Krithika Suresh

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10 years, 343 days

MaplePrimes Activity


These are answers submitted by Krithika Suresh

Hi again,

In case you were interested, I'm attaching a worksheet that shows you how you can use Maple's Jacobian Task template to compute the Jacobian matrix and determinant for your question.

 

Hope this helps!

Krithika

Hi Jose,

This is not a bug in Maple. The mysterious exponents you are seeing in the Jacobian is a result of introducing an empty symbol into your expressions by using the double back quotes (``). You have used the empty symbol in two sections of your worksheets for what I am assuming is formatting purposes. These "blanks" are being raised to the 4th power and that is why you see what seemed to be misplaced exponents.

If it is important that you output the expressions in a formatted form then I would recommend that you assign the expanded form of your expressions to different variables and use those in your computations, while outputting the factored forms. This will allow you to retain your formatting, while getting rid of your "mysterious" exponents. 

I have attached a worksheet that suggests how you might go about doing this.

I have replaced your for loop to produce your expression without the empty symbol. As well, you want to avoid the use of xGCD*``*xfactor because that introduces a spurious blank as part of the product.

 

Please let me know if you have further questions!

 

Krithika

Hi,

I have attached a worksheet that shows you how to combine 2D and 3D contour plots. If you did not mean for the 3D plot to be a contour plot then you can define the command to be of the form plot3d(...) instead of contourplot3d(...).

The worksheet contains a procedure called to3d which transforms a 2D plot on the xy-plane to a 3D plot. In the combined plot, the 2D plot will appear at whichever z-level you defined in the procedure. (i.e., in the procedure transform((x,y)->(x,y,0)) you can vary the last integer to move the 2D plot up or down the z-axis).

For more information on the procedure and combining 2D and 3D plots execute ?transform in your Maple worksheet or look it up in Maple Help.

Please let me know if you have further questions or if these commands did not work for your particular question.

 

Krithika

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Hi!

The numeric PDE solver in Maple will handle only evolutionary equations (i.e., parabolic and hyperbolic PDEs (wave and heat equations)) with one spatial dimension.

The equation you are trying to solve is elliptic and Maple does not have a numeric solver for this problem.

 

- Krithika

Hi!

Maple has the ability to compute the Smith Normal form for an m x n matrix and the Jordan Canonical and Rational Canonical (Frobenius) form for an n x n matrix.

It is hard to conceive of a Jordan form for anything orther than a square matrix. Could this have been a trick question?

Hi Jose,

I'm glad that we were able to clear up the simplification issue!

When using `` I was referring to the "Empty Symbol". Just in case you were wondering what Maple uses it for, the current version of Maple lists the following in its Help Menu:

A common use of the empty symbol is to display expressions in an unsimplified form, which Maple would normally automatically simplify. It can also display variables with their values substituted, in unsimplified form.

Have a great day!

 

Krithika

Hi Jose!

Maple does not directly factor the integer coefficients of an expression. As you found out, when you enter 1/4*(a+b+c) Maple outputs 1/4*a+1/4*b+1/4*c.

I've attached a worksheet that displays how you can maintain the expression 1/4*(a+b+c) without Maple simplifying it. I have also included how you can use use commands to factor out the integer coefficients of an expression.

For beginner Maple users, I have also included how to factor an expression using Maple's Context Menu.

Execute ?`` , ?content, ?primpart in your Maple worksheet for more information.

Note that to get the labels (e.g. (1)) press Ctrl+l (lowercase L) and enter your label reference.

 

Hope that helps!

Krithika

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Hi,

I've attached a worksheet that goes through some suggestions for how to solve your questions.

Let me know if you have further questions.

Have a great day!

 

Krithika

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Thanks for letting us know!

The best way to get the simplified answer would be to open the Context Menu (right-click on the integral expression) and select Simplify -> Simplify.

- Krithika

Hi,

Thank you for your feedback!

Another way that you can easily get the quotient and remainder in polynomial division is by inserting a Task Template into your worksheet.

  1. Go to Tools -> Tasks -> Browse and this should open up a window
  2. Open the Polynomials tab and then select "Polynomial Division Quotient and Remainder"
  3. Click the "Insert Default Content" button in the Task window and the task template should appear in your worksheet
  4. This allows you to manipulate the values in purple and execute the commands to determine the quotient and remainder.

This will allow you to compute numerous polynomial division questions without having to constantly reproduce the commands or know what the different command elements are. 

Hope that makes things a little easier!


Krithika

 

Hi!

I created a worksheet showing you the steps and screen shots of how you can solve your problem. Let me know if you have any questions about that or if you  need further clarification about how I got from one step to another.

As for your second question, yes it appears as code on my web browser as well. To insert Maple syntax on these forums you need to click the "Insert Maple Math Expression" on the toolbar (it is a red maple leaf) and then you can enter your expression and it should appear in a nice format.

int(1/((1+x^2)*(1+4*x^2)), x = 0 .. infinity);

Visit the "How to Post Math" link (http://www.maplesoft.com/academic/adoption/studentcenter/PostingMath.aspx) for more information!

Let me know if you have any more questions!

 

Krithika

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Hi Zarith,

Just a few comments about why you might be getting some of the other errors in your worksheet:

- to use the RiemannSum command you need to load the package Student[Calculus1]

- when you assigned the variable c you just had a colon you need to use := to assign a variable

- to resolve the "use midpoint method instead" error you can use "method=bvp[middefer]" in your command for Q2

 

However, looking at your functions, the system seems to be undefined. The a2 expression has the fourth derivative of f (f(4)) and when solving the system Q2 using dsolve, Maple will compute f(4)=a2/f . Since you have the condition B1:=f(0)=0 this will be undefined. This is why you get the singularity error.

 

You may need to redefine your boundaries or adjust your expressions.

 

Krithika

Hi,

To obtain partial fractions in a clickable way:

  1. Enter your expression into your Maple worksheet. E.g. (x^2+3*x+8)/(x^3-64)
  2. Open the Context Menu (right-click on the expression) and select Factor (Note: you can skip this step if you wish)
  3. Open the Context Menu and select:
    Conversions -> Partial Fractions -> x

This should provide you with the expression in terms of partial fractions.

 

If this result is not the one that you are looking for in polynomial division (i.e., you wish to get the quotient and remainder) then:

  1. To get the quotient type:
    quo(<your dividend here>, <your divisor here>, <the variable in which your polynomials are in terms of (usually x)>)
  2. To get the remainder type:
    rem(<your dividend here>, <your divisor here>, <the variable in which your polynomials are in terms of (usually x)>)

I have attached a worksheet with an example of each. Also, you can take a look at the Finding Partial Fractions worksheet and video tutorial. This worksheet provides you with a tool that goes through the steps of finding partial fractions.

http://www.maplesoft.com/academic/adoption/studentcenter/topic.aspx?sid=6952

Hope that helps!

 

Krithika

 

Download Attached File

Hi again,

I've attached another worksheet that solves the same problems that are in the previous worksheet using the Context Menu or Line Tutor. You might find this easier than using commands.

 

Let me know if you have any questions!

 

Krithika

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Hi,

I'm not quite sure what context you will be using this defined product in but I have created a worksheet that defines "&*" as an associative, non-commutative product.

So it takes (a&*b)&*c=a&*(b&*c) as true (associative) and a&*b=b&*a as false (non-commutative).

If this is still not what you are looking for then can you clarify the question by maybe providing an example of what elements you are using in your computations and what result you are looking for.

Hope that helps!

 

Krithika

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