 
 
Hello students myself Dr. Gajendra Purohit and today
I am going to teach jacobian in which
in the first part I told you that what is jacobian and how we calculate it
and today I am going to discuss that what are the properties of jacobian and with the help of properties many
questions can be easily solved. Students my
channel is especially for higher education
as students who are doing bsc, engineering or
doing preparation of any competitive exams where higher
education mathematics is asked it is dedicated to that.
So students I have request that please subscribe to my channel
and press the notification bell so that for all my upcoming videos
you keep getting the notifications. Students
I have a wish that in one day I upload around 2-3 videos but
I have less subscribers so
please help me in this so quickly
I will bring content for you all plus
for all competitive exams where higher education mathematics
is asked I am focusing on that also so that also
I am going to bring soon. So students see here jacobian
and what it is? what is jacobian that I have already told you so here on the I icon
you can see that. Now lets see the properties of jacobian
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
So students this is how with the help of property we find its value.
So I will take one more question based on this property only.
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
So this is how we will find its value.
Now I will tell you the second property. So students see here
the second property. Students the second property is like total
partial differentiation only that like
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
So students this is how here
we find its value and now I will discuss the third
property. So students now we are going to discuss the third property.
and what does the third property say? By chance
if the function u, v, w of the three
independent variable x, y, z are not independent
then the jacobian of this is 0. This means that
if a question is asked in the exam that u is this and v is this
then find the relation
between them. So what we have to do is that you have to
find its jacobian and proof that its jacobian
value is equal to 0 which means that
 
 
So this means that here it is
dependent and if the value is
not equal to 0 so this means that it is independent.
So students based on this question can come in the exam.
If the jacobian for this is 0 then u and v are
dependent or independent so what we have to is that
here u and v will be
dependent. So here the third property states that
if u, v, w are function of x, y , z
and this u, v, w together
will be dependent if the jacobian with respect to this
will be 0 otherwise it will be independent.
So the question here is that verify whether the following function
following functionally dependent and if so then find the relationship
between them. This means that you have to proof that u and v
are dependent on each other and
if they are so then find the relationship between them.
So students if you have to prove both of them dependent then
you have to prove that the jacobian for this is 0.
So what we will do is that keep this is mind.
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
Students I have made video on partial differentiation
that you can watch in the playlist and you can even see that here on the I icon.
So if you don't know how to do partial differentiation then you can learn from there.
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
SO keep this in mind that what is the meaning for dependency like you are dependent on your father
and you take money from your parents for
the education that you are doing so you are dependent on them and if you are dependent
then you have a relationship with them
like he is my father, he is my brother or what so ever.
So where ever there is dependency there will be a relationship so keep this in mind.
So in jacobian if they ask you
that is it dependent or not so you have to
proof that it jacobain is 0 and then find the relation between the two. So students
I feel that my videos must be helping you and
your exams are also near so I will try that
according to your comments I develop the content and
in future also I will bring good content for you all. So thank you so much
for watching my videos. Students I have only one request that
I tell you again and again that do subscribe to my channel
and press the notification bell and do share among your friends.
I am giving you knowledge so you spread it around.
Thank you so much for watching my videos. Thank you.
