Advanced Math for Engineers: Complex Var & Diff Eqns

[Pseudo Statistic]

Hey,
So the other day I was at this bookstore looking for a cheap book on differential equations to buy... when I found one in the Arabic section. (Over here English books on math are atleast $60USD even if they're around 200-400pages.. kind of a rip off..)
So I saw some books in an "Advanced Mathematics for Engineers" series...
But what kind of perplexed me was how book 1 pretty much focused on functions of a complex variable and book 2 then introduced differential equations.
This brings up two things to mind..
1) Of what use is functions of a complex variable to engineers? What exactly can it be applied to, and what can only be described with complex functions?
2) Would it be absolutely required to have a course in complex variables first before learning about differential equations?
Thanks a lot for any input.

 

[FredGarvin]

1) Ask any electrical engineer that. I had an entire semester of complex variable calc that was pretty much catering to the EE side of the fence. As a matter of fact, I was the only ME in the class.

2) No. Not at all. You should have basic knowledge of them, but not an entire course dedicated to them.

 

[Tide]

Pseudo Stat,

Electrical engineering uses complex analysis more than most other engineering fields. It is, in fact, quite possible to do electrical engineering without complex analysis - but you'll be exerting 10 to 20 times the effort in doing even the simplest tasks! It will wear you down.

I recommend at least a solid familiarity with complex numbers embarking on a study of differential equations.

 

[berkeman]

The complex exponential is an eigenfunction for linear time invariant systems, so you use complex analysis a lot in working with LTI systems like filters and other circuits. The combination of cos()+jsin() is a solution to many problems involving LTI systems, including ones involving DiffEqs. Fourier analysis, transforms, etc. all use complex math. And it really helps a lot to be able to visualize the complex plane and its extension through time (time axis perpendicular to the complex plane) when doing stability analysis in feedback systems.

I think you can study DiffEqs before having much complex analysis background -- that's how it was ordered at my school.

 

[Pseudo Statistic]

Alright, thanks... I'll probably look into getting that book on complex analysis then... because I want to make sure I understand all of the math down to the very last theorem rather than get lost, stop reading, and never look back.. :D
Also, would be nice to get a head start on the university work. :)

 

[berkeman]

Hey, check out this book for fun: "Designing Digital Filters" by Charles Williams. It's one of the best books I've found on the subject, and it is filled with practical uses of complex math. It also has a good tutorial appendix on complex math that will give you a quick start. You don't need a lot of previous background to learn about digital filters, and you'll use the concepts a lot in your upcoming univerity work.

 

[Pseudo Statistic]

Thanks, I'll look into it on Amazon and order it the next time I do my periodical ordering of math-related books. :D
And just out of curiosity, would anybody know how, or if, complex functions are of relevance to Mechanical Engineering?
Because I hear things such as "So and so can only be described using complex math..." but I don't exactly understand how that can be so.
Anyone care to elaborate? Thanks.

 

[berkeman]

I think complex math is mainly useful for situations that involve periodic functions (voltages, currents, mechanical oscillations), and LTI systems. So for mechanical systems, things like stability analysis of a bridge in wind conditions would involve complex math probably.