I'll write my differentials up front if I'm doing iterated integrals, to keep the variable of integration next to the limits of its domain. When you're 3 or 4 integrals deep, this can be a lifesaver. Also, at 6:45 you lost a minus sign from the chain rule. And you have to be careful with substitutions like A -> -A because A is the /exponential/ of a constant of integration, and therefore always positive (if you're limiting yourself to real analysis).
6:21 it really depends on what the original form of formula is . For example if it is like mr^2 omega for angular momentum we prefer writing as dm*r^2 omega if we wanted to integrate wrt mass . You might even find like rho * 4pi r^2 dr * r^2 omega too . Here rho is just the density = dm/dv. So like we write in middle too . Thats not odd . But if the element of differntiation is at the end we prefer writing at the end for ex kq /r^2 translates to k dq/ r^2 or k rho 4 pi dr for electric feild its just like the way we memorized the intial setup for formula
Is that a part of your ocd? The “ooookay..cool” i mean. Or just something you are trying to drill into your viewers’ psyche? It doesn’t really matter to me, I just love it in any case. Love your content, a lot of it is over my head, i get the solution but i wouldn’t be able to construct it myself.
Thank You Man But I want to ask Like where I can Start This High level Maths from, I am A High School Pass Student But I want to pursue high level maths but due to competition in my country i am quite not able to get my dream major of pursuing maths as a career option but still want to do it. I am currently looking forward to Mech. Eng. But can you Please tell me...
i dont care what excuses the physicists have, putting the dx in front of the function is illegal
I'll write my differentials up front if I'm doing iterated integrals, to keep the variable of integration next to the limits of its domain. When you're 3 or 4 integrals deep, this can be a lifesaver.
Also, at 6:45 you lost a minus sign from the chain rule. And you have to be careful with substitutions like A -> -A because A is the /exponential/ of a constant of integration, and therefore always positive (if you're limiting yourself to real analysis).
6:21 it really depends on what the original form of formula is . For example if it is like mr^2 omega for angular momentum we prefer writing as dm*r^2 omega if we wanted to integrate wrt mass . You might even find like rho * 4pi r^2 dr * r^2 omega too . Here rho is just the density = dm/dv. So like we write in middle too . Thats not odd . But if the element of differntiation is at the end we prefer writing at the end for ex kq /r^2 translates to k dq/ r^2 or k rho 4 pi dr for electric feild its just like the way we memorized the intial setup for formula
10:30 z^(1/3) not equals z^(2/3-1)
I was itching for a differential equation!!!! Awesome ❤
dx up front makes so much more sense.
1/3 is not 2/3 - 1 but 4/3 - 1, so the first argument of the incomplete gamma function should be 4/3.
dx in the back throw your hands in the air
Is that a part of your ocd? The “ooookay..cool” i mean. Or just something you are trying to drill into your viewers’ psyche?
It doesn’t really matter to me, I just love it in any case. Love your content, a lot of it is over my head, i get the solution but i wouldn’t be able to construct it myself.
u=dy/dx...=> (du/dy)u=1/√√(1-y)*u^2...du/u=dy(1-y)^(-1/4).…
Thank You Man But I want to ask Like where I can Start This High level Maths from, I am A High School Pass Student But I want to pursue high level maths but due to competition in my country i am quite not able to get my dream major of pursuing maths as a career option but still want to do it. I am currently looking forward to Mech. Eng. But can you Please tell me...