Partial differential equations Definition and 144 Threads

At my school, Physics majors are the only ones who HAVE to take PDE, math majors and engineers have the option as an elective, but none of them do that because it has the reputation of being the most difficult math course at my school. I'm going into Calc III in the spring, then DE is next...

Hi guys, I am a Erasmus student in Vienna. Due to the difference between the plans in my home universtity and Vienna, I have to deal with having to take Parcial differential equations without having done Differential Equations 1 or 2. In accordance with my university, I should take here...

Homework Statement w= f(x,y) x = u + v Verify that Wxx - Wyy = Wuv y = u - v Homework Equations The Attempt at a Solution I know how to find Wu or Wv but I have no idea on how to proceed to find the 2nd order derivative (or 3rd,4rth etc.. obviously). I...

Can anyone help with these problems? I have no idea where to start. What is the general approach? Determine the solution of ∂ρ/∂t = (sin x)ρ which satisfies ρ(x,0) = cos x. Determine the solution of ∂ρ/∂t = ρ which satisfies ρ(x,t) = 1 + sin x along x =-2t. Relevant equations: ∂ρ/∂t +...

Consider a string of length 5 which is fixed at its ends at x = 0 and x = 5. The speed of waves along the string is v = 2 and the displacement of points on a string is defined by the function f(x,t). At the initial time the string is pulled into the shape of a triangle, defined by f(x,0) =...

I have been given an equation : r^2 ( d^2R/dr^2) + 2r(dR/dr) - lambda*R = 0 It says to assume R~ r^β Then i can't seem to spot how from that information we can produce this equation: β(β − 1) rβ + 2β rβ − λ rβ = 0 Any help would be appreciated, thanks.

Ok so here's my summarized story. At the end of summer should be the start of my Senior year, but i dropped out and started college a year ago. I taught myself Calc I in two weeks while taking 18 credit hours and CLEPed out of it my first semester and received a 99.4% in Calc II the next...

The local university offers both partial differential equations and higher geometry I (both of which seem equally interesting to me!), but they are only offered during the same time! As I'm most likely going to major in physics when I go to college, which class would have more applications to...

hello, i just want to ask if mathematica 7 can solve nonlinear second order partial differential equations. i tried solving it with DSolve but it kept on giving me the question back as the output...please is there any way or syntax for solving it on mathematica 7?...thanks for any suggestions.

Hey.. I ran across some problems and the notation used is a little different from what I've seen before. considering U(x,y)=X(x)Y(y) Sometimes I'll see Uxx for \frac{d^{2}u}{dt^{2}} which equals X''Y Or Ux for \frac{du}{dt} which equals X'Y But what about U'x Is that a redundant way of...

Last night in a lecture my professor explained that some partial differential equations are used to observe events on minimal surface (e.g. membranes). A former advisor, someone that studied differential geometry, gave a brief summary of minimal surfaces but in a diffy G perspective. 1.)...

Hello, I joined a class on Partial Differential Equations 3 or 4 lectures late, so I have missed the classes outlining how to solve the simplest forms of them. I am trying to understand the textbook, but so far it is not going so well for me, so I just need to ask some questions about the...

can anyone help me to solve this equation ?. is this equation linear or not? knowing, this equation represents the equation of motion for frame members for materials which have different moduli in tension and compression (civil engineering). "EI" ("x,t" ) ("∂" ^"4" "u" ("x,t" ))/〖"∂x" 〗^"4"...

Is this linear homogeneous, linear inhomogeneous etc... u_{t}-u_{xx}+xu=0 From that first one I get this \frac{u_{t}-u_{xx}}{u}=-x which I'm not sure is linear. Edit: Similar questions involve the following equations: iu_{t}-u_{xx}+\frac{u}{x}=0 and u_{x}+e^{y}u_{y}=0 Another Edit: I...

