Are Numerical methods of any use for a physicist

[kini.Amith]

I am currently doing my bachelors in Mechanical engineering engineering and planning to pursue physics after completion. I have to choose an elective the coming semester. One of the electives offered is 'Numerical Methods for Engineers' and the modules covered include Error in numerical calculations, Solution of system of linear algebraic equations, Numerical differentiation and Boundary value problems.
Is this subject useful for a theoretical physicist? Can you mention any applications of numerical methods you have seen in your career as a physicist?

 

[SteamKing]

Unless you are a brainiac who can solve complicated equations in your head, you will need to know numerical methods, especially if your work involves the use of computers.

 

[f95toli]

It would be better to ask "are analytical methods useful for a physicist?".
There are VERY few interesting problems that can be solved analytically; just about evertything is solved numerically if you are working on "real-world" problems (which even most theorists do).

 

[Hercuflea]

Very useful. As a engineer/physicist the differential equations portion will probably of most use to you. As an example of what I have personally,seen (i am only an undergrad), I know a physicist who is working on solving the diffusion equation in cylindrical coordinates with an application to neurons and how they communicate. (I probably butchered this description but that is what I got out of his explanation).

 

[TomServo]

Yes. Take the class.

But if you want to help your chances of acceptance into a good program then it helps to have at least one semester of quantum mechanics, electricity and magnetism, and statistical mechanics.

 

[kini.Amith]

It would be better to ask "are analytical methods useful for a physicist?".
There are VERY few interesting problems that can be solved analytically; just about everything is solved numerically if you are working on "real-world" problems (which even most theorists do).

I understand that everyone uses numerical methods through computer softwares and calculators etc. What I meant to ask was whether knowing the ALGORITHM's like Newton-Raphson method, Runge Kutta methods are of any use.

 

[f95toli]

Yes, having at least some idea about how the algorithms work is a must if you are doing anything reasonably sophisticated, otherwise you e.g. won't know how to choose WHICH algorithm to choose for a certain problem (there are probably ten different ways of solving a time-dependent ODE in Matlab), nor will you be able to use the software efficiently. More importantly, you also need to know when NOT to trust the output (because e.g. the solution is not converging).
Moroeover, even sophisticated FEM software packages like Comsol require you to know a bit about meshing etc

 

[gravenewworld]

Try solving just some very simple partial diff eqs by hand, look at a real world problem described by a partial diff eq after that, and then re-ask this question.