#Partial differential equations

[isomorphismes]

Test functions and [tempered] distributions require the notion of topological vector space … distributions can be traced back to Green's functions in the 1830’s to solve ordinary differential equations … the 1936 work of Sergei Sobolev on hyperbolic PDE’s.

Laurent Schwartz introduced the term "distribution" by analogy with a distribution of electrical charge, possibly including not only point charges but also dipoles and so on.

tempered distribution

topological vector space

(^ if there is a dipole, there must be a notion of subtraction, hence the need for a vector, and to speak of this very conceptually, use a TVS)

[evil-jennifer-hamilton-wb]

There are few things in this world that I hate more than solving Partial Differential Equations Man was not meant to have calculus of more than one variable. We have flown too close to the sun and as a result I have to suffer calculating the heat dispersion across the wings of Icarus, using a second order 4 variable PDE.

[ultraweathercoremax]

Smooth waves

[maybeinanotherworld]

i love you phi-independence, i love you theta-independence, assume everything is spherically symmetric, boundary conditions are always zero, i love you steady state approximation

[cleverjudge]

Technique could efficiently solve partial differential equations for numerous applications | MIT News

In fields such as physics and engineering, partial differential equations (PDEs) are used to model complex physical processes to generate insight into how some of the most complicated physical and natural systems in the world function. To solve these difficult equations, researchers use high-fidelity numerical solvers, which can be very time-consuming and computationally expensive to run. The…

[nxghtshades]

now that I'm no longer drowning in coursework, I've been writing again!

[abiwaif]

BREAKING: Straight A's Streak Continues

Fall semester 2024 is in the books and all my grades are back. In all my classes I either stayed even or improved my grades since midterms.

I know that those of you who have followed me for some time know that I went to college against the wishes of my overly dominating and legalistic mother. She told me that I would fail college. I was smart in High School so I had no reason to believe her. Thus far I have completed eight semesters and have straight A's. Yes, that is right, straight A's - a perfect 4.0. I do not say that to spite my mother. My mom has been nothing but a thorn in my side since I started. All I know is that it is nice to prove her wrong. I do not say that arrogantly. It just feels good to know I am not what she thinks I am (which includes such a choice moniker as "the Spawn of Satan").

One more semester to go for my B.S. and then continuing for my Masters and PhD (I am on track for a PhD but will determine whether or not to get it as I go).

Here are my final grades

Statistical Learning I (95% A - +1%)

Computational Physics (96% A - Even)

Partial Differential Equations I (96% A - +2%)

Soft Matter and Biological Physics (94% A- - +1%)

Mechanics (95% A - Even)

So I am smart and sassy and smol all rolled up into one tidy little package. Now I just want to be wild and engage in some unspeakable acts. 🤪

Thanks for all the encouragement from you my followers. I really do not know why you follow me, but I a grateful for you all and am glad you do!

[o2studies]

Time for another live study

This time it's for math

Topics to get through:

• Graphs (translations)

• Radian measure

• Functions

• Trigonometric functions

• Trigonometric identities & equations

• Partial fractions & modulus

• Differentiation

• Integration

[calculatedliterature]

Wednesday, March 6

Some spring break study vibes. Trader Joe’s lunches, Starbucks and local coffee shops, reading, Partial Differential Equations homework…

I am sort of (definitely) behind on my math homework because I asked for an extension on my assignments during midterms since I was also moving out of my house at the same time. I finished 3 of 4 problems on the first assignment today, with a second assignment to worry about tomorrow. I’m stuck on the last problem of HW 1 so I’ll end up asking for help on that, I’m sure. Hopefully the second assignment is manageable. We’ll see tomorrow.

also tackling some much-needed attention to my social media. I usually post whatever I feel like, but every once in a while it’s important to take a look at my accounts and see how they make me feel and how I want to present myself to the world

[anyaharveyii]

damian: brother, I require some assistance with my homework.

dick: sure, let's take a look.

thirty minutes later:

dick: it is LITERALLY a partial differential equation—

jason: are you f*cking blind? it's a system of equations thingy, just substitute y—

tim: first of all, that's wrong, and second, even if it WERE true, you would substitute for X—

damian: *wishes he were literally anywhere else*

[mathscliniccounseling]

https://youtube.com/playlist?list=PLXty9dIfmxj87TZBHrd0ODfI7vvPOLh2j&si=1NVuqBSMaBrhU5fG

[tomorrowillbeyou]

utterly deranged. actually i think most americans are incapable of solving high order partial differential equations because they are really difficult to solve. and not because people are decent human beings

[theinsaneapp]

Physics Informed Neural Networks

Physics-informed neural networks, a deep learning method that bridges the gap between machine learning and scientific computing.

PINN has superior approximation and generalization capabilities, which made it gain popularity in solving high-dimensional partial differential equations (PDEs), and has been used in various applications such as weather modeling, healthcare, and manufacturing.

[maybeinanotherworld]

they made my differential equations partial :(

[importantwomensbirthdays]

Karen Uhlenbeck

Karen Uhlenbeck was born in 1942 in Cleveland, Ohio. Uhlenbeck is one of the world's leading mathematicians and a founder of modern geometric analysis. Her work focuses mainly on geometric partial differential equations. In 2000, Uhlenbeck won the National Medal of Science for work that led to advancements in mathematical physics and in the theory of partial differential equations. In 2019, she won the Abel Prize, one of the most prestigious awards in mathematics. Uhlenbeck was the first woman to achieve this honor.