Homework Statement There are two separate problems: 1) Consider the cube region defined between 0 and L in each of the three dimensions. A scalar field inside this cube satisfies \Delta \Psi = -c\Psi . c = 40/L2. The boundary conditions are specified. \Psi = 0 on the planes y =0/L, x=0/L...

solve the heat equation ut = kuxx -infinity < x < infinity and 0 < t < infinity with u(x,0)= x2 and uxxx(x,0)= 0 first i showed that uxxx(x,t) solves the equation (easy part) the next step is to conclude that u(x,t) must be of the form A(t)x2 + B(t)x + C(t). i...

I want to self-study partial differential equations. i have done some pure math course but I wish to keep proofs to minimal. If possible I don't want to be bothered with PDE proofs in my self study. Instead, I want to learn how to apply and solve PDEs. the ultimate goal is to prepare myself my...

Consider the following function of space and time for a propagating plane wave were nonlinear effects are included via a constant "B" u(x,t) = u[t - x/[c + Bu(x,t)]] show that u(x,t) satisfies a first order non linear PDE.

i'm interested in taking this course althought i heard it's harder but i really want to try it. do i need partial for engineering? or just ordinary

Partial differential equations represented as "operators" Homework Statement Partial differential equations (PDEs) can be represented in the form Lu=f(x,y) where L is an operator. Example: Input: u(x,y) Operator: L=∂xy + cos(x) + (∂y)2 => Output: Lu = uxy+cos(x) u + (uy)2 Homework...

Homework Statement Find the link between constants \omega and \beta so that http://www4e.wolframalpha.com/Calculate/MSP/MSP181963g2e5f4i43d3b00005ief8e24920ah323?MSPStoreType=image/gif&s=20 is a solution of \frac{\partial^{2} u}{\partial x^{2}}=2\frac{\partial u}{\partial t} (A & B are...

he said the class average was 57% with many fails then how did he ace it? i hear partial differential equations is very hard but does anyone sucessful know his secret to success?

Why is it impossible to find ALL of einstein's equations in one place? well I suppose its irrelevant, I'd just like to know what math I have to do to define the energy-momentum tensor for a particle if I know say... its energy and momentum, or is that illegal? I'm struggling to grasp general...

Hi. I'm not so well-versed in the topic of partial differential equations, but the following question has arisen. Suppose that for some unknown function u(s, t) of two variables, we have a set of differential equations \left\{ \begin{matrix} u_s(s, t) & {} = f(s, t, u(s, t)) \\ u_t(s, t) & {}...

Hi, why does the sign function need to be used in the following? --- The given equation is y_tt = 4 y_xx 0 < x < pi, t>0 where y_tt is the 2nd derivative with respect to t, y_xx is 2nd wrt x Boundary conditions y(0,t) = 0 and y(pi,t) = 0 And initial conditions y_t (x,0) = 0 = g(x) y(x,0) =...

Homework Statement (a) Solve the equation yu_{x} + xu_{y} = 0 with the condition u(0,y) = e^{-y^{2}}. Okay. My tex has gone wrong. Those are supposed to be subscripts in the the equation. I'm not sure why they aren't. (b) In which region of the xy plane is the solution uniquely...

Homework Statement Show that u=f(2x+y^2)+g(2x-y^2) satisfies the equation y^2 d^2u/dx^2 + (1/y) du/dy - d^2u/dy^2=0 where f and g are arbitrary (twice differentiable) functions. Homework Equations The Attempt at a Solution I came up with fxx=0 fyy=2 gxx=0 gyy= 2. But didn't...

Guys i need some advice, for the Spring semester i have to take 2 math courses but there is one that i am not sure if i should take it. that course is Partial Differential Equations, this is the description for MAP 4401 : A second course in differential equations. Topics may include:Heat...

Dear all, I'm interested in partial differential equations. I would like to find an introductory book with solutions methods of known mathematical phisycs equations, rigorous but no high-tech math, and one a more advanced in terms of math. Do you have any text to recommend? Thank you for...

