Timber & Steel Pty Ltd is looking for a skilled mathematician to assist with some differential calculus for one of our current projects. It's been more than 15 years since any of us have done any university-level calculus, and we need a little assistance. We have two parts that we need assistance with:
Part 1:
For an unknown surface, S(x), which for every point x = (x,y), we define as
S(x) = c(x) + u(x) r(x)
c(x) and r(x) are vectors, both of which are known, and u(x) is an unknown scalar quantity — which I need to solve for. We specify c(x) = a + w(x) o, where both a and o are vectors and do not depend on x, and w(x) is a scalar that does vary with x. As additional inputs, we know the partial derivatives of c(x) and r(x) with respect to (x,y). There's also a number of different partial differentials that can be extracted for the intermediate values that are used to compute r(x), but these are likely not required, as we can simply assume that c(x) and r(x) are vector fields and I have values for them already.
The normal to the surface is the cross product of the partial derivatives of S(x) with respect to x and y.
Part 2:
We now need to determine u(x), which is done with the cost function
K(x) = Norm( n(x) x r(x) )
where we normalize the length of the cross product of the vectors between the normal and the directon vector r(x).
Completing part 2 will provide the three terms for a quadratic equation of the form:
Au(x)^2 + Bu(x) + C = 0
This is not a homework/academic project.
I'm a mechanical engineer with a PhD degree, a thorough knowledge of math, including differential calculus (which is the basis for most of the mechanical science). Please visit My Profile to see my reviews. I'm an author of dozens of research papers in Computational Mechanical Science and Engineering. It would be my pleasure to help with your project.
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Hi,
I've been developing mathematical models using differential equations for several years and would like to work on your project. I'm looking forward to hearing from you.
Dear Employer,
I'm experienced in applied mathematics, therefore, I could handle your project well in appropriate time. To do this job I might write some codes in R or Matlab. I hope to do this work in 2 or 3 days but I need to know more details about your project to estimate my working time.
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To solve your problem I suppose it should be first of all reformulated in such a way that allows applying the common mathematical analysis and numerical solution. It is not totally clear in the way you describing and I hope I can help you with it. If the problem is formulated quite clear then the solution will be found easily.
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Hello Sir, We have gone through the details you have provided and we have already worked on a similar project before and can deliver as u have mentioned and would be pleased to work on this with you to deliver the results that you have expected and we have already worked on a similar project before and can deliver as u have mentioned
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I am ready to discuss with you
with best Regards