All Questions
4
questions
0
votes
0
answers
123
views
How to decompose the given function into several peaked functions like Gaussian or Lorentzian?
During applied mathematics, I am wondering how to decompose the data $[x,y]$ into several elliptic-shaped functions, namely
$$f[x,y]= H \cdot \left( 1 + \bigl( \frac{x-x_1}{a_1} \bigr)^2 + \bigl( \...
- 95
2
votes
4
answers
1k
views
How does Volume work with integration?
Using a cross section suppose, as described here: Area formula Paul Notes
Suppose this is: $y = f(x)$.
He says the volume is:
$$\int_{a}^{b} A(x) dx$$
But how does area over that interval give ...
- 11.2k
0
votes
1
answer
26
views
Volume of Revolution $f(x) = x^2$
Suppose you are given $y = f(x)$
I want to use double integrals, instead of the traditional washers.
Suppose even better, $f(x) = x^2$
Find the volume of $f(x) = x^2$, $x = 0$, $x = 4$, $y = 0$ &...
- 491
5
votes
1
answer
2k
views
Unexpected Practical Applications of Calculus
Calculus shows up in a lot of places in the world. Specifically, here are three areas where I see it used the most:
Optimization problems.
Anything involving rates of change (e.g. velocity $\...
- 1,389