Welcome back. I hope all of my readers are having an excellent start to the new semester. Over the last couple of months, we have discussed partial differential equations (PDEs) in some depth, which I hope has been interesting and at least somewhat enjoyable. Today, we will explore two of the most powerful and commonly used methods of solving PDEs: separation of variables and … [Read more...] about Separation of Variables and the Method of Characteristics: Two of the Most Useful Ways to Solve Partial Differential Equations
Archives for 2023
The Lebesgue Integral: A Newer and More Flexible Alternative to the Riemann Integral
Welcome back. This week, I am excited to delve into the Lebesgue integral, which is a more powerful alternative to the Riemann integral that we have dealt with so far. This new, more modern piece of mathematics is due to the work of Henri Lebesgue, a French mathematician who lived from 1875 to 1941. To actually define the Lebesgue integral, we will first develop some core ideas … [Read more...] about The Lebesgue Integral: A Newer and More Flexible Alternative to the Riemann Integral
Partial Differential Equations Meet Electricity & Magnetism: Maxwell’s Equations, Poisson’s Equation, and Eigenfunctions of the Laplacian
Welcome back. Over the last few weeks, we have studied what I hope are some fascinating results in mathematics. We have developed the theory behind multivariable calculus and applied it to describe well-behaved fluids. We have also put the classic Riemann integral on rigorous footing and proven the second Fundamental Theorem of Calculus. This week, we will continue our journey … [Read more...] about Partial Differential Equations Meet Electricity & Magnetism: Maxwell’s Equations, Poisson’s Equation, and Eigenfunctions of the Laplacian
The Digital Democracy of Music: Is Artistic Freedom Still Alive?
The music industry is notoriously unfair to artists. It's become a tragic love story: slimy executive meets young, hopeful artist - someone is bound to get hurt. Without direct industry experience, the general public suspects that record labels are greedy and take unfair portions of artist revenues. Over the years, the music industry has attempted to rectify these inequalities … [Read more...] about The Digital Democracy of Music: Is Artistic Freedom Still Alive?
The Triumph of WAP in Destabilizing Cultural Mysogynoir
Within a medium as pervasive as the pop music industry, the designation of a work as a “cultural reset” influences all those who take note of its meaning. A “cultural reset,” as first coined by actress Rose McGowan, is defined as a power shift, a vehicle through which normative culture is examined and questioned (Rennex et al.). The modernity of the term pairs accordingly with … [Read more...] about The Triumph of WAP in Destabilizing Cultural Mysogynoir