I would like to extend a sincere and warm welcome back to our “Introduction to Flight” blog series. Today, we will return to fluid dynamics, which is a difficult, yet immensely fascinating subject. In our everyday lives, fluid flows are all around us, from the coffee in our cups, to the wind in the trees, to the air we breathe. In the laboratory, we can visualize flows by … [Read more...] about The Structures of Fluid Flows and Our Efforts to Understand Them
Archives for 2023
The Benefits of Immersive Education
It’s a Wednesday in September. I’m in my Marine Biology lecture. I open my pencil bag for a freshly sharpened pencil, and reach down into my bag for a lined piece of paper. But before I can fish out a sheet from my binder, my professor claps her hands at the front of the classroom, signaling for us to look up and give her our attention. “Today, we’re doing something a … [Read more...] about The Benefits of Immersive Education
Exploring Los Angeles Through XR
I always think of Los Angeles in the present, if that makes sense. As if the Los Angeles that I know is the only Los Angeles that ever was or will be. But, that’s not true. It’s often easy to forget that the very ground beneath our feet has been around long before me. This soil has been passed from generation to generation, changing a bit with each pocket of passed time. My … [Read more...] about Exploring Los Angeles Through XR
The Calculus of Variations, the Euler-Lagrange Equation, and Classical Mechanics
Welcome back. This week, we will take a short break from partial differential equations and have a brief foray into the calculus of variations, a field of mathematics that is concerned with optimizing functionals. A functional, essentially, is a real-valued function that takes functions in as inputs. For example, F[f] = ∫[0,1] f dx, is a functional that takes in a function, f, … [Read more...] about The Calculus of Variations, the Euler-Lagrange Equation, and Classical Mechanics
Higher Dimensional Integration By Parts and Some Results on Harmonic Functions
Welcome back. Integration by parts is a very useful technique that usually shows up in introductory calculus courses. It allows us to efficiently integrate the product of two functions by transforming a difficult integral into an easier one. When working with a single variable, the integration by parts formula appears as follows: ∫[a,b] g(x) (df/dx) dx = g(b)f(b) - g(a)f(a) … [Read more...] about Higher Dimensional Integration By Parts and Some Results on Harmonic Functions