Dude, after many hours of reading different book chapters about the matter, this is the very best explanation about finite difference approximation I could ever had. THANK YOU
Hi Alex, Thanks so much for making this video! I'm a few days away from an exam and this was perfect! This was an excellent explanation for a non-mathmatician. It really helped me to understand the Taylor expansion and how it is used for approximating atom positions using the velocity verlet integration algorithm and the leap frog algorithm. You're star!!!
I have an exam coming up on next week, acing it can boost my gpa which I'm desperate for at this moment, and this video saved me on this topic. the best I've watched so far, thank u so much for this.
Hello @Arjun Sekar, the forward, backward, and central difference method are all methods used to find the derivative. I am not completely familiar with the backward euler method, but for the part of this method that requires a slope (the derivative), I would insert the definition of the central difference method. I hope this is helpful.
+Seb Reni When I introduce the meaning of each variable at 1:35, I explain that x_i+1 and x_i-1 means the point of interest plus or minus one step size, respectively. If you were initially evaluating x at the value of 1.0 and you had a step size of 0.2, then the next term in the sequence (x_i+1) would be 1.2. I hope this clarifies things.
The point of interest, X, is the point at which you want to estimate the slope. If the statement says X is from 0 to 1, perhaps they want you to estimate the slope at various points instead of just a single point. For instance, the central difference method can be used to approximate the slope at X = 0 and X = 1. With a step size of 0.2, you would need f(-0.2) and f(0.2) to determine f'(0). Similarly, you would need f(0.8) and f(1.2) to determine f'(1). Hope this helps!
Basically you are expanding f(x) about the point xi in a Taylor Series. The truncation error for the forward and backward differences is the 2nd derivative and higher terms. You can take the forward difference and subtract the backward differences to get the central difference formula. If the step sizes are the same forward and backward, some errors will cancel out, making the central difference formula the most accurate of the 3 for a given mesh size.
I am only familiar with using the forward, backward, and central difference method to calculate the first derivative. However, one option to find the second derivative is to take the first derivative and then apply these methods. Following the example here, f'(x) = 2x + 2. From here, f''(x) could be found using a similar procedure.
Is there a video about how to do differencing with for example f(x,y)= -ye^sinx . I mean with two variables? PLEASE I HAVE A FİNAL WITHIN FEW HOURS HELPPPP😭😭
Actually there's a formula for finding the error which is (xi/2 * the second derivative of the xi) . You subtract it from the actual derivative formula to find a better result.In this case it gave me the exact solution which is 9,but this may change due to the type of the question that we're supposed to answer so this could be an exception.Thanks for helping us poor students good sir.
Dude, after many hours of reading different book chapters about the matter, this is the very best explanation about finite difference approximation I could ever had. THANK YOU
agree
Great explanation!
Forward Difference 2:25
Backward Difference 5:57
Central Difference 7:23
Graphic Representation 10:15
This 10 min video outshined two hours of crappy lecture in uni. Thank you!
I put off studying this until the night before my exam because it looked intimidating as hell! The example really helped!!!
10/10 video. i watching a day before exam and i have never seen a better explanation.
Hi Alex,
Thanks so much for making this video! I'm a few days away from an exam and this was perfect! This was an excellent explanation for a non-mathmatician.
It really helped me to understand the Taylor expansion and how it is used for approximating atom positions using the velocity verlet integration algorithm and the leap frog algorithm.
You're star!!!
I have an exam coming up on next week, acing it can boost my gpa which I'm desperate for at this moment, and this video saved me on this topic. the best I've watched so far, thank u so much for this.
Hello @Arjun Sekar, the forward, backward, and central difference method are all methods used to find the derivative. I am not completely familiar with the backward euler method, but for the part of this method that requires a slope (the derivative), I would insert the definition of the central difference method. I hope this is helpful.
Thanks for such a helpful video! Watching this right before my exam and it's clarified more than what my lectures did
after watching different videos, l really come across this, thank you so much
Great explanation. You made me understand on a big day which was my exam day. More success to us 😇
Hello from California. Great video, great explanation. Thank you.
Very clear explanation and detailed working steps!!..thank you!!
Thank you for this. I am grateful to you. Keep making more videos, you are doing a wonderful job!
Thank you so much for your effort, your tutorial actually helped in improving my understanding on the three difference methods.
A straight forward example is so helpful after hours of painfully dry lectures and readings lol
sir keep your videous about this god damn class which named numerical methods.thank you for saving me from lot of hardwork and for quick understanding
Thank you sir.
