ME 413 Systems Dynamics & Control Chapter Two: Laplace transform CCCCCCCChhhhhhhhaaaaaaaapppppppptttttttteeeeeeeerrrrrrrr 22222222 Summary: ME 413 Systems Dynamics & Control Chapter Two: Laplace transform 1/36 CCCCCCCChhhhhhhhaaaaaaaapppppppptttttttteeeeeeeerrrrrrrr 22222222 LLLLLLLLaaaaaaaappppppppllllllllaaaaaaaacccccccceeeeeeee TTTTTTTTrrrrrrrraaaaaaaannnnnnnnssssssssffffffffoooooooorrrrrrrrmmmmmmmm 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. 2-1 Complex plane representation of a complex number z . Collections: Engineering