Please make a video on 2nd order higher degree diff equations Sir.
@gayansamarasekara28 күн бұрын
Thanks for your suggestion, sir. I will keep it in mind. My initial plan was to use this fall for calculus - 1, and then work back on calculus - 2 during next Spring. Kind of planning a systematic collection of videos as time permits.
@gentlemandude1Ай бұрын
Where can we find the video with the complete proof? Thanks.
Very nice professor, I didn’t know this method. Very good for my studies!
@gayansamarasekara3 ай бұрын
Thanks for the comment. I’m glad you find it helpful for your studies.
@ShamiSamarasekara3 ай бұрын
👍👍👍👍👌👌👌👍👍👍👍
@gayansamarasekara3 ай бұрын
👍🏻👍🏻👍🏻👍🏻😊👍🏻👍🏻👍🏻👍🏻
@ShamiSamarasekara3 ай бұрын
👍👌👍 superb work sir
@gayansamarasekara3 ай бұрын
👍🏻👍🏻👍🏻 thank you so much.
@justabunga13 ай бұрын
When you integrate √((x-2)^2)dx, shouldn't you integrate the one with the absolute value of (x-2) as the integral of |x-2|dx? The answer should be (x-2)|x-2|/2+C. Sometimes when the value of x is negative, it can lead to positive answer. Because there's no limits of integration, the absolute value is needed. If the limits of integration are there, then the answer changes.
@gayansamarasekara3 ай бұрын
Yes, you’ve got a valid point. Ideally to keep all math majors calm, and without getting too complicated to non-math majors, the problem should’ve been given as X>2. The suggested answer in your comment works, and an alternative popular answer for the same is using two indicator functions, I(x<2) and I(x>2), instead of the absolute values. I’ll have another video at some future point on this. Thanks for the comment.
@justabunga13 ай бұрын
@@gayansamarasekara no problem. Are you assuming that everything is positive if that's what you're talking about?
@gayansamarasekara3 ай бұрын
@@justabunga1well, I think I wasn’t clear enough, sorry about that: For indicator functions, there will be a negative sign with I(x<2) and positive sign with I(x>2), with ( (x-2)^2)/2 multiplied with each, so not limiting x to be greater than 2. However, if it was given x>2 in the problem itself, no indicator functions or absolute sign needed, since x-2 is positive only. I think that’s what I was trying to comment that day. Thanks.
@PhilomenaOdjugo3 ай бұрын
Please i need a solution to this integral sir 1/3^x + e^-x dx
@gayansamarasekara3 ай бұрын
You may integrate those two, one by one. The integral of e^-x is easy: -e^-x. Similarly, use the result integral of a^x, for a>0, which is: (a^x)/(ln a), for the other part with a=1/3. Just a tiny bit more simplifications can be done. Hope this will help. I’ll try to have a video on that next week or so. Thanks for your question.
@PhilomenaOdjugo3 ай бұрын
@@gayansamarasekara actually 3^x + e^-x are together like 1/(3^x + e^-x) dx
@nemanjaantic70643 ай бұрын
Where were you when i was learning this, great vids, good job man! 🤗
@gayansamarasekara3 ай бұрын
Thank you for your nice comment. Those days I was trying to make travel videos, which nobody watched. Then switched to math, hah ha 😁🤗.
@simongross31223 ай бұрын
Another incredibly useful theorem that I never learned. Thank you for the proof. Do these two theorems have names?
@gayansamarasekara3 ай бұрын
Thanks for your nice comment. Yes it’s for sure a very useful theorem. Many substitutions can be eliminated, and many standard results (e.g: integral of cot x, etc.), can be obtained directly without much effort. I’m not too sure what the names of those theorems are, I learned them some 25+ years ago, in a book of worked examples, which had those theorems labeled as theorem 1, and 2, without any specific names (if I remember right). In my calculus classes, I teach them as special theorem 1 and 2, under the section of integrations by substitutions. I haven’t seen those two theorems in any popular textbooks that they use for teaching calculus in the US universities.
@simongross31223 ай бұрын
Wow, thank you. I don't know why I never learned this at school or university. It's obviously a very useful result.
@gayansamarasekara3 ай бұрын
My pleasure. Indeed it’s a very useful theorem, it has many applications, plenty of substitutions can be eliminated using the theorem. Unfortunately many US calculus textbooks don’t have this theorem, so they usually don’t teach it. I learned it some 25+ years ago while getting ready for an extremely competitive university entrance exam, I found it those days in a book of target problems, under a set of worked examples. Thanks for your comment.
