Ramakrishnan

Ramakrishnan Vaidyanathan

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11 years, 155 days

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With twenty years of Industrial experience and twenty years of teaching experience, I am now as retired Professor, using Maple to teach mathematics subject for students studying X to XII standards. Published XII Mathematics books.

MaplePrimes Activity


These are replies submitted by Ramakrishnan

@mehdi jafari 

when x and y are between numbers about -100 and 100 this circle like diagram is included ! but when the range is changed to -10000 and 10000 this is not circle is not so in this scale.

The basics can best be understand from the simple logic that a rail though parallel is not so in long view. In a moving train, all objects move backwards in long view. A circle becomes a dot from a long view.

The same is the case here because what is big in a smaller scale becomes negligible in a larger scale.

The same diagram becomes a yellow rectangle in a different scale large in x direction only.

I attach my doc with different plots for different scales. A careful look at these will clear our doubts that it is same except for the view.


 

eq := 8.620689655172415*10^(-16)*(-3.11*10^23*x^2*y^(7/6)-3.92*10^19*y^(25/6)+2.14545039999999*10^29*(0.108e-1*exp(-45.07/y)+exp(-19.98/y^(1/3)-0.935317203476387e-2*y^2)))/(x*y^(2/3)*(x+0.15e-1*y^1.2)); plots:-inequal(eq > 0, x = -10 .. 10, y = 0 .. 100, color = yellow)

 

plots:-inequal(eq < 0, x = -10 .. 10, y = 0 .. 100, color = yellow)

 

plots:-inequal(eq < 0, x = -1330 .. 1330, y = 0 .. 100, color = yellow)

 

plots:-inequal(eq < 0, x = -10 .. 10, y = 0 .. 1000, color = yellow)

 

``


 

Download solveee2_vrk.mwsolveee2_vrk.mw

Very nice. Thank you for the solution and exact command. Ramakrishnan V

@vv 

@Samir Khan 

Thank you very much.

Ramakrishnan V

The report is very good and I appreciate. I am a novice learning maple and would be interested in looking at your worksheet to get to know something about how to get the data in any location with a flow chart in a monitor.

I will be greatful if the relevant worksheet or manual explaining this aspect is made available for use.

A simple example i would be satisfied with is a rectangle with value by the side. If the value is 0, 0.5 or 1, then the rectangle would be in blue, orange or red.

Thanks.

@Rouben Rostamian  

If you permit, may I raise the following points.

Appending and prepending a data in the format one is already used to in a statement may be  more comfortable for the user than adding a new programme code as follows. (No doubt, more subject knowledge the code gives)

piecewise(s < x[1], y[1], op(tmp)[1 .. -2], s < x[-1], op(tmp)[-1], y[-1])

The above code was not by maple on its own. Maple has to be instructed as above by the user.

data2D := [[1, 2], [3, 4], [5, 10], [20, 30], [40, 50]]

data2D := [[0, 2], [1, 2], [3, 4], [5, 10], [20, 30], [40, 50], [50, 50]]

The statement

piecewise(s < x[1], y[1], op(tmp)[1 .. -2], s < x[-1], op(tmp)[-1], y[-1])

is just replaced by 

[0, 2], [50, 50]

for the same answer and new user knows what he wants.

However your points are well taken and I learnt a different perspective of the solution.

Thanks

Ramakrishnan V

@ThU 

My version is maplesim2015 and hence could not get the document properly. Is it possible to change the doc to open in old version and send?. Explanation in words woud be more useful. Relevant help page reference also could be useful for me to try out the excel input and plot that i want.

Thanks.

Ramakrishnan V

@ThU 

Thank you so much. Your document will be very useful to know how to do it.

Ramakrishnan V

@Ramakrishnan 

Dear Professor,

The constants need to be known. As simple as adding another data at the end by repeating the y data value once more for any x data value in order. Also If you want to see the horizontal give a wider range for x and view (y range).

Hope the attached doc is more closer than what was wanted.

 

Kindly check if i am correct, Maple result earlier would give only an abrupt end and not continuously growing.
 

restart; with(LinearAlgebra); with(CurveFitting); with(plots); with(Statistics)

data2D := [[0, 2], [1, 2], [3, 4], [5, 10], [20, 30], [40, 50], [50, 50]]

[[0, 2], [1, 2], [3, 4], [5, 10], [20, 30], [40, 50], [50, 50]]

(1)

``

f := Spline(data2D, v, degree = 1)

piecewise(v < 1, 2, v < 3, 1+v, v < 5, -5+3*v, v < 20, 10/3+(4/3)*v, v < 40, 10+v, 50)

(2)

"->"``

 

 

plot(piecewise(v < 1, 2, v < 3, 1+v, v < 5, -5+3*v, v < 20, 10/3+(4/3)*v, v < 40, 10+v, 50), v = -30.0 .. 60.0, view = 0 .. 50)

 

``


 

Download Modified_spline_for_mapleprime_26062017.mw

Thanks for reviewing and comments. Cheers.

Ramakrishnan VModified_spline_for_mapleprime_26062017.mw

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Thank you very much.

