Math in Electrical Engineering

Date: 05/01/2003 at 20:41:21
From: Nikki
Subject: Electronical and Electrical Engineering

What math is involved in electronical and electrical engineering?

Date: 05/02/2003 at 12:48:29
From: Doctor Roy
Subject: Re: Electronical and Electrical Engineering

Hi,

Thanks for writing to Dr. Math.

There's really a lot of math involved in electrical and electronic
engineering. How much you do depends on what area of EE (shorthand for 
electrical and electronic engineer) you do. For example, there's a lot 
more abstract math in communication theory and signal processing, and 
many more very direct calculation differential equations in circuit 
theory and systems design.

Let me begin with basic systems / circuit theory. Circuit theory at 
its simplest form is really differential equations, which is basically
solving equations involving derivatives, so you need some calculus.
And algebra and trigonometry are fundamental to understanding it. 
Every basic circuit element (resistor, capacitor, inductor) has a
related current-voltage relation determined by its impedance. This is
where complex numbers come in. For example:

Resistor:   V = IR   (V = voltage, I = current, R = resistance)
Capacitor:  V = (jwC)I (C = capacitance, w = frequency, j =sqrt(-1))
Inductor:   V = I/(jwL)   (L = inductance)

So, even in the first area of EE, circuit theory, there's already
calculus, complex numbers, and the Laplace transform (if you look
carefully based on physical properties).

If we move on to the theory of "how" electromagnetism works, we have
Maxwell's equations. These pretty much form the basis for EE. They are 
written in both integral and derivative forms and involve vectors. So, 
suddenly, we also have vector calculus.

Let's go on to networks. Networks involve nodes communicating with 
each other. A lot of computers linked together form a network. Cell 
phone users form a network. Networking involves the study of the best 
way of implementing a network. Much work has been done to find the 
best protocol, or method, for doing so. It involves a lot statistical/
probability calculation. We really can't tell how people will use 
networks, so we need statistical models.  

If we move to Communication Theory/Information Theory, a mathematician
named Claude Shannon developed a mathematical theory to explain 
various quantities related to how to communicate between devices.
Communication Theory is used everywhere, from RADAR, to telephones, to 
devices within computers. The underlying theory requires at least 
calculus, some linear algebra, some measure theory, etc.

If you look at modern EE, researchers have basically looted libraries 
looking for abstract mathematics done in the last few hundred years.  
Each abstract mathematical theorem somehow finds its use in EE. Even 
wavelets, which have revolutionized signal processing, were discovered 
by mathematicians early in the 20th century, but not used by engineers 
until 20 years ago. 

If I seem to be answering in general, it's because it is not possible 
to do EE without math. And depending on whether you do research or 
implementation, you use a different amount of math, either a lot of 
math at a very high level or some very basic calculus. A specific 
answer could potentially fill books.

I hope this helps.

- Doctor Roy, The Math Forum
  http://mathforum.org/dr.math/ 

Date: 05/04/2003 at 19:45:31
From: Nikki
Subject: Thank you (Electronical and Electrical Engineering)

Thank you for the great response! It helped a lot.