22: Gradient Theorem - Valuable Vector Calculus

[@SL-lv8et]

I have a nice number theory problem for you Mr Osman The problem: Find all integers (a,b,c,d) such that 1

[@narayanasiyer21]

well explained. Your presentation skill is awesome.

[@divyanshukumar4470]

namaskaar chacha kaisan baa sab thik baa na bada videshi video dekhal ja rahal baa

[@tomashernandez8711]

In 2:21, is that a sort of chain rule? I don't understand why you multiply for magnitud of the change. Thank you and congratulations, what a nice video. :)

[@MuPrimeMath]

The reasoning is similar to the chain rule. The directional derivative tells us how much the output of f changes per unit length in the direction of r', but if the input to f is r(t) then the input changes by r'(t) for every unit length in t. If we want the derivative with respect to t, that means we have to multiply by the length of r'(t) to account for that!

[@NKProductions139]

perfect explanation.

[@xy-mw9nx]

Very well-explained

[@AuratticStride]

So, suppose we don't have a closed form for the original function, but we know the gradient, and we want to compute the line integral of the gradient over some curve. Does this mean we could replace a complex curve with a simple line from the start point to the end point to get a more amiable integral?

[@MuPrimeMath]

That's right! However, in that case, it's often easier to figure out the original function and just plug in the endpoints. There are a few methods to do this once we know that the vector field is a gradient. The original function is sometimes also called a "potential function" for the vector field. Here is an example of how to calculate a potential function: tutorial.math.lamar.edu/Solutions/CalcIII/ConservativeVectorField/Prob7.aspx

[@3manthing]

Well explained. As always, duh xD. One of my favourite things about maths for sure. Next to single variable calculus that is. :)

[@Zodiaczero2]

Thank you!!!

[@MarkusDarkess]

I think this math can be very helpful with what I have been working on. But I only have had algebra classes and geometry classes. Never took calculus sadly. I really enjoy working on numbers. And finding patterns.

[@MarkusDarkess]

If you want to check it out. I understand the concept of vector points. But there is no end point its only A to infinity I have 3 number lines a,b,c. The graphing and math should lead through a and b showing a symmetry of where twin primes should be. More so then what I broke it down to. My hypothesis is that math formula might be what I need to prove or dis prove the twin prime conjectures. But alas.. I do not know. I know at least it should make it far easier to find twin primes or primes alone. Across vast gaps instead of 100000! We would just lead over blank gaps in just a couple of intervals. Plus it would be easier to prove or disprove hypothesis. kzbin.info/www/bejne/Z3m6dIKrmdGHnLM