@PhilomenaOdjugo3 ай бұрын
Thank you sir
@gayansamarasekara3 ай бұрын
You are welcome.
@ShamiSamarasekara4 ай бұрын
good job keep it up sir
@gayansamarasekara4 ай бұрын
Thanks ma’am 👍🏻
@sirlimatematika75714 ай бұрын
Very good
@gayansamarasekara4 ай бұрын
Thank you.
@sirlimatematika75714 ай бұрын
Assalomu aleykum
@gayansamarasekara4 ай бұрын
Wa Alaikum Salam ✅
@samueldeandrade85354 ай бұрын
You could do the general case ...
@gayansamarasekara4 ай бұрын
Yes, a generalization of the theorem can be found here: CAN YOU EVALUATE THIS DEFINITE INTEGRAL? kzbin.info/www/bejne/gaHWpaFvepaGm9U
@sirlimatematika75714 ай бұрын
Very good video
@gayansamarasekara4 ай бұрын
Thank you.
@sirlimatematika75714 ай бұрын
Very good video
@gayansamarasekara4 ай бұрын
Thank you.
@sirlimatematika75714 ай бұрын
How are you Mr
@gayansamarasekara4 ай бұрын
I’m good, thank you. How are you?
@sirlimatematika75714 ай бұрын
I'm okay
@sirlimatematika75714 ай бұрын
Assalomu aleykum
@gayansamarasekara4 ай бұрын
Wa Alaikum Assalam (this time I used AI to generate the response - still kind of difficult to remember the phrase, and spelling).
@sirlimatematika75714 ай бұрын
Assalamu Alaikum is an Arabic word that means I wish you health and safety. As-Salam is a name of Allah
@haythamba49904 ай бұрын
معلم
@sirlimatematika75714 ай бұрын
❤❤❤❤ very good
@gayansamarasekara4 ай бұрын
❤️❤️❤️❤️ thank you
@sirlimatematika75714 ай бұрын
Very good
@gayansamarasekara4 ай бұрын
Indeed 👍🏻
@sirlimatematika75714 ай бұрын
Assalomu alaykum Mr
@gayansamarasekara4 ай бұрын
Wasalamu Alaikum Mr
@sirlimatematika75714 ай бұрын
Great. Keep making videos like this
@gayansamarasekara4 ай бұрын
Thank you, I’ll always try.
@sirlimatematika75714 ай бұрын
Assalomu alaykum
@gayansamarasekara4 ай бұрын
Wasalamu Alaikum
@felipefred12794 ай бұрын
Thanks for the proofs professor 👏
@gayansamarasekara4 ай бұрын
You are welcome 👏
@felipefred12794 ай бұрын
I am interested in the proof for the theorem that you show in the partial fraction problem the ln|f(x)| one
@gayansamarasekara4 ай бұрын
Please check it here: THEOREM 2 OF 2: INTEGRATIONS BY SUBSTITUTIONS kzbin.info/www/bejne/gIKmeJKkrpuUmq8
@rudycummings46714 ай бұрын
When i was in college many years ago, we referred to that method as the 'cover up' method.
@gayansamarasekara4 ай бұрын
That is correct, it’s a popularly used name for the method in many textbooks.
@alejandrocastillo-garcia54184 ай бұрын
cheers guv
@gayansamarasekara4 ай бұрын
Cheers
@idontknow-wl6su4 ай бұрын
I forgoted the b^2-4ac jajaja, thanks a lot, now, i will sure that a wont forgot again :)
@gayansamarasekara4 ай бұрын
You are welcome a lot.
@sirlimatematika75714 ай бұрын
❤❤❤❤
@gayansamarasekara4 ай бұрын
❤️❤️❤️❤️
@sirlimatematika75714 ай бұрын
Very good Mr
@gayansamarasekara4 ай бұрын
Thank you…!
@sirlimatematika75714 ай бұрын
Do you know Demidovich's book? It would be great if you could solve this book. Do you have Facebook, Instagram or Telegram messenger?
@sirlimatematika75714 ай бұрын
Assalomu aleykum
@gayansamarasekara4 ай бұрын
Wa-Alaikum Salam…! I think I got it right (last time I had a Muslim friend sitting next to me, he helped me figuring out the correct response. Today it’s all by myself 😊).
