(COMING SOON)
The integral theorems of Stokes and Gauss (the latter also known as the Divergence theorem) are two further analogs of the fundamental theorem for the two new types of derivatives defined above. Here we shall give heuristic arguments for their validity.
The integral theorems of Stokes and Gauss (the latter also known as the Divergence theorem) are two further analogs of the fundamental theorem for the two new types of derivatives defined above. Here we shall give heuristic arguments for their validity.
(COMING SOON)
Calculus is all about slopes and area: and so by its nature is a very visual field. Here we talk about the geometric meaning behind the linearity of the derivative and integral, and explain pictorially the fundamental theorem of calculus.
Calculus is all about slopes and area: and so by its nature is a very visual field. Here we talk about the geometric meaning behind the linearity of the derivative and integral, and explain pictorially the fundamental theorem of calculus.
(COMING SOON)
What does it mean to raise a number to an imaginary power? No longer can we just extrapolate from the idea of "repeated multiplication" - we need other means to decide what this means. Here we look at a couple of justifications for Euler's formula: $e^{ix}=\cos(x)+i\sin(x)$.
What does it mean to raise a number to an imaginary power? No longer can we just extrapolate from the idea of "repeated multiplication" - we need other means to decide what this means. Here we look at a couple of justifications for Euler's formula: $e^{ix}=\cos(x)+i\sin(x)$.
Staring at the Sky
Space is big. Space is really, really big. I remember one day as a young boy telling myself that I wanted someday to truly understand how far away the moon is. And while I still can't truly comprehend distances on the order of a quarter million miles, my interest in our greater universe has grown from that question. Check out the "fun" tab if you'd like to see the kind of things I find amazing out there.
Speaking
Nothing is more human than our languages - the thousands of complex systems through which we filter all of our thoughts. I am a big proponent of linguistic diversity, and help where possible with language preservation efforts - bdewákhaŋthuŋwaŋ iápi kiŋ de thewáȟ'iŋda do! Check out the "fun" tab for some information about the Dakhóta language!
Cooking.
Even graduate students need to eat - and so I figured I might as well make cooking a hobby of mine! Check the "fun" tab for some recipes I've created.