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.
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