This module is part of the collection, A First Course in Electrical and Computer Engineering. The LaTeX source files for this collection were created using an optical character recognition technology, and because of this process there may be more errors than usual. Please contact us if you discover any errors.
It is essential to write out, term-by-term, every sequence and sum in
this chapter. This demystifies the seemingly mysterious notation. The example on compound interest shows the value of limiting arguments in everyday
life and gives
e
x
e
x
some real meaning. The function ejθejθ, covered in the section "The Function of ejθ and the Unit Circle
and "Numerical Experiment (Approximating ejθ, must be understood by all students before proceeding to "Phasors" .
The Euler and De Moivre identities provide every tool that students need to
derive trigonometric formulas. The properties of roots of unity are invaluable
for the study of phasors in "Phasors" .
The MATLAB programs in this chapter are used to illustrate sequences
and series and to explore approximations to
sin
θ
sinθ and
cos
θ
cosθ. The numerical
experiment in "Numerical Experiment (Approximating ejθ illustrates, geometrically and algebraically, how
approximations to ejθejθ converge.
“Second-Order Differential and Difference Equations” is a
little demanding for freshmen, but we give it a once-over-lightly to illustrate
the power of quadratic equations and the functions ex and ejθejθ. This section
also gives a sneak preview of more advanced courses in circuits and systems.
It is probably not too strong a statement to say that the function
e
x
e
x
is the most important function in engineering and applied science. In this
chapter we study the function
e
x
e
x
and extend its definition to the function
ejθejθ. This study clarifies our definition of ejθejθ from "Complex Numbers" and leads us to
an investigation of sequences and series. We use the function ejθejθ to derive
the Euler and De Moivre identities and to produce a number of important
trigonometric identities. We define the complex roots of unity and study
their partial sums. The results of this chapter will be used in "Phasors" when
we study the phasor representation of sinusoidal signals.
(What does "Endorsed by" mean?)
"Reviewer's Comments: 'I recommend this book as a "required primary textbook." This text attempts to lower the barriers for students that take courses such as Principles of Electrical Engineering, […]"