I think not, since γ’dt is just (dγ/dt)dt, saving us from t being implicit. Writing it in the form f(γ)dγ, the conjugation only affects f(γ). This means only f(γ) is the integrand, while γ‘ is part of the „integration step“. If it would be complex conjugated, we would step in the wrong direction along the imaginary axis. An operation on the integrand shouldn’t affect the way the integration itself works. γ‘ should always behave the same way. Definitely no expert here, just sharing my thoughts.
He wants to describe the line that goes from the starting point (5) to the end point (2+3i). He created this line by using the formula: Line(t) = [starting point] + t*([end point] - [starting point]), where t is the variable in this case and can be described as the flowing of time. By creating the line this way we will always get that Line(t=0) = starting point and Line(t=1) = end point. He could have created another formula for the line, but by doing it this way the limits will always be 0 and 1. Let me know if you want any more clarification on the subject.
Can somebody explains to me how did Cauchy made this theory? I always wanted to know how did those scientists made theories, I don't need calculation I need to understand the theory and where it exist in nature, I think that we should know where did those theory come from?
el-mehdi Benchaib Oftentimes these theories just drop out of math without a relation to nature... sometimes they do... I think if you want to understand this theory you most probably have to read a proof of some sort.
u saved a life sir, i've been crying 2 days about this
Are you still crying? Becuase I am.
I've watched so many of your videos this quarter I could say you were one of my professors.
I'd rather just watch your videos than go to class, you explain it so much better!
Thank you
Great series! Good format, and really clear explanation. Makes it seem quite simple really :). Also love the "thank you" on the end, haha.
10:27 Shouldn't there be *(-1)3ie^(-it) ?
I think not, since γ’dt is just (dγ/dt)dt, saving us from t being implicit. Writing it in the form f(γ)dγ, the conjugation only affects f(γ). This means only f(γ) is the integrand, while γ‘ is part of the „integration step“. If it would be complex conjugated, we would step in the wrong direction along the imaginary axis.
An operation on the integrand shouldn’t affect the way the integration itself works. γ‘ should always behave the same way.
Definitely no expert here, just sharing my thoughts.
No because z is same only you want to integrate the conjugate
Thank you so much, your lessons made a difference :)
how to find the gamma function ? Could you elaborate on that part ?
When you differentiate 3e^it is that not just i3e^it
+mungo3012
there is no 3e^it in the expression once it has been expanded
at 02:30 how can I derive limits of "t". I couldnt understand this
He wants to describe the line that goes from the starting point (5) to the end point (2+3i). He created this line by using the formula: Line(t) = [starting point] + t*([end point] - [starting point]), where t is the variable in this case and can be described as the flowing of time. By creating the line this way we will always get that Line(t=0) = starting point and Line(t=1) = end point.
He could have created another formula for the line, but by doing it this way the limits will always be 0 and 1. Let me know if you want any more clarification on the subject.
how did you find gama(t)?
I couldnt understand sir :(
thank u very much sir for these explanations
Why isn't z bar analytic here?
When integrating zbar, are we integrating dz or dzbar
if gamma denotes the contour with {Im(z)=4} in the comlex plane what we'll be the gamma of t ?
t +4i
t€(-1/0, 1/0)
(Can't get the symbol for infinity :P)
Man only if you were my professor! I won't be struggling as much
i want to know how to get f(gamma(t))?
Can somebody explains to me how did Cauchy made this theory? I always wanted to know how did those scientists made theories, I don't need calculation I need to understand the theory and where it exist in nature, I think that we should know where did those theory come from?
el-mehdi Benchaib Oftentimes these theories just drop out of math without a relation to nature... sometimes they do... I think if you want to understand this theory you most probably have to read a proof of some sort.
great vid:) helped a lot
at 6:42, the question is ambiguous. The 1/4 circle curve can be clockwise or
counterclockwise.
great video
Is this topic is there for her mains
I love you so much lol
stari ti si tak mužicl