What Math Topic Should I Learn Next?

[Jow]

I am self teaching myself some of the math that will be needed for university physics. I have just finished Calculus 1 and most of 2. I have been told I should learn ordinary and partial differential equations, vector calculus and linear algebra. In what order should I learn these topics?

 

[dustbin]

I would say linear algebra first. It is helpful to know before taking Calc 3 and Vector Calculus. I cannot say with ODE/PDE, as I have no experience there...

 

[Klungo]

There are many ways to do this.

I recommend you do calc 3 (vector + multivariable) or linear algebra first, then ODE(a must for PDE), then PDE.

There are more courses like Fourier analysis, and complex variables that you can do after ODEs.

As far as I know, these are all the most useful maths for physics. There could be more.

 

[bossman27]

I agree with Klungo, calc 3 is probably the best place to start. I would say though, that I actually took calc 3 and linear algebra at the same time and found linear algebra to be significantly easier... so you wouldn't be lost if you chose to look at it first, provided you understand the basics of vectors. The main thing is that you should probably learn calc 3 before ODE's, and ODE's before PDE's, though technically you could learn ODE's without knowing much, or any, multivariable calc.

At my university the sequence is: Calc 3 ---> ODE ---> advanced vector/multivar. calc ---> PDE/complex analysis/etc.

You can really mix linear algebra in anywhere... probably the sooner, the better, though.

 

[MarneMath]

I don't know why people say calc III before linear algebra. I've found that that knowing linear algebra makes everything in Calc III and ODE a lot easier. Note, it isn't impossible to do well in those courses without linear algebra, but it is nice to already have a good feel for vectors, and matrix operations. In my experience, it brings a lot more clarity to things that otherwise would have to just be memorized or glazed over.

 

[Klungo]

Linear algebra is directly relevant for ODEs. For Calc III, if you actually have a good course in it, you do see linear algebra (my CC course in it wasn't good).

It sure feels great taking linear algebra now and actually completing what I've learned in ODEs that first seemed unnecessary (lin indep, gen sol, etc).

 

[stf]

I think linear algebra is kind of like the flour that holds the calc 3 cakes and diff eq pastries together. It seems kind of weird at first, but when put into context really is handy to know. That said I think you can easily do calc 3 prior, I would take linear algebra prior to diff eq as the subject makes much more sense with it especially when you get into systems.

 

[DrummingAtom]

I don't know why people say calc III before linear algebra. I've found that that knowing linear algebra makes everything in Calc III and ODE a lot easier. Note, it isn't impossible to do well in those courses without linear algebra, but it is nice to already have a good feel for vectors, and matrix operations. In my experience, it brings a lot more clarity to things that otherwise would have to just be memorized or glazed over.

I agree. I took a combined linear algebra/Diffy Q class and it felt disjointed because we applied linear algebra without really knowing the what it meant. After that semester I went back and learned linear algebra separately and everything made more sense. I think linear algebra should be taught as early as possible because it comes up all the time.