most of them are already bitten out. 😒
What we need is someone as sharp as a knife who knows how to instruct Scipy to take a stab at it;
or owns a woodsman's Hatchet that helps him hack the function to bits. 🙄
"numerical numbers" 😁
Timestamps mentioned @42 seconds.... none to be seen.
Sorry about this, I knew I forgot something. I'll get them up in the next 30 minutes.
I dragged my mouse. & it Bit me...😢...😅❤
f = sp.exp(-x**4) - $\frac{\gamma\left(\frac{1}{4}, 1
ight)}{4} + \frac{\gamma\left(\frac{1}{4}, 16
ight)}{4}$
Therefore the Integral has a definite solution that can be further evaluated to return a numeric result for the given area under the curve:
intgral_sol.evalf() = 0.0615638789309999
you guys can try this code snippet that i made , just the difference is in my case you won't need quad method to solve integrals numerically.check it out .
def integrate_analytically():
import numpy as np
import scipy as sp
import sympy as smp
from scipy.integrate import quad
x=smp.symbols('x',real=True)
a,b=smp.symbols('a b',real=True,positive=True)
f=eval(input("ENTER FUNCTION WHOSE INTEGRAL IS NEEDED : "))
print("")
print("")
print(" IF YOU NEED INTEGRAL AS EXPRESSION PRESS - 1 ")
print("")
print("")
print(" IF YOU NEED ANSWER AS AREA UNDER THE CURVE PRESS - 2 ")
q1=eval(input(" ENTER 1 OR 2 :"))
if q1==1:
print("")
print("")
fdx=smp.integrate(f,x).simplify()
print("THE INTEGRAL OF f(x) is = ",fdx)
print("")
print("")
print("THE INTEGRAL OF ",f," is = ",fdx)
return fdx
if q1==2:
r=eval(input("ENTER LOWER LIMIT :"))
s=eval(input("ENTER UPPER LIMIT :"))
print("")
print("")
fdx=smp.integrate(f,(x,r,s)).evalf()
print("The Area under curve (",f,") between",r,"and",s,"is = ",fdx)
return fdx
Of course, SymPy can't give us an analytical solution when the variables [a, b = 2, 3] are not defined.
By pre-defining, `a` and `b`, our functions look much more manageable ==> $\color{blue}{\frac{1}{\left(2 - \cos{\left(x
ight)}
ight)^{2} + \left(3 - \sin{\left(x
ight)}
ight)^{2}}}$
Hence:
sp.integrate(f, (x, 0, 2*sp.pi)).simplify() = π/6, rather than, 0.5235987755982989