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>taught laplace transfroms

Anonymous Wed 03 Mar 06:04:27 2021 No.12779308 View Reply Original Report

Quoted By: >>12779342 >>12779483 >>12779643

AHHHHHHHHHHHHHHHHHHH
WHY WASN'T I TAUGHT THIS IN THE FIRST PLACE WHY DO THEY ENJOY GIVING US HELL
REEEEEEEEEEEEEE
>itt /sci/ things you wish you learned earlier

Anonymous

Anonymous Wed 03 Mar 2021 06:18:44 No.12779342 Report

Quoted By:

>>12779308
I didn't learn this shit yet. Is this going to be like the hospital rule from calculus where they waste half the course torturing you with retarded methods of solving problems that can be done in one line?

Anonymous

Anonymous Wed 03 Mar 2021 06:31:43 No.12779375 Report

Quoted By: >>12780158

$\displaystyle \sum_{n=0}^{\infty} a_n x^n = A(x) \\ \sum_{n=0}^{\infty} a(n) x^n = A(x) \\ a(n) \sim \! \sim \! \sim \! \! \! > A(x) \\ a(n) = 1 \sim \! \sim \! \sim \! \! \! > \frac{1}{1-x} \: \: \, ,\: \: \: \left | x \right | < 1 \\ a(n) = \frac{1}{n!} \sim \! \sim \! \sim \! \! \! > e^x \\ \text{continuous analog:} \\ \int_{0}^{\infty} a(t) x^t dt = A(x) \: \: \, ,\: \: \: 0 < x < 1 \Rightarrow ln(x) < 0 \\ x^t = \left ( e^{ln(x)} \right )^t \: \: \, ,\: \: \: -s = ln(x) \Rightarrow x = e^{-s} \\ \int_{0}^{\infty} f(t) e^{-st} dt = F(s) $

https://youtu.be/sZ2qulI6GEk?t=1m

Anonymous

Anonymous Wed 03 Mar 2021 07:16:15 No.12779456 Report

Quoted By:

https://www.youtube.com/watch?v=n2y7n6jw5d0

Anonymous

Anonymous Wed 03 Mar 2021 07:31:16 No.12779483 Report

Quoted By:

>>12779308
It's called the Heaviside Calculus.

Anonymous

Anonymous Wed 03 Mar 2021 08:47:36 No.12779643 Report

Quoted By: >>12779903

>>12779308
Wait until you learn fourier transforms anon, you will question why you had to learn Laplace first.

Anonymous

Anonymous Wed 03 Mar 2021 11:01:46 No.12779903 Report

Quoted By:

>>12779643
At what point in my sad miserable pathetic math career will I begin considering suicide?
gradschool?

Anonymous

Anonymous Wed 03 Mar 2021 12:52:17 No.12780158 Report

Quoted By:

>>12779375
I prefer integrating f(st)e^(-t)dt
It just converts Exponential Generating Functions into their corresponding Ordinary Generating Functions.
f(t) = Sum[a(n)(t^n)/n!] --> Sum[a(n)(s^n)] = F(s)
This is very easy to see from the integral formula for the gamma function.
I'm a bit biased because I work in combinatorics.
I care more about a(n) than f(t) or F(s) (although the singularities of f or F can tell you a lot about the asymptotics of a(n)).

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