@sirlimatematika75714 ай бұрын
Please advise me I learn mathematics better no matter what literature I read Have you written a book on mathematics?
@gayansamarasekara4 ай бұрын
Nice to hear that. To go beyond college, there are scholarships available at grad schools around the US. Please check their entry requirements. Almost all the PhD programs are available at no cost out of pocket for the graduate students, who are willing to work as GRA or GTA, which will be 20 hours per week (practically less than that, but they pay for 20). You’ll need GRE, recommendation letters (2 or 3), a personal statement, online application and fee, under graduate transcript, technically for any graduate program. I haven’t authored any textbooks yet, I have some research publications only. Thanks for checking.
@meedonexus4 ай бұрын
Bundle thanks to you for this brilliant rule
@gayansamarasekara4 ай бұрын
My pleasure. Thanks for your comment.
@michaelguenther71054 ай бұрын
I love your handwriting, it is a pleasure to read and enhances the presentation.
@gayansamarasekara4 ай бұрын
Thank you so much. Your comment gives me confidence.
@rogermigdow24264 ай бұрын
Thanks! They usually have us use the power-reducing formula for sin^2…
@gayansamarasekara4 ай бұрын
My pleasure, and thanks for the comment. Yes, the power reducing formula can also be used, though it may be better for larger powers, such as the discussion here: HOW TO DERIVE AND USE REDUCTION FORMULA FOR INTEGRATING SINE N-TH POWER - A WORKED EXAMPLE INCLUDED kzbin.info/www/bejne/aJyQaaiMaLqlaqM
@idontknow-wl6su4 ай бұрын
I like the formula, but, n can be any number real :p?
@gayansamarasekara4 ай бұрын
Good question. Yes, n can be technically any real number greater than 2, in order to reduce. However, after reducing it to an integral whose power is less than 2, you’ll have to manually evaluate an integral, which may be difficult. For example, if n = 5/2, after applying the formula once, you’ll have to evaluate an integral involving 3/2 power. Since that power is less than 2, further reductions won’t help, and integrating tangent raised to 3/2 power is difficult (could be not so difficult as a definite integral, if the limits are given, at the very least the Simpson’s Rule can be applied, therefore, for any practical engineering/design matters, the solution is easily reachable, and therefore reduction still helps to convert a higher order integral into a lesser order integral).
@jaydenleeds55874 ай бұрын
Oh wow so soon. Nice!
@gayansamarasekara4 ай бұрын
Thanks for the comment…! Thanks for staying with my channel.
@ShamiSamarasekara4 ай бұрын
👍👍👍
@gayansamarasekara4 ай бұрын
👍🏻👍🏻👍🏻
@sirlimatematika75714 ай бұрын
Where in America do you live?
@gayansamarasekara4 ай бұрын
Kansas.
@sirlimatematika75714 ай бұрын
My name is Bekzod I'm from Uzbekistan Nice to meet you I am also interested in mathematics I'm a teacher
@gayansamarasekara4 ай бұрын
Nice to meet you too. I go by Sam, I am a professor. I am also interested in mathematics.
@sirlimatematika75714 ай бұрын
Very good Mr @@gayansamarasekara
@FisherAdam4 ай бұрын
Very good.
@gayansamarasekara4 ай бұрын
Of course. Thanks for the comment…!
@utuberaj604 ай бұрын
Tabular Integration or the so-called D-I method does the job straight away. I learnt it from Blackpenredpen channel.
@gayansamarasekara4 ай бұрын
Of course. Glad to hear you already knew the method. Thanks for the comment.
@matejcataric22594 ай бұрын
I absolutely love integrals and this channel provides great content!
@gayansamarasekara4 ай бұрын
Wonderful to hear that. Thank you so much for the comment…!
@jaydenleeds55874 ай бұрын
Whats the answer to the hw question? I want to know if I understood method correctly
@gayansamarasekara4 ай бұрын
Thanks for your question. Right now, I’m working on something, I’ll get back to you tomorrow. Sorry about the delaying. If you paid attention to the changing + / - signs of the integrals (because sine/ cosine repeated integration leads to alternating signs), along with the method specific changes of + / - signs, your answer should be correct, provided you followed differentiation and integration in each step correctly.