 
Summary: ME 413 Systems Dynamics & Control Chapter Two: Laplace transform
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A. Bazoune
2222....1111 INTRODUCTIONINTRODUCTIONINTRODUCTIONINTRODUCTION
Laplace Transform is one of the most important mathematical tools available for
modeling and analyzing linear systems.
2222....2222 COMPLEX NUMBERS, COMPLEX VARIABLES, ANDCOMPLEX NUMBERS, COMPLEX VARIABLES, ANDCOMPLEX NUMBERS, COMPLEX VARIABLES, ANDCOMPLEX NUMBERS, COMPLEX VARIABLES, AND
COMPLEX FUNCTIONSCOMPLEX FUNCTIONSCOMPLEX FUNCTIONSCOMPLEX FUNCTIONS
Complex Numbers Using the notation 1= j , one can
express all complex numbers in engineering calculations as
= +z x jy
where x is the real part and jy is the imaginary part. Notice that both x and y
are real and that j is the only imaginary quantity in the expression above.
x
y
z
Fig. 21 Complex plane representation of a complex number z .
