What Should a 16-Year-Old Aspiring Astrophysicist Learn Next?

[QuantumTheory]

I'm 16 years old. I'm interested in physics, especially astrophysics.

I've learned this much so far:
Derivatives
Integration
Up to Taylor Series

Question is..now what? What should I learn now? I understand there is an infinite amount of calculus knowledge out there (Excuse my slack on the word 'infinite' :) )

But I don't know what would be good to learn next. I've heard Fourier Series is a great place to start to learn about Astrophysics, but to understand stuff like Einsteins theroums, etc, (the really high stuff, such as Heisenburgs equations, etc)

What should I have to know?

Should I learn a lot about vectors? I'm also interested in computer graphics, and I know that deals with vectors, but mainly astrophysics :(

Any suggestions?

 

[hypermorphism]

Study Linear Algebra and Combinatorics/Discrete Mathematics. These two topics are the gateway to the language and techniques of modern mathematics, including Fourier Analysis and the rest, and are quite easy to understand, depending on what books you use.

 

[fourier jr]

maybe do analysis (fancy calculus) or multivariable calculus, and/or matrix theory or linear algebra

 

[misogynisticfeminist]

Since you posted it in the DE forum, DE is a very good place to start ! Make sure you know besides, calculus, manipulation of complex numbers as well as factorizing n degree polynomials. You would need that a lot in DE. If you're interested in math used in physics, linear algebra would also be good.

the MIT open courseware site has video lectures on DE as well as linear algebra, which is quite good imo. And as far as I have studied, linear algebra requires very little mathematical background unlike in DE where you need to have pretty strong knowledge on calculus.

I would also recommend Mathematical methods for physics and engineering by KF riley, MP hobson and SJ Bence, it is very comprehensive, even though most topics are not given enough coverage. But it covers everything from the quadratic formula to intros to tensors, differential geometry, complex integrals,complex variables etc.

 

[ReyChiquito]

how about learning some physics? classical mechanics for starters...

 

[QuantumTheory]

Hmm, damn.

I have to learn to factor.

This is killing me.

I've gone though all the way up to Taylor Series understanding everything compleletey, only when I they give me a problem I can't solve it due to very tricky (and deciecive) methods they fool me into for complex multi varibles!

UGH.

Like this:
If $$f(x,y,z) = x^3y^2z^4 + 2xy + z$$, then

(Differentiating with respect to x, holding y and z constant. NOTE: I Do not know how to create the partial deriviative symbol or the f sub x symbol [indicating a different form of the partial dervi. curled 'd' form]:

$$f$$(sub x)$$(x,y,z) = 3x^2y^2z^4 + 2y$$

(More mess with respect to y and z goes here.)

Then out of the blue, with NO EXPLANATION, another function of z appears (right below the first one!) with substitued values:
[tex](-1,1,2) = 4(-1)^3(1)^2(2)^3 + 1 = -31<br /> <br /> What I DON'T understand is the mysterious above function and how they got the results , and how the tricky $$y$$ manipulation works, as it is held constant yet he subtracts a power from another coeffiecent and sticks it on to another y? <br /> <br /> :([/tex]

 

[hypermorphism]

Then out of the blue, with NO EXPLANATION, another function of z appears (right below the first one!) with substitued values:
[tex](-1,1,2) = 4(-1)^3(1)^2(2)^3 + 1 = -31<br /> <br /> What I DON'T understand is the mysterious above function and how they got the results , and how the tricky $$y$$ manipulation works, as it is held constant yet he subtracts a power from another coeffiecent and sticks it on to another y? <br /> <br /> :([/tex]

[tex] That's the partial derivative with respect to z of the function f at the point (-1,1,2). <br /> It really should say $$f_z(-1,1,2) = \frac{\partial f}{\partial z}(-1,1,2) = 4(-1)^31^22^3 + 1 = -31$$. <br /> You can click on any LaTeX formatted text to view the LaTeX markup for it. Since I don't have your text, I don't know why the author would be referring to the partial with respect to z. <img src="https://cdn.jsdelivr.net/joypixels/assets/8.0/png/unicode/64/1f642.png" class="smilie smilie--emoji" loading="lazy" width="64" height="64" alt=":smile:" title="Smile :smile:" data-smilie="1"data-shortname=":smile:" />[/tex]

 

[saltydog]

A golden rule

Differential equations is the place to be: be as good at it as a math major. Work all the problems, use several books, and never skip steps. Remember one golden rule: If you encounter a tough problem you can't solve, put it away and work first with a similar simple problem, solve it, add some to it, solve it, continue that way until you get to the original problem. Lots of work to do it this way but usually is successful.

SD