There's a subtle, but powerful, art to teaching; and teaching well. Individuals don't fully appreciate the impact a great teacher has on a class. Any class. Whether it's maths, science, politics or whatever, if you're being taught by someone that exudes the same level of enthusiasm he or she wishes to impart on everyone else, then that's an absolute game-changer.
Again thanks for this videos.... Calculus is some kind of difficult part of my maths knowledge but, I know u videos will help me a lot.... Love from India 😍😍😍
Conviction/beliefs - the world needs educators, though, I can’t accuse/humiliate someone for their disabilities, people should work on! I need to thank you, 'coz you’re one of those educators who believe in diligence!
Eddie Woo is Chinese. Sensei Japanese. You should know this. Do you not tire of making meaningless youtube comments referencing only your personal obssesion with yourself?
Thank you teacher. I think that I understand it all!😮 We have a curve. We have a straight line crossing at two points. It's called a secant. Each point has its coordinates. Eg. [x1, y1], [x2, y2]. The gradient can be found by the quotient of the difference of their coordinates. Eg. [ y2-y1/ x2-x1 ] or [ dy/dx ] or [ ∆y/∆x ] or [ y2-y1/h] where 'h'= x2-x1 or ∆x. If the curve is described by a function 'f', the gradient of the secant be described as f(x). What if that secant is displaced so that it touches the curve at one point? That is, the line is now a tangent to the curve. We can find the gradient of the tangent at that point by deriving a gradient of a tangent function f' from the gradient of a secant function f. To do so, first we will limit the change in x to be approaching 0. Eg. [ lim ∆x -> 0] or [ lim h -> 0 ]. Next we would use the function f' (x) which is the function that outputs the gradient of a tangent. DIFFERENTIATION is the process used for deriving gradient of tangent function f'(x) from a gradient of a secant function f(x). The output function f'(x) is called the DERIVATIVE. Question. What is the input 'x' the functions f(x) and its derivative f' (x)?
both pronunciations of secant are accepted I suppose. I think one's more dominant than the other though. Just like how there are two ways to pronounce laboratory.
With regard to Laboratory, one is British English and the other is American English. In the future bo one will say either. Just Lab. What are the different ways of saying Secant ?
@@AugustinSteven one way is the first syllable being more similar to the word "see" while the other pronunciation is more similar to the first syllable in "sector" /ˈsiːk(ə)nt,ˈsɛk(ə)nt/ The former being more used. With laboratory, I hear both here in Australia. It seems the "younger generation" are using the American pronunciation and the "older generation" use the British pronunciation. I use both interchangeably depending on who I speak with. Same with the word "privacy".
@@V21IC I've heard it been used in british english but yes f prime of x is the most common. Made this comment 4 years ago, mustn't of had much of a childhood if I was learning calculus at 15 🤣
Joshua Tamer Unfortunately it isn’t very easy to explain. But the way it has been done is by using field theory. Idk how much you know about that, but that is only integrals in terms of non elementary functions since it is integrable iff (1/(sqrt(1-u^2)))*e^u is integrable (you can get this by u substitution). Then from the result in this paper I am going to link, it is not integrable. www.math.dartmouth.edu//~dana/bookspapers/elementary.pdf
@@everettmeekins1582 if you use the definition that e^x is the sum of (x^n)/n! from 0 to infinity, can you replace the integrand so that it is the functions corresponding Taylor series so that you get sin^n x/n! then get a recurrence relation in terms of sin^n ? But is it defined whether using the taylor polynomial for a function when integrating is equivalent to integrating the function itself? Also if the integral had limits would you be able to find some value using residues?
This a comment about maths terminology differences between countries. His Rise over Run reminded me that he normally says On for divide as in 3 on 7 for 3/7. I'm from England and I always use Over as in 3 over 7 for 3/7. He should really say Rise on Run to be consistency.
I am 14 too, dang!! What a great teacher, Mr Woo! He made 14-year-olds understand a concept most 17 or 18-year-olds fail to decipher, fathom and understand! He helped me discover my inner nerd.