It gives a clear understanding of the possible (one more) mistake that i must be aware of. Short circuiting through the capacitor (component) itself did not occur to me at all!

This also hs given me a confidence to post umpteen such questions that I gave up whiile doing examples as well as my creations.

The answer with the diagram is superb technique; It made me to understand just in seconds!

Cheers. Ramakrishnan V

Hi!

I followed acer idea. It works. I attach the doc with answer.

Hope it clarifies.

Ramakrishnan V
 

restart

``

expr := (x^2-x-12)/(x-4)

expr

(x^2-x-12)/(x-4)

(1)

evalb(expr = simplify(expr))

false

(2)

simplify(expr)

x+3

(3)

``False answer in line (2) confirms that it is not simplified. It is verified by the simplified answer that we get as (x+3)


 

Download rough.mwrough.mw

Excellent update on Maple 2017.

Hope pde enhancements are explained with examples. It will be most useful for all practical applications.
Congratulations.

{a[1](2, 1) = 2/3,

a[2](2, 1) = 2/3,

a[3](1, 1) = a[3](1, 1),

a[3](1, 2) = -a[3](1, 1),

a[3](2, 1) = a[3](2, 1),

a[3](2, 2) = -a[3](2, 1)+2/3,

b[1](1) = 1/4,

b[1](2) = 3/4,

b[2](1) = 1/4,

b[2](2) = 3/4,

b[3](1) = b[3](1), assume 1 or zero and check

b[3](2) = b[3](2) assume 1 or zero and check}

Hi! Thank you very much!

The answer was very useful, though I could not get the directly using the commands given.

The reasons being

(1) My document has data coordinates and not functions like sin, and cos.

(2) Data has x coordinates ranging from 1000.. and therefore constrained command did not give me curves.

(3)command 'discont' troubled me a lot. I am yet to find out what it did? It gave me good mind exercise when answers did not come.

(4) I appreciated MAPLE only once when it gave me a frank msg. The meaning of it was 'Donot give me y options, I know what to do?". I had to delete y = -4..4!

It was worth trying out your suggestions since I am exposed more to maple mind. 

I also got a crisp suggestion from my close friend. I quote the same here

Quote, " then do exactly those three steps. Give each set of points a name such as d1, d2,...

Use the least-squared command four times, and give the resulting expressions the names c1,c2,...

Then, use the plot command plot([c1,c2,...],x=...)" unquote.

I followed this meticulously (not making mistakes, reading each alphabet, balancing parenthesis and curly braces..).

This also gave me several learnings about how agile we have to be while using MAPLE.

Finally I got the answer from him. I am attaching the doc link as well as doc below.

Thank you both
 

 

data1 := [[1000, 20], [2000, 21], [3000, 32], [4000, 23], [5000, 23]]

``

Equn1 := CurveFitting[LeastSquares](data1, x, curve = y)

52/5+(179/17500)*x-(11/7000000)*x^2

(1)

data2 := [[1000, 25], [2000, 26], [3000, 33], [4000, 25], [5000, 24]]

Equn2 := CurveFitting[LeastSquares](data2, x, curve = y)

18+(549/70000)*x-(19/14000000)*x^2

(2)

data3 := [[1000, 26], [2000, 27], [3000, 34], [4000, 26], [5000, 25]]

Equn3 := CurveFitting[LeastSquares](data3, x, curve = y)

19+(549/70000)*x-(19/14000000)*x^2

(3)

data4 := [[1000, 27], [2000, 28], [3000, 35], [4000, 27], [5000, 25]]

Equn4 := CurveFitting[LeastSquares](data4, x, curve = y)

97/5+(17/2000)*x-(3/2000000)*x^2

(4)

``

y := a*x^2+b*x+c

a*x^2+b*x+c

(5)

``

``

 

 

``

``

 

 

plot(Equn2, x = 1000 .. 5000)

 

plot([Equn1, Equn2, Equn3, Equn4], x = 1000 .. 5000)

 

plot([Equn1, Equn2, Equn3, Equn4], x = 1000 .. 5000, color = [red, blue, green, gold], size = [800, 500], scaling = unconstrained, discont)

 

 

Dear Professor, I got the answer.. Thanks. Regards.

 

Ramakrishnan V


 

Download Doubt_AnsweredByRobert.mwDoubt_AnsweredByRobert.mw

very much.

Ramakrishnan V

Very useful command that can be used to plot curves of generat form y=mxk +c

Explore(plot(m*x^k+c));

Explore(plot(m*x^k+c), parameters = [[c = 0 .. 10, controller = slider], [k = 0 .. 10, controller = slider], [m = 0 .. 10, controller = slider]], loop = never, size = NoUserValue, numeric = false, echoexpression = true)

(1)

y = 5*x^5+5

y = 5*x^5+5

(2)

"->"

 

``


Download explore_command.mw

Ramakrishnan V

rukmini_ramki@hotmail.com

There are experts who could have answered your question if the exact problem is mentioned instead of just Navier Stokes equation which involves density, viscosity, velocity, pressure all as variaables. A complete problem with Boundary and Initial conditions would help maple experts to help us. Hope Maple experts would be ready.Thanks.

Ramakrishnan V

rukmini_ramki@hotmail.com

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