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Applications of Mathematics
Joanna Grochowska-Angielczyk

Econometrics – What Is It Exactly?

Econometrics Lecture 1 Topic: What is econometrics? Many people have asked me: econometrics – what exactly is it? Especially after hearing that I study “computer

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Indeterminate integrals
Krystian Karczyński

Hyperbolic Functions to the Rescue – My New Lecture on the Blog

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.

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Definite integrals
Krystian Karczyński

The Volume of an Ellipsoid (But Not a Rotational One, Just a Wild Type) Calculated by a Definite Integral

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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