Econometrics Lecture 1 Topic: What is econometrics? Many people have asked me: econometrics – what exactly is it? Especially after hearing that I study “computer
I wrote a new Lecture entirely dedicated to hyperbolic functions and their inverses. In it, I explain what hyperbolic functions are, when – for example – they are useful, and why they sometimes appear in Wolfram results, generally causing panic among students. However, the hyperbolic sine isn’t that scary – I invite you to the Lecture.
Professors at universities have their own requirements. Many of them, for the good of their students, of course, will not hesitate to specify the rules for solving problems in great detail.
Some do not recognize ready-made formulas for some indefinite integrals. See where they came from.
As a curiosity, I’ll calculate the limit of the function: (x^x^x – cosx).
More interesting than the calculations themselves are the two morals that can be drawn from them. But the morals are at the end (has anyone ever seen a story with a moral at the beginning)?
Let’s say we need to calculate the volume of an ellipsoid: {x^2}/4+{y^2}/5+{z^2}/9=1. This is an ellipsoid that intersects the x, y, z axes at coordinates 2, \sqrt{5}, and 3, respectively.
This is not a rotational ellipsoid, it is not formed by rotating any curve around any axis, so we can’t use the standard formula for the volume of a rotational solid. We need to figure out another way.
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