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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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Quiz 1 / Re: Quiz 1 - Variant 2E - Problem 2
« on: January 29, 2021, 11:45:32 AM »
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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Quiz 1 / Re: Quiz 1 - Variant 2E - Problem 1
« on: January 29, 2021, 11:41:45 AM »
Indeed, this equation has $u=0$ as a solution but the notion of "homogeneou"s does not apply to nonlinear.
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Quiz 1 / Re: LEC9101 Quiz#1 B Question#2
« on: January 28, 2021, 08:01:17 PM »
not $sin(x)$ but $\sin(x)$ (it is \sin, \cos, \ln, \sum, \int and so on for "math operators")
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Chapter 1 / Re: Math Notation Question
« on: January 24, 2021, 07:56:05 AM »
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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Chapter 3 / Re: Rouché's Theorem
« on: December 12, 2020, 06:25:05 PM »
You need to indicate that there are no zeroes on $\gamma$
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Chapter 7 / Re: Drawing phase portrait with complex eigenvalues question
« on: December 01, 2020, 08:46:13 PM »
"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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Chapter 4 / Re: Section 4.4 Past Final Exam Question
« on: November 22, 2020, 05:19:33 AM »
There could be misprints
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Chapter 4 / Re: General Question related to something in Section 4.1
« on: November 13, 2020, 12:54:44 PM »
For higher order equations it is covered in MAT244-LEC0201-W6L2 (see modules). It is mandatory material.
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Chapter 4 / Re: 4.2 question 28
« on: October 25, 2020, 01:13:50 PM »
you need to write it, if you hope for any answer
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Test 1 / Re: 2020TT1 Deferred Sitting #1
« on: October 15, 2020, 08:17:16 AM »
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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Test 1 / Re: Abel's Theorem
« on: October 15, 2020, 08:11:23 AM »
Of some fundamental set (remember a constant factor!)
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Chapter 2 / Re: Section 2.2 "closed form" Qs
« on: October 13, 2020, 09:35:57 AM »
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 $\frac{1}{(1-z)^m}$ ,...