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Chapter 3 / Re: Chapter 3.2 Problem 9
« on: February 06, 2022, 02:21:30 PM »
Indeed. You got it!
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Chapter 3 / Re: Homework Assignment Week5
« on: February 06, 2022, 01:53:33 PM »
Thanks! Fixed online TB
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Chapter 3 / Re: Chapter 3.2 Problem 9
« on: February 06, 2022, 01:25:46 PM »
You almost there. Think!
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Chapter 2 / Re: S2.2 Q1
« on: February 02, 2022, 06:25:02 PM »- If you do not know this integral you need to refresh Calcuus I. one of basic integrals. Or have a table of basic integrals handy.
- Since $x^2+y^2=c^2$ is a circle, you can substitute $x=c\cos(s)$ and $y=c\sin(s)$ and then observe that $s=D-s$. It gives you the answer, less nicely looking than the one you wrote.
- Expressing $x, y$ through $t,c,d$ you can express $C=c\cos(d)$ and $D=c\sin(d)$ through $x,y,t$ which would give you that nice answer.
Write \cos , \sin , \log .... to produce proper (upright) expressions with proper spacing
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Chapter 2 / Re: Ut+xUx=0
« on: February 01, 2022, 12:16:37 PM »
As $x>0$ it is a correct calculation. However $f(xe^{-t})$ re,mains valid for $x<0$ while $f(t-\ln (x))$ does not.
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Chapter 2 / Re: f(x) in Method of Characteristics
« on: February 01, 2022, 12:12:52 PM »
Yes, there are many answers which are correct because they include arbitrary functions (and in ODE arbitrary constants)
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Chapter 2 / Re: Online textbook, Chapter 2.6, example 7
« on: February 01, 2022, 05:56:58 AM »For the middle region in red, since $\psi(x - \frac{t}{3})$ is undefined,It is defined, because on the line $\{x=-t, t>0\}$ we have not 1 but 2 boundary conditions, so in the domain $\{x>-t, t>0\}$ we have essentially a Cauchy problem with the date on the line consisting of two rays: $\{x>0,t=0\}$ and $\{x=-t, t>0\}$.
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Chapter 1 / Re: HW1 Problem 1 （2）
« on: January 29, 2022, 05:35:01 AM »
You should ask everybody, not just me. And the question was a bit different anyway: to classify an equation
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Chapter 1 / Re: HW1 Problem 6 （41）
« on: January 28, 2022, 01:41:36 AM »
Yes, it is correct: $u=H(x)+m(y,z)$ where $H$ and $m$ are arbitrary functions.
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Chapter 1 / Re: Question about the posted solution for HW1 3c
« on: January 27, 2022, 03:59:38 PM »
It was a misprint; it should be $e^{u(x',y)}$ in the denominator
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Chapter 2 / Re: Chapter 2.2 problem 2
« on: January 27, 2022, 08:04:10 AM »
Both signs. What are curves $x^2-y^2=C$?
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Quiz 1 / Re: Second Order PDE Classification on Quiz 1?
« on: January 24, 2022, 05:48:42 AM »
Please post non-mathematical questions in Quercus discussions.
Please read description of Quiz 1.
Please read description of Quiz 1.
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Chapter 2 / Re: Transport Equation Derivation
« on: January 24, 2022, 05:46:09 AM »
Then your best shot would be
- either to ask during Prof Kennedy's Office hours
- or to formulate the problem and define everything (that is $u, v, S, \tilde{S}$) here by yourself without screenshots
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Chapter 2 / Re: Transport Equation Derivation
« on: January 19, 2022, 05:06:34 AM »
It would be really helpfull if you explained where you took this from (if online TextBook--then section and equation number, if lecture then which lecture and which part).