Insights Blog
-- Browse All Articles --
Physics Articles
Physics Tutorials
Physics Guides
Physics FAQ
Math Articles
Math Tutorials
Math Guides
Math FAQ
Education Articles
Education Guides
Bio/Chem Articles
Technology Guides
Computer Science Tutorials
Forums
Intro Physics Homework Help
Advanced Physics Homework Help
Precalculus Homework Help
Calculus Homework Help
Bio/Chem Homework Help
Engineering Homework Help
Trending
Featured Threads
Log in
Register
What's new
Search
Search
Search titles only
By:
Intro Physics Homework Help
Advanced Physics Homework Help
Precalculus Homework Help
Calculus Homework Help
Bio/Chem Homework Help
Engineering Homework Help
Menu
Log in
Register
Navigation
More options
Contact us
Close Menu
JavaScript is disabled. For a better experience, please enable JavaScript in your browser before proceeding.
You are using an out of date browser. It may not display this or other websites correctly.
You should upgrade or use an
alternative browser
.
Forums
Homework Help
Calculus and Beyond Homework Help
Method of characteristics. pde. limits of integral question
Reply to thread
Message
[QUOTE="binbagsss, post: 4972979, member: 252335"] [B]I'm using the method of characteristics to solve a pde of the from ## au_{x}+bu_{y}=c##[/B] [I]where ## a=\frac{dx}{d \tau} , b= a=\frac{dy}{d \tau}, c=a=\frac{du}{d \tau}## where initial data is parameterised by ##s## and initial curve given by ##x( \tau)=x_{0}(s)##, ##y( \tau)=y_{0}(s)## and ##u( \tau)=u_{0}(s)## at ## \tau = 0## .[/I] [B]Question: [/B] Questions been given so far on my course have ## c ## given explicitly. I'm trying to solve: ##u_{x} + u_{y} =f(x,y)##. subject to initial data ##u=g(y)## on ##x=0##, functions ##f## and ##g## given. [B]Attempt:[/B] Solving ## \frac{du}{d\tau} = f(x,y)## i get ##u= \int f(x(\tau),y(\tau))d\tau+ u_{0}.## [B]QUESTION: [/B]In the solution the limits of this integral run from ##\tau## to 0. I'm not used to doing these with limits, and if I'm honest, I'm totally clueless where this comes from... can someone please explain the integral limits to me? usually when it's just given explicitly I just integrate. So the solution has : ##u= \int^{\tau} _{0} f(x(\tau '),y(\tau ')) d\tau '+ u_{0}## [B]Many thanks in advance.[/B] [/QUOTE]
Insert quotes…
Post reply
Forums
Homework Help
Calculus and Beyond Homework Help
Method of characteristics. pde. limits of integral question
Back
Top