1. G

    Generalized Fourier Integral and Steepest descent path, Saddle point near the endpoin

    I am looking forward to solving the integration in the following equation with the assumption that $ka$ is very large \begin{align} H = 2jka\int_{-\pi/2}^{\pi/2}\cos{(\varphi-\phi)}e^{jka[\cos{\varphi}+\cos{(\varphi-\phi)}]}\ d\varphi \end{align} I used the steepest descent path method to...
  2. B

    Find relative extrema and saddle points

    Given f(x,y) = x^3 + 3xy + y^3 + 4, find all relative extrema and saddle points... can someone help me? I don't know how to do this problem. I can get fx and fy, but I don't know from there.
  3. M

    Local max, local min, or saddle point

    I have a function g(x,y) = x^2*y - x - 1 for which my partial derivatives set equal to 0 are 2xy - 1 = 0 and x^2 = 0. Solving the 2nd equation, I get x = 0. If I plug in 0 into the first equation, both x and y goes away because they are being multiplied by 0. What to do in this case ? I have to...
  4. D

    Strange Saddle

    Let f (x,y) = (y-x^2)(y-x^4): (a) Verify that (0; 0) is a critical point for f and that the discriminant at (0; 0) is zero. (b) Verify that 0 = f(0;0) is the minimum value of f(x,y) along every line through (0,0). (These lines are of the form y = kx and x = 0) (c) Show f does not have a local...
  5. A

    saddle point

    When we talk about functions and their gradients, is the term "saddle point" synonymous of stationary point (derivative = 0) ? thanks
  6. L

    saddle point

    What should be a rigorous explanation that near the saddle point the function cannot be put in an explicit form? By ex: f(x,y)=x*e^y + y* e^x it cannot be written an explicit solution y=y(x) in the neighborhood of (0,0). Much obliged for an answer! Louis --
  7. G

    saddle point methode

    I have to use this methode to solve a integral but I have no idea about it. I do not find also a lot of information in internet. Could some one explain it? Thank you