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**Chapter 3 / Re: 3.1 Heaviside step function**

« **on:**February 09, 2021, 05:11:06 AM »

Everything is correct. You need to look carefully at limits in the integrals

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Everything is correct. You need to look carefully at limits in the integrals

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Try to avoid high-riser notations. Several years ago I was a referee for a paper which used notations like this $\widehat{\dot{\widetilde{\mathcal{D}}}}$ and sometimes this little pesky dot was missing

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Indeed, this equation has $u=0$ as a solution but the notion of "homogeneou"s does not apply to nonlinear.

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not $sin(x)$ but $\sin(x)$ (it is \sin, \cos, \ln, \sum, \int and so on for "math operators")

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it depends: if $u=u(x)$ you can use either. If $u=u(x,y)$ then **only** partial derivative would be correct.

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You need to indicate that there are no zeroes on $\gamma$

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"How ellipses wouls look like" means the directions and relative size of their semi-axis. See frame 4 of MAT244_W8L3 handout

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There could be misprints

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For higher order equations it is covered in MAT244-LEC0201-W6L2 (see modules). It is mandatory material.

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you need to write it, if you hope for any answer

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Indeed, instead of $\log(\pm w)$ with $+2\pi mi$ we write $\log(w)$ with $+\pi mi$ since $\log (-w)=\log(w)+\i i$

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Of **some** fundamental set (remember a constant factor!)

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Yes, some of them are geometric series, and some of $e^{z}$, $\sin(z)$, $\sinh(z)$ and so on. However some can be derived from those, ether by substitution (f.e. $z^2$ instead of $z$), some by integration, differentiation, multiplication by $z^m$ or combination of both. F.e. consider geometric $\dfrac{1}{1-z}$. Integratinfg we can get power series for $-\Log (1-z)$, diffeerentiating for $\frac{1}{(1-z)^m}$ ,...