Your explanation helps alot.
this video just saved me hours !!!!!!
straightforward, explained it well. Good job sir!
Thanks god finally I got what I want.
Thank you buddy
Not me watching this 20 minutes before an exam
Thank you so much, you were so straightforward ❤❤❤ God bless you.
Just what i was looking for. Thanks for the help.
Thanks Alex. This is very helpful for me.
this is sooo much easier. thank you
Great explanation
thank you very much, the explanation is easy to understand
Very nice explation. Thank you sir.
straight to the point.. amazing.. thanks
Alexander Maltagliati, sir can you upload the video for the second derivative example
th-cam.com/video/CrBxnaqM5RY/w-d-xo.html
What is the reason not to always use the central difference method?
Very useful mathematics 👍👌🤗👍
when you did x_i+1 and x_i-1 did you choose '1' because it was step = 1? if the step had been 0.2 would that then make it x_i+0.2 and x_i-0.2?
+Seb Reni When I introduce the meaning of each variable at 1:35, I explain that x_i+1 and x_i-1 means the point of interest plus or minus one step size, respectively. If you were initially evaluating x at the value of 1.0 and you had a step size of 0.2, then the next term in the sequence (x_i+1) would be 1.2. I hope this clarifies things.
Thanks brother that's helped me a lot❤️❤️
How would it work if you were trying to find the second derivative for central difference.
there is a seperate equartion for that
skipped my lecture and went here to see what I missed. Thanx
Thanks a lot
How did you get the 15 and 24?
What if the question doesn't give the step size? How we going to find the step size?
Studying this because I flunked a subject. If I fail the exam even after watching this then I guess I really am worthless
Thanks !!
Very useful !!
+Kaiser You're welcome! I am glad to know these videos are having a positive impact
How would you use this to find the second derivative? Please help
thank you so much, a massive help.
If step size is unknown .so how to find step size.
Very helpful .. Thanx
what if the point of interest was 4 for the forward difference
How would you use this if the statement says X is from 0 to 1 and step size is 0.2
The point of interest, X, is the point at which you want to estimate the slope. If the statement says X is from 0 to 1, perhaps they want you to estimate the slope at various points instead of just a single point.
For instance, the central difference method can be used to approximate the slope at X = 0 and X = 1. With a step size of 0.2, you would need f(-0.2) and f(0.2) to determine f'(0). Similarly, you would need f(0.8) and f(1.2) to determine f'(1). Hope this helps!
Thank you sir
Aren't there 2 forms of the forward method?
Numerical Reservoir Simulation at Curtin
are these Euler's forward and backward methods?
What if it's a second order derivative?
it was so clear. thank u.
thank you so much sir
sir alex please i need this for second derivative
is this the same thing as the newton methods?
Thank you so much
Can someone explain why the central difference method is equal to the secant of the graph?
Basically you are expanding f(x) about the point xi in a Taylor Series. The truncation error for the forward and backward differences is the 2nd derivative and higher terms.
You can take the forward difference and subtract the backward differences to get the central difference formula. If the step sizes are the same forward and backward, some errors will cancel out, making the central difference formula the most accurate of the 3 for a given mesh size.
how to determine higher order of f...like
f''/f'''/f""....so on??
I am only familiar with using the forward, backward, and central difference method to calculate the first derivative. However, one option to find the second derivative is to take the first derivative and then apply these methods. Following the example here, f'(x) = 2x + 2. From here, f''(x) could be found using a similar procedure.
Alexander Maltagliati ok thanks ☺
This video helped, Thanks
THANK YOU 😊
To approximate what?
thank you😇
Sweet Elf what do you stady??
Thanku thanku so much
Is there a video about how to do differencing with for example f(x,y)= -ye^sinx . I mean with two variables? PLEASE I HAVE A FİNAL WITHIN FEW HOURS HELPPPP😭😭
Thanks a lot
Actually there's a formula for finding the error which is (xi/2 * the second derivative of the xi) . You subtract it from the actual derivative formula to find a better result.In this case it gave me the exact solution which is 9,but this may change due to the type of the question that we're supposed to answer so this could be an exception.Thanks for helping us poor students good sir.
Thanks!
thank you !!
Thank you.
THANK YOU!
Thank youu so much
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The explaination is very good but the screeching from the pen really make the lesson unpleasant
thanks
Great
ty
thank u
this is being filmed by a laptop webcam?? genius
I have exams in 12hours times
My nigga! Thanks.
Change your sketch pen.. It is irritating
Bakw
First
Bakws
thank you.