Thank you. It is useful. Cheers. Ramakrishnan V

Thank you Dharr,

It will be useful when explaining to students, division and remainder..

RK

For integral problems if graphical plots are included by default with default parameter values where possible would be great help to Design of Experiments experts and for those wanting to use RSM (Response Surface Methods) for optimizing parameters for product quality. One need to learn a deep extent to do these things in maplesoft. It is just an opinion. The product is anyway an excellent tool and answers complicated problems as of now. Cheers. Ramakrishnan 

Is not this simple solve command give the solutions?

I have attached the doc for help.

Download solve_polynomials.mw

@mapleatha 

Dear sir,

Text font can be anything as you like.

I have used Vivaldi style font here.

Hope this is useful.

Ramakrishnan,
plots:-textplot({[4.2, 1.9, sin(nprintf(`#mn("%a°");`, 30))]}, symbol = point, color = black, font = ["Vivaldi", "Bold", 25]);

Download NumberTextPlot.mw

@Rouben Rostamian  

Dear sir,

In my opinion, (3,4) and (4, 3) are pairs of numbers giving the domain points by coordinates (x, y).

We say (x, y) < (3, 4) which means x takes values less than 3 and y takes values less than 4

OR or (x, y) < (4, 3)  which means x takes values less than 4 and y takes values less than 3

For all the points in the domain, valid function can be prescribed. the function gives valid unique numbers for each pair of the points in the given domain.

Comparing two coordinate values can be done differently as mentioned , though not done generally.

Comparing coordinates (3, 4) < (4, 3) results in false as 4 is >3.

Comparing coordinates (3, 4) < (5, 7) results in true as 3 < 5 and 4 < 7.

Thanks.

Ramakrishnan V

@mmcdara 

Dear sir,

The domain data and function described by me are just a sample and not to do with any expected results.

In fact I was interested in feeding the doamain ( x and y range and the valid  function for this domain) to get the expected image from the maple.

In fact carl love has given a solution to get a plot of hemisphere, which is the answer for my earlier question.

I wanted to know  how to give two dimensional piece wise function in maple for the same and plot.

I attach relevent documents just for reference.

plot of a hemisphere with input domain (x,y) as a circle of radius 3 cm and function representing hemisphere (sphere) as mathematical relation x sq + y sq = r sq

plot3d(-sqrt(-x^2 - y^2 + 9), y = -sqrt(-x^2 + 9) .. sqrt(-x^2 + 9), x = -3 .. 3, scaling = constrained)

recommended by Dr. Robert Lopez is a very good way of describing the domain and function and it displayed perfect hemisphere (upside as well as down side).

The plot command recommended by you is very interesting, but an explanation for the plot3d statement would very much help me. Like the " 'and ' and ' + ' notation purpose. What does u stand for ? Are all u, v, a and b refer to intervals?

Thanks for the immense help.

Ramakrishnan V

plot3d(-sqrt(x^2 - y^2 + 9), y = -sqrt(-x^2 + 9) .. sqrt(-x^2 + 9), x = -3 .. 3, scaling = constrained);

@Carl Love 

Thank you very much.

This command is super useful.

Ramakrishnan.

@ 

Dear Crossley Mjojo,

I understand that you have a problem at hand.

The problem is whether to find the variable values or prediction parameters.

Here x is the location and T is the temperature at this location x. These two are variables as they vary with locations.

The parameters here are r and s as they define the complicated equation suggested by you for the application you are trying to understand. They are fixed by the domain of (x, T).

Therefore there are two problems at hand.

(1) To find the prediction equation (r , s and the equation)

(2) Using the prediction, finding the T values at various S.

No realtime applications in my opinion involve more than a second order differential equation.

Since you want to find the s value, either you need as many conditions as there are variables unknown or the field data (x, T).

Once the formation is known, then Maple will do it for you instantly. Maple needs what you want and how do you want?

Hope these opinions shared here contribute to a little more clarity in understanding.

Cheers.

@Carl Love 

Thank you sir. I will certainly follow the suggestion.

Ramakrishnan V

I have posted the following msg with youtube URL explaining my example for adding a doc to my post.

Hope this will be useful. Thanks.

Ramakrishnan V

This doc is just an example for uploading with my post.Sample_doc_for_adding_to_my_Mapleprime_Post.mw

The above doc/worksheet can be clicked and viewed.

Youtube URL is given below. 

https://www.youtube.com/watch?v=cGNOGxXDvWM&t=293s

This question and the response makes it clear that all solutions can be obtained by playing with mouse clicks and observe what maple says. In this way, I have solved many doubts without wastine much time and at the same time learning new rules followed and behaviour of maple.

Thank you both the question raiser and respense sender.

Cheers.

Ramakrishnnan V

@Carl Love 

ODEs are mentioned as PDEs. It is a mistake, I made. My Apologies. I stand corrected. Thanks.

Regarding, the directions, I get opposite directions with just "<" in place of  ">" or vice versa. This may not be the solution. but best one is your code with newer version of maple.

Cheers.

Ramakrishnan V

@Carl Love 

Great work. Congratulations.

I am sure, complete solution is given to problem. I just added one more arrow for ics3 with cyan color.

plots:-display([PrePlot, Arrows(ics1, color = red), Arrows(ics2, color = blue), Arrows(ics3, color = cyan)]) It worked for all the curves therein!!.

Just with one word, one curve added!! So simple a solution, once understood!

It is worth taking as an example problem for teaching PDE plot! in advanced mathematics.

Cheers.

Ramakrishnan V

@Carl Love 

Thank you so much

Ramakrishnan V