Equation(s) you believe have had much influence. (2 Viewers)

[Uncle]

Post an equation that you believe is useful, preferably you have used it yourself.
State the assumptions and terms/variables and comment about it.

e.g.

Bernoulli's Equation

[maths]P_{1} + \frac{1}{2}\rho v_{1}^{2} + \rho g h_{1} = P_{2} + \frac{1}{2}\rho v_{2}^{2} + \rho g h_{2}[/maths]

Where:

[maths]P[/maths] is the hydrostatic pressure.
[maths]\frac{1}{2}\rho v^{2}[/maths] is the dynamic pressure.
[maths]\rho g h[/maths] is the elevation pressure.


Assumptions:
No losses due to pipe friction, etc.
The flow is steady.
The cross-sectional change between two points must not be sudden.
The fluid is incompressible i.e. the density doesn't change at all.

Although this is a more simple equation to use in fluid mechanics, it has been heavily misused often because the situations it is used in do not meet the assumptions of the above equation.

 

[Studentleader]

Because I couldn't think of anything prettier



a!=0
b^2 > 4ac for solutions in N

 

[CIV1501]

Post an equation that you believe is useful, preferably you have used it yourself.
State the assumptions and terms/variables and comment about it.

e.g.

Bernoulli's Equation

[maths]P_{1} + \frac{1}{2}\rho v_{1}^{2} + \rho g h_{1} = P_{2} + \frac{1}{2}\rho v_{2}^{2} + \rho g h_{2}[/maths]

Where:

[maths]P[/maths] is the hydrostatic pressure.
[maths]\frac{1}{2}\rho v^{2}[/maths] is the dynamic pressure.
[maths]\rho g h[/maths] is the elevation pressure.


Assumptions:
No losses due to pipe friction, etc.
The flow is steady.
The cross-sectional change between two points must not be sudden.
The fluid is incompressible i.e. the density doesn't change at all.

Although this is a more simple equation to use in fluid mechanics, it has been heavily misused often because the situations it is used in do not meet the assumptions of the above equation.

lol same

 

[pman]

quaratic formula
e=mc^2 (used it for a yr 3 speech)

 

[untouchablecuz]

F=ma

its like the basis of newtonian mechanics

 

[pman]

F=ma

its like the basis of newtonian mechanics

the master equation that nobody knows yet, the one string theory is leading towards

 

[CIV1501]

none of you are addressing the OP properly

 

[Einsteinium_101]

Go the Pythagora's Theorem!!

 

[daryl-d]

projectile motion and einstein's e=mc^2

 

[kaz1]

Maxwell's equations. I heard that if you burn all the books about classical physics but you still have Maxwell's equations you can get everyting back.

Maxwell's equations - Wikipedia, the free encyclopedia

 

[boo92]

even though i love maths i dont have a favourite - and any nonmaths people (if there is such a thing) will think u r all nerds!

 

[Uncle]

I expected better.
I thought someone would consider Newton's Law of Universal Gravitation or Faraday's Law of induction.

Maxwell's equations. I heard that if you burn all the books about classical physics but you still have Maxwell's equations you can get everyting back.

Maxwell's equations - Wikipedia, the free encyclopedia

considering matter isnt comprised entirely of electrons.

 

[Studentleader]

Is there some kind of formal proof to prove a function is monotonic on a domain like [a,inf) or (-inf,a]? Optimization in first year is a pain that you have to state every theorm and etc. though when their is a open domain we just say "it is decreasing on [b,inf) so the local max must be on (-inf,b).

 

[Trebla]

The standard normal density function (i.e. equation of the normal curve with mean 0 and variance 1)



It's usefulness across every scientific discipline which involves data collection is self explanatory.

 

[tommykins]

Is there some kind of formal proof to prove a function is monotonic on a domain like [a,inf) or (-inf,a]? Optimization in first year is a pain that you have to state every theorm and etc. though when their is a open domain we just say "it is decreasing on [b,inf) so the local max must be on (-inf,b).

MVT to prove that it's monotonous.
IVT to prove it's continuous and hence the local max must be in that domain. (namely the end point)

 

[vandretta]

\frac{r^{3}}{T^{2}}= \frac{GM_{e}}{4\pi ^{2}}

One of the most pain in the butt things our physics teacher has ever made us derive. Still pretty proud I managed it hence my most influential equation

 

[vandretta]

i'll try that again

 

[annabackwards]

It was the first equation that i learnt and i still use it

 

[lolwth]

i'll try that again

what
so hard
so fresh

 

[Studentleader]

MVT to prove that it's monotonous.
IVT to prove it's continuous and hence the local max must be in that domain. (namely the end point)

MVT requires a closed interval. Looking at my notes on the geometric interpretation of the MVT it says 'for some interior point the instentaneous change = average change' which wouldn't help aswell.