What does it take to learn linear algebra and differential equations?

>>8895811
You just need algebra for linear algebra.

>>8895819
And for differential equations?

>>8895821
differential equations is basically calc4

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>>8895811
Common core teaches us the fallacies of the maths we've been teaching for centuries
>pic related

>>8895821
The absolute minimum would be everything till calc 2. The things you need from linear algebra aren't that much if you don't go into systems of equations.

>>8897272
Common Core got it right in this case desu, / and * should have equal precedence.
Operator precedence really is the big question.

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>>8895811
Don't say common core

>>8897291
No it shouldn't and it shouldn't be part of the curriculum.

>>8897272
>>8897286

There wouldn't be any confusion if only people used fucking brackets for fuck sake.

(20/5)*(2*2) = 16

20/[5*(2*2)] = 1

>>8897304
Brackets wouldn't be necessary if people weren't retarded, and if common core didn't say they are "both right".
Multiplication and devision have equal precedence, meaning that, when left with only multiplication and devision, you do them from left to right. 16 is the correct answer, and it is the ONLY answer.

>>8897272
So....Americans don't want to be called racist so they dumb down all the subjects in school so the old wrong answers are now the new right ones? Not even Sweden does this.

>>8895821
you need to know equations

>>8897314
> if common core didn't say they are "both right".
image is shopped.

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>>8897320
My country, South Africa, is dropping the Mathematics pass rate to 20%, if they havnt already. Its not so much that the students are stupid and lack the interest or motivation to atleast get a pity pass. Its that my government thinks its a good idea. Especially when we have maths literacy

>>8897314
>answer is 16
But the brackets anon
20/5(2*2)
20/5(4)
Left to right as you said
4(4)=16 oops my bad
Why are they saying both are right?

>>8895811
>Do you need all the comon core: algebra, trigonometry, analytic geometry and calculus?
No.
That isn't nearly enough.

>>8898208
yes it is

>>8898242
Differential equations without linear algebra and atleast some advanced calculus is not possible.

>>8898250
op mentioned calculus and linear algebra, and anyway you often learn what linear algebra you need in an ODE course anyway

>>8898250
What?
In college, we took Differential Equations before Linear Algebra just fine.

>>8895811
linear algebra is easy. it doesn't even take calculus.

differential equations require a lot of calculus.

calculus takes algebra, trig, (and i think analytic geometry falls under trig category)

>>8898324
ya.

differential requires minimal linear algebra if any at all (iirc), certainly not a whole course in linear algebra.

>>8898250
Not true. We took differential equations parallel with linear algebra, and the physics students took differential equations without linear algebra. The book we used has a whole section dedicated to the little linear algebra you needed (this is a matrix, this is how you find eigenvalues) for differential equations.

>>8898308
>>8898324
You are both ridiculous. Even our second semester courses which involved DEs needed ATLEAST solving systems of linear equations, determinants and the exponential function of matrices.

Additionally to gain any meaningful insights something like functional analysis and the topology of function spaces are required, but that is obviously not a first year course.

>>8898332
>has a whole section dedicated to the little linear algebra you needed (this is a matrix, this is how you find eigenvalues) for differential equations.
Yes. This is exactly what I said. You need linear algebra for DEs.

>>8898336
Okay, fair enough. You don't need to take a linear algebra course, though.

>>8898332
matrices used in differential equations don't really get that big. 2x2 rarely 3x3. iirc

but its been a while admittedly

>>8898333
All thlse except the exponetial matrix isn't really college level linear algebra. Hell, I saw that shit in HS and it's more of a general algebra course. In analytical geometry I saw the operational aspects of diagonalization which is really easy and can be covered in a day if you only care about the practical stuff. Though I have taken two linear algebra courses covering in great detail all of the aspects of a college level course and I didn't really see the exponetial matrix which I think "needs" analyisis. And yea we are talking about baby's first ODEs.

>>8898341
Went through the book (DiPrima/Boyce), and this is the linear algebra they presented:

>matrices and operations on them, including invertible matrices, transposing one etc
>gaussian elimination
>matrix/vector equation, linear independence (for the Wronskian, perhaps?), eigenvalues, eigenvectors

Covered in about 15 pages. The book presents it as review, though.

>>8898341
because there are practically no real world applications of 3rd order differential equations

or something along those lines....

>>8898345
>All thlse except the exponetial matrix isn't really college level linear algebra.
So what?
You still need it for DEs.
Whether or not it is part of your highschool education is irrelevant (although I doubt you covered it rigoursly there), you still need to know it and that was all I was arguing.

>>8898348
I can't even remember what book.

Its been so long.

I think the eigen vector stuff went into derivations in pdes but you don't need to know that to solve problems.

even the most complicated problems in fluids/quantum never had that many variables even.

its would be easy to go crazy with linear algebra

>>8898355
But I doubt you weren't exposed to the operational methods before your linear algebra course. As I said, many unis have some sort of "general algebra" which presents most of what you say.

>>8895828
You don't even need calc2 for linear algebra desu. Fuck Calc2. You can do linear algebra or Calc3 right after Calc1

>>8898348
but ya I learned all that too.

It did not come up much in odes/pdes is all I remember

certainly not the way >>8898355
makes it seem

>>8898358
But I never argued whether or not you need to take a specific linear algebra course.
I just argued that you need some linear algebra to take a course about DEs.

>>8897314
After the 2's multiply to 4's, you are still left with the parentheses around the 4, which you multiply with the 5 (PEMDAS its literally the first fucking letter)
Agree with BracketAnon, about brackets and that people/common core are fucking retarded.

>>8898362
>>8898348 here again

The only thing we really needed (this was a year and a half ago) from the section was how to find eigenvalues/eigenvectors so we could find solutions of 2nd order systems and sketch their phase portraits. We might have needed to know a thing or two about linear independence for the Wronskian? Think we just used Abel's formula for that, though. So, with that in mind, at least for the course I took, all you needed to do was a) find eigenvalues of matrix, b) find eigenvectors, done. No more linear algebra needed. More emphasis was put on the wave/heat equations, desu.

>>8897272
I'm trying to figure out how "the old way" is supposed to work here. I mean it doesn't even matter what order you do the operations in this case. How the fuck would you not get 16?

>>8898369
sounds familiar for pdes

Legendre polynomials for solutions those in spherical coordinates too

(I think)

lol

>>8898371
Its a tongue in cheek way of undermining our ancestors. We do it all the time by saying oh shame so primitive, oh shame they didn't know better. Atleast we're smarter now right, so very smart. Its Hubris

>>8898871
>the slide literally says "both answers are equally correct"

>>8898877
And what do you think when you find out its not?

Would it be feasible to take diff eq, linear algebra, and calc 3 all at the same time? (Pls say yes im going to have to next spring so i can finally transfer to uni)

>>8898361
>You can Calc3 right after Calc1

but who was integrals

>>8899277
if you can handle all fo the work it should be fine

>>8899280
sometimes calc 1 includes integrals and in calc 2 you just talk abotu taylor series and some other stuff. but that stuff is important and shouldn't be missed

>>8899280
>not learning integration in calc 1