# Partial Differential Equations vs Linear Algebra

## Main Question or Discussion Point

This semester I'm a bit stuck with classes to progress my Electrical Engineering major (having going into it so late), so the only class I can take to progress is a physics course about electricity and the likes. I need at least a three unit class in order to get at least half time so I won't look bad on my financial aid record and also because I need pizza money. :tongue:

So the class I'm deciding between: Partial Differential Equations (Partial differential equations of physics and engineering, Fourier series, Legendre polynomials, Bessel functions, orthogonal functions, the Sturm-Liouville equation) vs Linear Algebra I (Matrices, systems of linear equations, vector geometry, matrix transformations, determinants, eigenvectors and eigenvalues, orthogonality, diagonalization, applications, computer exercises. Theory in Rn emphasized; general real vector spaces and linear transformations introduced).

Last semester I took Ordinary Differential Equations (First order differential equations, first order linear systems, second order linear equations, applications, Laplace transforms, series solutions) since the EE major required it, and I did pretty well in it. The major didn't require me to take Linear Algebra, though.

So which of those two classes are better/more useful for the major as well as in general (Career-wise and such)? My current interests are learning the basics of how things work (tinkering and designing circuits, computer assembly language and data structures, etc...) so I can explore about different systems' vulnerabilities (Computer and electronics/digital security). Though sometimes I find myself interested in electromagnetic researches and quantum electrodynamics, learning about how electricity and electromagnetism works on different levels.

Thank you.

SteamKing
Staff Emeritus
Homework Helper
I would say take the linear algebra course first. You can certainly take PDEs later, but LA can be used to analyze circuits, among other things. If you get into solving PDEs numerically, using finite elements or boundary elements, LA will be an essential part of understanding how these methods can be applied to PDEs.

You should definitely take linear first. Fourier, Legendre, and Bessel functions are all cases of orthogonal functions. Understanding a basis at a more fundamental level will help you understand when you see infinite series of these functions when solving PDEs.

jasonRF
Gold Member
As an EE in industry I will be yet another person to recommend Linear Algebra. I am surprised that it is not required, since it is really important for signal processing, communications systems, circuit analysis, and for PDEs as mentioned by JardEBland and SteamKing. Along with probability and stochastic processes, linear algebra is the most useful math I learned.

jason

PDE is extremely important in signal processing and communications. LA for understanding circuits. Linear Algebra is relevant in what i do but i don't use it as a basis for understanding problems. For that i use circuits . With PDE it's far more useful in understanding how electronic devices operate when integrated in already existing systems.

Astronuc
Staff Emeritus
This semester I'm a bit stuck with classes to progress my Electrical Engineering major (having going into it so late), so the only class I can take to progress is a physics course about electricity and the likes. I need at least a three unit class in order to get at least half time so I won't look bad on my financial aid record and also because I need pizza money. :tongue:

So the class I'm deciding between: Partial Differential Equations (Partial differential equations of physics and engineering, Fourier series, Legendre polynomials, Bessel functions, orthogonal functions, the Sturm-Liouville equation) vs Linear Algebra I (Matrices, systems of linear equations, vector geometry, matrix transformations, determinants, eigenvectors and eigenvalues, orthogonality, diagonalization, applications, computer exercises. Theory in Rn emphasized; general real vector spaces and linear transformations introduced).

Last semester I took Ordinary Differential Equations (First order differential equations, first order linear systems, second order linear equations, applications, Laplace transforms, series solutions) since the EE major required it, and I did pretty well in it. The major didn't require me to take Linear Algebra, though.

So which of those two classes are better/more useful for the major as well as in general (Career-wise and such)? My current interests are learning the basics of how things work (tinkering and designing circuits, computer assembly language and data structures, etc...) so I can explore about different systems' vulnerabilities (Computer and electronics/digital security). Though sometimes I find myself interested in electromagnetic researches and quantum electrodynamics, learning about how electricity and electromagnetism works on different levels.

Thank you.
I'd do both, which is what I did during my 2nd year at university.

In computational physics, one encounters coupled systems of non-linear PDE/ODEs, so it's useful to have the knowledge from PDE and LA courses.

I feel like PDEs are something you just kind of pick up as you go along, or do on a really deep level. Linear algebra you can't really get the big picture unless you have a class on it.

mathwonk