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  1. vktsn0303

    Streamlines from strain rate tensor

    I was reading about strain rate tensors and other kinematic properties of fluids that can be obtained if we know the velocity field V = (u, v, w). It got me wondering if I can sketch streamlines if I have the strain rate tensor with me to start with. Let's say I have the strain rate tensor...
  2. vktsn0303

    A Convolution, singularity, kernel, principle values, linear stability analysis, quadrature points

    Thanks a lot for the information, fresh_42. I'll try to look up lecture notes that are made available online. I think that's the easier way to learn too.
  3. vktsn0303

    A Convolution, singularity, kernel, principle values, linear stability analysis, quadrature points

    Yes, I agree it's a rather broad question. Sorry about that. I would actually like to learn about singularities in a strict mathematical sense. So, if I have to learn about convolution, singularity and kernels in particular where should I start looking? I did google about them a bit, found some...
  4. vktsn0303

    A Convolution, singularity, kernel, principle values, linear stability analysis, quadrature points

    I'm reading a book on vortex methods and I came across the above mentioned terms, however, I don't understand what they mean in mathematical terms. The book seems to be quite valuable with its content and therefore I would like to understand what the author is trying to say using the above...
  5. vktsn0303

    I Express x in terms of the constants

    I have the expression, A(Bx + 1) = C*d^(2x) where A,B,C and d are constants. How to arrive at an expression for x in terms of A,B,C and d? I have tried doing this: Log [A(Bx + 1)/C] = Log [d^(2x)] 2xLog(d) = Log[A(Bx + 1)/C] but I'm unable to arrive at an explicit expression of x in terms...
  6. vktsn0303

    I Order of derivatives

    If v is of order δ, what is the order of ∂v/∂x and ∂2v/∂x2 ?
  7. vktsn0303

    What does this mean? (equation for viscous flows)

    While reading a text book on viscous flows, I came across the following interpretation of an equation: where, v is the vertical component of the free stream velocity and y is the vertical distance from the surface of a solid and Re is the reynolds number. Can someone please help me...
  8. vktsn0303

    The Determinant

    What is the main idea behind the determinant? What was the main purpose for which it was conceived?
  9. vktsn0303

    Tangent vector

    But the rate of change at a point can never be a tangent at that point. It has to be integrated to obtain the equation of the tangent.
  10. vktsn0303

    Tangent vector

    Then why is the rate of change called the tangent vector itself?
  11. vktsn0303

    Tangent vector

    I was reading about the tangent vector at a point on a curve. It is formulated as r' = Lim Δt→0 [r(t+Δt) - r(t)] / Δt (sorry for the misrepresentation of the 'Lim Δt→0 ') where r(t) is a position vector to the curve and t is a parameter and r' is the derivative of r(t). All I can...
  12. vktsn0303

    Straight line in a plane

    Post #2 helped me understand the negative reciprocal rule for perpendicularity. Post #11 helped me understand the negative reciprocal rule for perpendicularity being applicable, in context of post #10, only after A.B=0 being valid. The combination of both posts helped me understand everything...
  13. vktsn0303

    Straight line in a plane

    Thank you RyanH42.
  14. vktsn0303

    Straight line in a plane

    How is it right to say that A is perpendicular to ax+by=0 just because A is perpendicular to B?
  15. vktsn0303

    Straight line in a plane

    I think the above quoted message is misleading here. My question would have been as follows: Is it OK to say that A is perpendicular to ax+by=0 because A is perpendicular to B?
  16. vktsn0303

    Straight line in a plane

    Please explain.
  17. vktsn0303

    Straight line in a plane

    Is it OK to say that A is perpendicular to ax+by=0 because A.B=0? Another statement from the same book conveying this meaning.
  18. vktsn0303

    Straight line in a plane

    Thanks Mark44, I had forgotten the negative reciprocal rule of slopes for perpendicular lines. Everything makes sense now.
  19. vktsn0303

    Straight line in a plane

    The title does not say much. But my actual question is as follows. Let us suppose a line ax+by=0. This means A.B = 0 with A and B being vectors, where A = [a,b] and B = [x,y]. Therefore, A is perpendicular to B. Now my question is if A is also perpendicular to line ax+by=0 (I'm not sure if this...
  20. vktsn0303

    What is an integrating factor exactly?

    I'm sorry about the question not matching the title. I didn't realize when posting it. Your guess sounds right. Thanks.
  21. vktsn0303

    What is an integrating factor exactly?

    While solving non-homogenous linear ODEs we make use of the integrating factor to allow us to arrive at a solution of the unknown function. Same applies to non linear ODEs where the ODEs are converted to exact differentials. But what I don't understand is how and why would someone have come up...
  22. vktsn0303

    Current issues faced by the aerospace industry

    I was mainly looking for issues being faced by the commercial aviation and the spacecraft industry.
  23. vktsn0303

    Current issues faced by the aerospace industry

    Hello everyone, I wanted to learn about the issues that the aerospace industry is currently facing. Could anyone please help me in this regard. I searched on the internet but could not find a proper web site that explained this. So I thought this forum was the right place to ask about this...
  24. vktsn0303

    Concept of limit

    Well, I actually had a fundamental doubt (silly even) for which reason I had posted the question mainly. I am a newbie to the concept of limits. My doubt is as follows. Why should we look to modify the numerator or the denominator or both? Why not just consider that as n tends to infinity the...
  25. vktsn0303

    Concept of limit

    How can it be proved that as lim n tends to infinity, (n2-1)/(n2 + n + 1) tends to 1 ?
  26. vktsn0303

    Help with deriving time, velocity, displacement

    Sorry. A small correction in my previous reply. t is not velocity*distance.
  27. vktsn0303

    Help with deriving time, velocity, displacement

    I don't understand why you used 2(-Vi-Vf)d=t t is not velocity/distance if there is acceleration. I am assuming the acceleration to be a constant here. Use the laws of motion to find the acceleration. Once acceleration is determined it is easy to find how long the dog took to reach a final...
  28. vktsn0303

    Representing ratios with division

    Ratios between two quantities give us the comparison of a quantity with a unit value of the other quantity. Now lets say a bag contains 10 oranges and 5 mangoes. the ratio is 10:2 or 10/2 = 5. That is, for every one mango we have 5 oranges in the bag or we can say 5 oranges per mango. Same...
  29. vktsn0303

    Why are transcendental functions called so?

    I see. Thank you pwsnafu.
  30. vktsn0303

    Why are transcendental functions called so?

    I have learnt that they are called so because they cannot be expressed with the help of elemental methods of mathematics such as addition, subtraction, multiplication and division. But then isn't the whole of mathematics itself based on the elemental methods?
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