/sci/ - Science & Math

>>14812146
Yeah, Rudin is terrible. Awful exposition and intuition. The topology section is especially awful considering how unintuitive it really is. I don't know what he was smoking for the last two chapters. Does he really think his approach to differential forms makes sense? At least the problems are good. I struggled through this for a semester until I picked up Rosenlicht's book and read 150 pages in a weekend, then immediately I understood what I was doing and how crap Rudin was.
There's no point in reading the book. Just do the problems, that's it.

>>14683757
>>14684268
We get

[math]I= u^1M_1 + u^2 M_2 + u^3 M_3[/math]

where [math]\mathbf{M}=(M_1, M_2, M_3)\in \mathbb{R}^3[/math] (or rather a vector in the dual space to [math]\mathfrak{so}(3)[/math]) is given by

[math]\mathbf{M}=\sum_{a=1}^N \mathbf{r}_a \times \frac{\partial \mathcal{L} }{\partial \dot{\mathbf{r}}_a}[/math].

The vector [math]\mathbf{M}[/math] is called the angular momentum of the system. Explicitly,

[math]\mathbf{M}=\sum_{a=1}^N \mathbf{r}_a \times m_a\dot{\mathbf{r}}_a[/math]

so that the total angular momentum of a closed system is the sum of angular momenta of individual particles. Conservation of angular momentum is a fundamental physical law that reflects the isotropy of space. Get fucked, John. Now stop bothering the big boys with your schizophasia.

>>14610601
>>14610636
There are metabolic ward experiments and feeding trials showing the direct consequences of consumption of high fat, high protein meal on markers of endothelial function: increases in markers of peripheral inflammation, reduction in serotonin metabolism in the brain, and these can be extrapolated to disease pathology because we can observe the direct consequences of lipotoxicity and endotoxicity within the brain and reduction in cognitive function and metabolic homeostasis through an understanding of the hypothalamic model of metabolic disorder
pubmed.ncbi.nlm.nih.gov/28677618
pubmed.ncbi.nlm.nih.gov/9036757
ncbi.nlm.nih.gov/pmc/articles/PMC2858203
pubmed.ncbi.nlm.nih.gov/28045396
pubmed.ncbi.nlm.nih.gov/19116375
ncbi.nlm.nih.gov/pmc/articles/PMC2853195
ncbi.nlm.nih.gov/pmc/articles/PMC4424797
pubmed.ncbi.nlm.nih.gov/28323986
ncbi.nlm.nih.gov/pmc/articles/PMC6506390
ncbi.nlm.nih.gov/pmc/articles/PMC6814438
sciencedirect.com/science/article/pii/S2211124716307331
ncbi.nlm.nih.gov/pmc/articles/PMC2728689
ncbi.nlm.nih.gov/pmc/articles/PMC5813603

You only ever get one brain, stop being such a careless retard with it.

>>14585582
>all Landau & Lifshitz books
I'm so fucking confused. So you're telling me L&L is undergrad? Whenever I look those books up on the internet, it's grad students talking about how great they are.
Also, what the fuck is up with all of these books? How many fucking books do you have to read to study theoretical physics? How much math do you actually need? Some say just up to differential geometry, some say you just need one of those mathematical methods books, and others seem to act like you need a degree in math first and then specialize in theoretical physics? I'm so confused.