# Solving Differentiating a Streamfunction with Maple Help

• Maple
• neilgregge
In summary, the conversation involved a problem of differentiating a given streamfunction to find its x and y velocities. The use of Maple was mentioned and the success of dpsi/dx was noted, while dpsi/dy produced a result with an unexpected variable introduced through the chain rule. After realizing the mistake of not explicitly stating multiplication in the input, the conversation ended with a clarification on the interpretation of the brackets in Maple.
neilgregge
Hello,

I was set the problem to differentiate the following streamfunction in order to find its x and y velocities:

psi=psinought*tanh(y/d)+mu*exp(-((x-L)^2+y^2)/2*sigma^2)*cos(k(y-vt)).

Being the lazy sort I am, I called in Maple.

dpsi/dx worked out perfectly (in that I got the same answer by hand)

dpsi/dy, however, threw up the following:

dpsi/dy=(psinought/d)*(1-tanh(y/d)^2)-(mu*y/sigma^2)*exp(...)*cos(...)-mu*exp(...)*sin(...)*D(k)(y-vt)

the last term D(k)... makes no sense to me. How can differentiating introduce a new variable?

I know I'm probably being a moron, and I'm certainly no expert in using maple, but anyone who can shine a light in my general direction would be muchly appreciated.

neilgregge said:
*cos(k(y-vt))

Should be k*(y-v*t). Maple has to be told explicitly about multiplication.

Maple applied the chain rule. It interpreted the brackets as saying that k is a function evaluated at argument y-v*t.

That makes perfect sense. Thank you.

## What is a streamfunction and why is it important in fluid dynamics?

A streamfunction is a mathematical function used to describe the flow of a fluid. It is an important tool in fluid dynamics because it simplifies the equations that govern fluid motion, making it easier to analyze and solve problems.

## How can Maple help in solving differentiating a streamfunction?

Maple is a powerful software program that can assist in solving differentiating a streamfunction by performing complex mathematical operations and providing step-by-step solutions. It can also handle large data sets and produce visual representations of the results.

## What are the key steps in solving differentiating a streamfunction using Maple?

The key steps in solving differentiating a streamfunction with Maple are: 1) defining the streamfunction function, 2) specifying the variables and their ranges, 3) setting up the desired differentiation, and 4) using the built-in differentiation function in Maple to obtain the solution.

## Is Maple suitable for both simple and complex streamfunction differentiation problems?

Yes, Maple is suitable for both simple and complex streamfunction differentiation problems. It has a user-friendly interface that allows for easy input and manipulation of equations, making it suitable for beginners. It also has advanced capabilities for handling more complex problems, making it a valuable tool for experienced users as well.

## Are there any limitations to using Maple for solving differentiating a streamfunction?

Like any software, Maple has its limitations. It may not be able to handle extremely large or complex problems, and it may not always provide the most efficient solution. It is important to have a solid understanding of the underlying mathematics to ensure accurate and meaningful results.

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