# Partial Differential Equations?

## Main Question or Discussion Point

What math subject comes after partial differential equations for physics and electrical engineering majors?

For undergrad, that's more than you need.

SteamKing
Staff Emeritus
Homework Helper
In physics and many other graduate engineering courses, PDEs are a pre-requisite to studying things like harmonic functions, elasticity, hydrodynamics, EM and electrodynamics, etc. Also, you will need a healthy dose of vector calculus and complex analysis.

So next is complex analysis? Is that pure math or applied math?

lurflurf
Homework Helper
There is not a certain order to learn topics. The usual things to learn around the same time as elementary partial differential equations (and covered in the same books) are ordinary differential equations, linear algebra, vector/tensor calculus, calculus of variations, complex variables, integral transforms, probability/statistics, and numerical analysis. One always seems to have more mathematics to learn than time to learn it.

I can't speak to engineering too much, but from a physics point of view any comprehensive math course is a useful math course. Even things like number theory find themselves popping up in research.

That being said, some of the key starting points are linear algebra, differential equations (ordinary and partial), and complex variables.

Basically piggybacking off of lurflurf "One always seems to have more mathematics to learn than time to learn it."

SteamKing
Staff Emeritus
Homework Helper
So next is complex analysis? Is that pure math or applied math?
It can go either way. Typically, complex analysis is usually introduced to engineering undergrads as part of vector calculus.

Is complex variables a hard course?

Depends on how complex is taught. If you see it in a sort of "Math Methods" kind of class, it could be a lot of fun. Doing problems like contour integration and such.

If you take a math majors complex analysis, it is going to be a stranger version of real analysis which is all proof based.

Now some find doing proofs hard, some find it challenging but fun.

So the course is called complex variables or complex analysis?

WannabeNewton
Just check your course roster for physics/math. Some schools offer both a pure complex analysis class and an applied complex analysis class whereas others might only offer one or the other. You would have to choose based on your needs/requirements and interests, amongst other things. For example here are the course descriptions for the introductory pure and applied complex analysis classes at my university:

"MATH 4180 - Complex Analysis
...
Students interested in the applications of complex analysis should consider MATH 4220 rather than MATH 4180; however, undergraduates who plan to attend graduate school in mathematics should take MATH 4180.
...
Theoretical and rigorous introduction to complex variable theory. Topics include complex numbers, differential and integral calculus for functions of a complex variable including Cauchy's theorem and the calculus of residues, elements of conformal mapping."

"MATH 4220 - Applied Complex Analysis
...