Inner Product and Orthogonal Functions , Quick Example

In this video, I give the definition of the inner product of two functions and what it means for those functions to be orthogonal. I work a quick example showing that two functions are orthogonal.

[atishaytiwari]

God bless dude. People around the internet have created such a fuss about a thing which can be explained in exactly 3.28 minutes

[the_moooon]

finally an explanation that makes sense and doesnt rely on 1000 different references

[patrickjmt]

After a TON of requests, I am gonna do a little discussion about Fourier Series. This video is the beginning of some important ideas we will need so that we can discuss Fourier Series.

[patrickjmt]

for one thing, it will make calculations easier when i talk about finding coefficients of fourier series since a lot of stuff will end up canceling out.

[srishtikumar]

Everything in 3 minutes. Fabulously explained.

[pAwLinNe]

Please do a video for orthogonal trajectories... like how to find them or some sample problems? It would be a great help. You are so good in explaining stuff, pretty please

[ThePharphis]

To add to what Patrick said, the first thing that comes to mind to a chemist is that all Atomic Orbital wavefunctions must be orthogonal to one another. fourier series is the only other example I've seen, too. Can't wait for these videos!

[anikbarua]

1-hour video vs 3.28 min
The best explanation.

[kirtiverma]

That's the perfect explaination we want 🌸.

[MechanicalEI]

+patrickJMT, The example helped understand the definition a lot better. Thanks for uploading.

[MandyMaeGirl]

do you have a video on how to find orthogonal trajectories, not just proving them?

[Toby_Gomez]

Holy crap, so easy compared to how the book explained it

[HotPepperLala]

If so, please include a video on the convergence conditions of Fourier Series too!

[duhboss]

What's the significance of two functions being orthogonal?

[mortezakhoshbin]

i wonder they dont intersect eachother on this interval how the could be orthagonal. is orthagonality depend on intersecting or not.thanks

[kdu]

Hey patrick. You should do a video on orthogonal trajectory of a family of curve. :D

[frankolovrat]

If we have two functions, like f1=(x-1), and f2=(x^2+k). where k is a constant that we need to determine so that the function are orthonormal on the interval [-2, 2].Dose the inner product need to be 1 or something else?.sorry for bad english

[jameljamel]

this is the same decomposition in the polynomial chaos expansion ?

[chekmengkheang]

My name is Sam. I am currently a sophomore at Paris Junior College.
I am writing this letter to you hoping that you can help me with one my math
problem.I would like to ask summation of sin(2x) / 1 + (cosx)^4 as x
starting from 1 to infinity. Is it converge or diverge and state the test you
are using. I’ve been read and watched lots of video and gone to meet my
professor, however it seems like no one can help.
I hope you can take away my nightmare because it’s hard for
me to sleep without having a solution for my math problem.
I am looking forward to hear from you soon.
Sincerely,
Sam

[balazsgonczy]

PLS be so dear to explain, why is it good that the polynomials are orthogonial? I am doing polinomical regression in R and I do not know wheter to turn on the orthogonial function on or off.