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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

    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...
  3. 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...
  4. vktsn0303

    I Order of derivatives

    If v is of order δ, what is the order of ∂v/∂x and ∂2v/∂x2 ?
  5. 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...
  6. vktsn0303

    The Determinant

    What is the main idea behind the determinant? What was the main purpose for which it was conceived?
  7. 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...
  8. 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...
  9. 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...
  10. 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...
  11. vktsn0303

    Concept of limit

    How can it be proved that as lim n tends to infinity, (n2-1)/(n2 + n + 1) tends to 1 ?
  12. 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?