"A PDE satisfied by a suitably differentiable function u of the independent variables x1, ... ,xn, is said to be linear if u and its partial derivatives only occur linearly and, posibly, with coefficients that are functions of independent variables. This PDE may, or may not, contain a function f...

Hi, I'm barely a high school senior who is somewhat overwhelmed by a univ. course. Anyway, we are just learning to solve some basic PDEs using the method of separation of variables. With this method (and the questions we are given) we check three cases to find the eigenvalues of Sturm-Liouville...

Hi, I'm an undergrad student on Mechanical Engineer, right now I am taking my last math class in my curriculum, Numerical Analysis. I was thinking of taking the partial differential equations class, that is not in my curriculum, to improve my math skills and knowledge. But my question is...

I was wondering what you guys think of my textbook. My textbook is called: A First Course in Differential Eqations (Eight Edition) Author: Dennis G. Zill ISBN: 0534418783 I have been using this book for my DE class, and I do not feel like I am really learning anything. This class...

SR uses spacetime diagrams which is what is used to solve hyperbolic and parabolic PDEs but what is the connection between SR and PDEs? Are there PDEs in SR? I have done a first course in SR using Taylor and Wheeler but don't seem to recall any.

Homework Statement Solve the partial differential equation using laplas transforms: U`(x)=a^2*U``(t) given U(x,0)=2 There are more initial conditions but i am just trying to get to the general solution The Attempt at a Solution First take laplas of the equation. Then I am...

Hi there, Does anyone know of a proof of why, in partial DEs, one can assume the existence of variable seperable solutions, then take the linear combination of all of them to be the general solution? Why can't there be any other funny solutions that fall outside the space spanned by these...

I have a 2nd order homogenous P.D.E: (d^2)V/((dx)^2) + (d^2)V/((dy)^2) + 6(d^2)V/(dx dy) = 0 where all derivatives are partial derivatives. I need to transform this to form a*(d^2)f/(dX^2) + b*(d^2)f/(dY^2) = 0 where a, b are constants and the derivatives are again partial, and f(X,Y) =...

I need help with Diffusion on the Whole Line. For instance, my first homework problem is: Solve the diffusion equation Ut = Uxx with the initial value conditions phi(x) = 1 for |x| > l, phi(x) = 0 for |x| < l. I don't know what to do, and the book I'm using isn't the least bit enlightening.

There have been a number of questions on Partial Differential Equations. Within the Math & Science Tutorials (https://www.physicsforums.com/forumdisplay.php?f=160 ) are - http://www.physics.miami.edu/nearing/mathmethods/ - link in thread (Mathematical Tools for Physics) posted by ranger, which...

Solve using separation of variables and find particular solution \frac{\partial^2 u}{\partial t^2} - \frac{\partial^2 u}{\partial x^2} - u = 0 \ for\ 0 <x<1, t >0 \frac{\partial u}{\partial t} (x,0) = 0 0,t) = u(1,t) = 0 to assume u(x,t) = X(x) T(t) then \frac{X''}{X} = \frac{T'' -...

Does anybody know of any decent books on PDEs? I'm looking for one that has a good amount of solved problems. I really need one. My class is using Yehuda Pinchover and Jacab Rubinstein's An Introduction to Partial Differential Equations. It's just not enough for me.

Here is one of them - i posted it in another thread and i am getting help in there https://www.physicsforums.com/showthread.php?t=91781 this is another of my problems Show that if C is a piecewise continuously differentiable closed curve bounding D then the problem \nabla^2 u= -F(x,y) \...

Hi, my engineering degree does not require a partial differential course. However, one of my calculus professors suggested it may be important when applying for a masters. I was thinking of taking this course and maybe special functions... would it really be useful? It would be a lot of work...

I'm currently taking a symmetry analysis course. It is really interesting. I would recommend it to any math major or anyone interested in ODE's and PDE'S. I am enjoying it very much.