M Dash Foundation: C Cube Learning

Category: calculus of variation

  • The method of Lagrange Multiplier ! Optimize multivariate functions.

    Yesterday I learned the beautiful method of Lagrange Multiplier, to find the minima or maxima of multivariate functions. eg If I ask you what’s the minimum value of a function, f(x,y) = xy, subject to the constraint 5x-y = 4, the answer would be -4/5. The method is this. Ensure that first-partials of function f(x,y)…

  • What are Gauge Potential, Whats a “Theory” in Physics?

    Potential was, as said above, is, energy per unit mass or charge. So, we see that, in defining the higher quantity energy or potential (higher therefore closer to action, hence more fundamental or unified) we have to INTEGRATE the lower variable, here, Force, Field or (Any ) 3-vector. This entails therefore arbitrariness into the Physical…

  • Still some gravity !!

    So talking about gravity fondly I have made a remark “Its not gravity that makes you fall”. You would be shocked as if you fell down but its not due to gravity but something else is at work, Am I a Physicist propounding a phantom theory? The actual statement I made is “Its not gravity…

  • Optical Path and Fermat’s Principle.

    Optical Path and Fermat’s Principle.

    Mirror and Fermat’s principle: We can see ourselves in the mirror and take our mirror reflected selfie as a consequence of Fermat’s Principle, the topic of discussion of the blog. … Snell’s Law governs refraction which is adjustment of optical paths in in-homogeneous media because light can no more travel at its speed in free-space.…

  • Equivalence from simple notions of Geometry ? Yes.

    Now it may also be related that light bends in a denser media compared to a rarer media because an additional rotational force is working. In other words, the definition of straight line has to change in the medium, that is of different density, because path of light is changing. Light is the guy who…