tsunamiBTP

I am running MAPLE 12 on WINDOWS XP & recently updated my JAVA and now anytime I try to use HELP, MAPLE hangs.  I have to enter the TASK MGR to terminate MAPLE, because I cannot do anything else.

Anyone have a FIX on this?

I have a nonlinear partial diff eq which I am sure has been categorized.  How do I go about finding literature on the eq & the approach to solve it.  I have visited various websites that have catalogs of nonlinear partial diff eq's.  The problem is notation is so NONSTANDARD I have no IDEA what I am reading.  I have included a PDF eq_of_choice.pdf with my notation which I am familiar with. ...

Included below is vector partial diff eq I am working with.  To get rid of the time deriv's I took the LaPlace transform & the remaining spatial eq in the s-domain is listed.  To make matters simpler I set beta = 0 to get rid of the curl of the field.  What remains is essentially the Helmholtz eq.  To simplify further I just found the homogeneous soln for the x direction only.

As can be seen the eigenfunctions are exponentials with s beneath...

Not sure why pdsolve is choking on my input.  The file is attached below.  It works fine for my first expression if the term without the square root sign is not included.  When I include that term as you will see at the end it simply does nothing?

Any advice??

I was successful @ splitting the coupled eq into the 3 constituent PDE's but have been unsuccessful to get MAPLE to generate the characteristic solutions except for the 1st one for X which is the basic solution to the Helmholtz eq.

Can someone with more savy with MAPLE verify whar I have so far & advise me how to proceed to solve for Y & Z?  I have uploaded my file.  My expereince with MAPLE vector calc package is limited.

appreciate the assistance

I am working with a 3 dimensional vector partial diff eq that resembles the Helmholtz equation, but there is a curl of the vecotr field as the middle term.

ie-->LaPlacian(F)+2beta*gamma^2*curl(F)+gamma^2*F = 0

Anyone have knowledge or references for me to look over to solve this equation?

I am attempting to define the rotation angle of an ellipse about the cartesian coord frame @ (0,0).  I am pretty sure the slope of the tangency vector @ both the major & semi-major axis is orthogonal to the vector originating from the origin from (0,0) with a length of a or b depending on which axis I am using.

My thought was in the case of the major axis that x = a*cos(theta) & the slope of the vector emanating from the origin is tan(theta).  So if I set dy/dx = -1/tan...

I input into MAPLE the following differential eq & it returned that it is classified as an Emden-Fowler Differential Equation:

r^2*F"+1/r*F'-k^2*F=0   where F is a function of r

MAPLE was able to generate a solution.  I am attempting to figure out how this eq is actually solved & I typed in Emden-Fowler into the SEARCH window on this website & got ZERO results.

See the post link below which gives the ability to find the gradient of a vector, not a scalar field.

http://www.mapleprimes.com/forum/gradientvectornotgradientscalarfunction

The solution was to use the Jacobian command.  Now I need to take the time derivative of that expression because now the velocity is a function in time.  Unfortunately, MAPLE wants an algebraic expression for d/dt operations.  What command to I need to use for this operation??

Operations on matrices that presumably contain information on a physical field such as stress, voltage potential, or temperatures should essentially be the same between tensor vs vector operations is my understanding.  The only difference is conventions in how the expressions are conveyed on paper, ie- indicial vs vector notation?

If I am correct is the gradient of a the 3X3 tensor each element on the same row differentiated with each coordinate variable x, y ,z or is that a different operation?  I am unable to find the correct operation or I am not using the MAPLE command correctly to get an output.  I did load the Vector Calculus package.

What is my problem??

I replied to the following thread but after further thought I probably start a new thread:

http://www.mapleprimes.com/forum/multivariate-directional-derivative-0

I am attempting to get MAPLE to generate indefinite integrals that are of the form:

exp(-k[r^2-a^2*cos(x)]^0.5)

from fundamental calculus principles I might set u = [r^2-a^2*cos(x)]^0.5 which then should yield du/dx = 1/2*(a*sin(x)/[r^2-a^2*cos(x)]^0.5).

Then if my math is correct the result should end up:

2*(r^2-a^2*cos(x)]^0.5)*exp(-k[r^2-a^2*cos(x)]^0.5)/[-k*a*sin(x)]

I am attempting to obtain the analytical form of the integral of [exp(-cx)]/[a^2+x^2]^1/2 with respect to x.  Unfortunately, this form does not appear in any of the indefinite integral tables that I have been perusing.  I am attempting to utilize MAPLE but it simply outputs the integral in symbolic form & does not generate the actual function.

Anyone have any leads where I might find the correct form of this integral or how to get MAPLE to cooperate & generate the expression form me in a form that is inddtuitive???

I have multiple XY pairs from multiple sensor data which I would like to display on the same plot.  I can easily do this in MATLAB, but referencing Chapt 5 of the User's Manual indicates ways to plot multiple plots when plotting relations, but nothing I found pertains to actual numeric data sets.  The only plot command I found was "PointPlot" & it appears it can only plot a single data set at a time.

Any suggestions?