Which should I take: Vector analysis or Differential Equations?

College Majors Engineering Majors
1

Please help me! I am an electrical engineer with a minor in Physics and I plan on taking either Vector Analysis or Differential Equations as my final course before transferring, but I have trouble on which I should take first. My advisor is of no use since he is not giving me helpful advice. One person told me that Diffy-Q would be more important and vector analysis is unimportant.

Vector Analysis covers: Introduction to matrices, system of linear equations, determinants, cross products and Jacobian, inverse matrix, coordinates and change in coordinates, eigenvalues, vector fields, line integrals, fundamental theorem of line integrals, Green’s theorem, curl and divergence, Parametric Surfaces and Their Areas, surface integrals, Stoke’s theorem, Divergence theorem, generalized coordinates.

Differential Equations covers: Differential Equations and models, slope fields, separable differential equations, homogeneous and non-homogeneous linear equations, substitution methods, exact differential equations, population models, numerical methods, second order linear equations, mechanical vibrations, electrical circuits, boundary eigenvalue problems, power series solution, fourier series, laplace transforms, introduction to matrices, system of linear equations, inverse matrix, determinants, superposition principle, eigenvalues and eigenvectors, homogeneous linear systems.

Also, which seems harder? I have taken all the Calculus sequence, but i’ve been taken other classes, that I forgot some things, but I know how to do derivatives and integrals. What else do I need to brush up on for both classes? They are both 4 credit courses.

2

Vector analysis sounds like a combo of linear algebra and some calc 3 topics. Which calc courses have you taken?

3

I’ve taken Calculus 1 and 2 and have taken Multivariable Calculus (Calculus 3), but I’ve taken Calculus 3 last fall semester of 2016, so I might have forgotten a few things, but remember how to do Partial Derivatives and how to solve multiple integrals (though I forgot how to set one up).

4

Vector analysis will be just as useful as differential equations. Whoever told you otherwise has their head in the sand. I don’t know, honestly, what that means in terms of which you take first. Will you take the other after you transfer?

Also, what do you mean by “setting up” a multiple integral?

5

Since you took multivariable calculus, i would say differential equations

6

Oops, there was a typo. I didn’t mean “what to take first”, what I mean was “which should I take that is more relevant for my major and minor”.

And what I mean from “setting up a multiple integral”, I mean determining whether dx or dy or dz goes first and which goes last on the integral, or in the case of a double integral, determining whether dx or dy goes first over a general region. Did that make any sense or get the idea lol? I do need to brush up on a few stuff.

The guy who told me vector analysis was useless told me he took a course where it combines the vector analysis and differential equations course topics above (the ones I listed) into one. But he was the only person who gave me the advice, so I’m not sure whether to trust him.

7

Oh and also, I forgot how to change the order of integration (dxdy to dydx)

8

As boneH3ad as said both vector analysis and differential equations are important. In fact the backbone of EE, Maxwell’s equations require both. You’ll be hard pressed to find any math that is not useful for EE. EE is vast, and depending on what focus on dictates what math you should be well versed in.

With that being said, Differential Equations and Vector Analysis (which by your description sounds more like linear algebra) are bare-bone necessities.

Undergrad EE will need the following:

Linear Algebra, Calculus, Differential Equations (Ordinary and Partial), Complex Analysis, Discrete Mathematics (this is vast, includes: Boolean Algebra & Directed Graphs & Number Theory), Symbolic Logic (which could almost be considered a subject in Discrete Math). Somewhere in there you will need to know Fourier Analysis (for signals and systems), as well as a bunch of integral transforms (Laplace, Z, Fourier, etc.). If you start delving into the AI/Machine learning part (the data sciences as some may call it) you will need Statistics and Probability.

9

Is your community college stronger in math teaching (class size, good profs on rate my professor, etc) or your four-year transfer school? Take DiffEQ at the school where it will be taught well, and take the other after transfer.

10

Diff Eq is usually 'Calc 4" in the engineering math sequence…i think I would take that and take Vector analysis at your new school.