# Mathematics question

1. Nov 2, 2005

### 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.

2. Nov 2, 2005

### 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.

3. Nov 3, 2005

### 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.

4. Nov 3, 2005

### Staff: Mentor

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.

5. Nov 4, 2005

### 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. :)

6. Nov 4, 2005

### Staff: Mentor

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.

7. Nov 4, 2005

### 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.

8. Nov 4, 2005

### Staff: Mentor

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.