From: Andrew Lorimer Date: Tue, 21 May 2019 02:22:28 +0000 (+1000) Subject: [spec] concentration integration and separation of variables X-Git-Tag: yr12~129 X-Git-Url: https://git.lorimer.id.au/notes.git/diff_plain/befe17c800bf6752581f9e2eb53e8c05d1275ef3 [spec] concentration integration and separation of variables --- diff --git a/spec/calculus.md b/spec/calculus.md index 43cf752..97bc926 100644 --- a/spec/calculus.md +++ b/spec/calculus.md @@ -398,3 +398,13 @@ Start with $y=\dots$, and differentiate. Substitute into original equation. ### Function of the dependent variable If ${dy \over dx}=g(y)$, then ${dx \over dy} = 1 \div {dy \over dx} = {1 \over g(y)}$. Integrate both sides to solve equation. Only add $c$ on one side. Express $e^c$ as $A$. + +### Mixing problems + +$$\left({dm \over dt}\right)_\Sigma = \left({dm \over dt}\right)_{\text{in}} - \left({dm \over dt}\)_{\text{out}}$$ + +### Separation of variables + +If ${dy \over dx}=f(x)g(y)$, then: + +$$\int f(x) \> dx = \int {1 \over g(y)} \> dy$$