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To the teacher:

An incomplete understanding of complex numbers and phasors handicaps students in circuits and electronics courses, and even more so in advancedcourses such as electromagnetics. optics, linear systems, control, and communication systems. Our faculty has decided to address this problem as early as possible in the curriculum by designing a course that drills complex numbers and phasors into the minds of beginning engineering students. We haveused power signals, musical tones, Lissajous figures, light scattering, and RLC circuits to illustrate the usefulness of phasor calculus. "Linear Algebra" through "Binary Codes" introduce students to a handful of modern ideas in electrical and computer engineering. The motivation is to whet students' appetites for more advancedproblems. The topics we have chosen – linear algebra, vector graphics, filtering, and binary codes – are only representative.

At first glance, many of the equations in this book look intimidating to beginning students. For this reason, we proceed at a very measured pace. Inour lectures, we write out in agonizing detail every equation that involves a sequence or series. For example, the sum n = 0 N - 1 z n is written out as

1 + z + z 2 + + z N - 1 ,

and then it is evaluated for some specific value of z before we derive the analytical result 1 - z N 1 - z Similarly, an infinite sequence like lim n ( 1 + x n ) n is written out as

( 1 + x ) , ( 1 + x 2 ) 2 , ( 1 + x 3 ) 3 , ... , ( 1 + x 100 ) 100 , ... ,

and then it is evaluated for some specific x and for several values of n before the limit is derived. We try to preserve this practice of pedantic excess untilit is clear that every student is comfortable with an idea and the notation for coding the idea.

To the student:

These are exciting times for electrical and computer engineering. To celebrate its silver anniversary, the National Academy of Engineering announced in February of 1990 the top ten engineering feats of the previous twenty-fiveyears. The Apollo moon landing, a truly Olympian and protean achievement, ranked number one. However, a number of other achievements in the topten were also readily identifiable as the products of electrical and computer engineers:

  1. communication and remote sensing satellites,
  2. the microprocessor,
  3. computer-aided design and manufacturing (CADCAM),
  4. computerized axial tomography (CAT scan),
  5. lasers, and
  6. fiber optic communication.

As engineering students, you recognize these achievements to be important milestones for humanity; you take pride in the role that engineers have playedin the technological revolution of the twentieth century.

So how do we harness your enthusiasm for the grand enterprise of engineering? Historically, we have enrolled you in a freshman curriculum of mathematics, science, and humanities. If you succeeded, we enrolled you in an engineering curriculum. We then taught you the details of your professionand encouraged your faith that what you were studying is what you must study to be creative and productive engineers. The longer your faith held,the more likely you were to complete your studies. This seems like an imperious approach to engineering education, even though mathematics, physics, and the humanities are the foundation of engineering, and details are whatform the structure of engineering. It seems to us that a better way to stimulate your enthusiasm and encourage your faith is to introduce you early in yourstudies to engineering teachers who will share their insights about some of the fascinating advanced topics in engineering, while teaching you the mathematical and physical principles of engineering. But you must match the teacher's commitment with your own commitment to study. This means that you mustattend lectures, read texts, and work problems. You must be inquisitive and skeptical. Ask yourself how an idea is limited in scope and how it might beextended to apply to a wider range of problems. For, after all, one of the great themes of engineering is that a few fundamental ideas from mathematics andscience, coupled with a few principles of design, may be applied to a wide range of engineering problems. Good luck with your studies.

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Source:  OpenStax, A first course in electrical and computer engineering. OpenStax CNX. Sep 14, 2009 Download for free at http://cnx.org/content/col10685/1.2
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