ELEC3002/ELEC7005 Lecture 2
Complex Analysis (chapter 1 in Glyn James) complex differentiation
This lecture covers sections 1.3 and 1.4 ITEE
complex 2/1
Complex differentiation
The derivative of a real function is straightforward. ( x )  f ( x0
Demonstration problem sheet, Vectors 1. A 3D vector a is given by a = [ a1 , a2 , a3 ] . Find a unit vector parallel to a . 2. The initial point of a vector is P ( x1 , y1 , z1 ) , the terminal point is P2 ( x2 , y2 , z2 ) . What is the 1
The University of Queensland School of Information Technology & Electrical Engineering ELEC3002/ELEC7005 Computational Mathematics for Engineers Tutorial Complex #2 Q1 The mapping w = z + (, both constant complex numbers) maps the point z =1+ j to t
The University of Queensland School of Information Technology & Electrical Engineering ELEC3002/ELEC7005 Computational Mathematics for Engineers Tutorial Complex #1 Q1 Show that cos =
1 j 1 j e + e  j ; sin = e  e  j . 2 2j
15  8 j
(
)
(
Solutions to Tutorial Complex#1 Q1. This is fundamental, begin with the deMoivre relationships: e j = cos + j sin
e  j = cos  j sin then add and subtract these to get the result. 1 1 j cos = e j + e  j sin = e  e  j 2 2j
(
)
(
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Q2

MIDI AND THE AVR
I N T R O TO U S I N G T H E AV R I N M I D I A P P L I C A T I O N S
PAUL MADDOX
MARCH 2002
TABLE OF CONTENTS
Introduction ..2 MIDI, what is it? .2 MIDI specs, a quick guide ..3 MIDI; the hardware.4 MIDI gotcha's..7 MIDI to CV conv
ELEC3002/ELEC7005 Lecture 5
An application using complex analysis: The TimeFrequency Domain
Complex 5/1
ITEE
Timefrequency domain. What is it?
We are well acquainted with both time and frequency representations of a signal. Let's consider a few
ELEC3002/ELEC7005 Lecture 4
Residue Calculus
(Section 1.64 end in James)
Complex 4/1
ITEE
What's it good for?
Well, the coefficients of bk are interesting, since the first one
b1 = 1 2 j f ( z ) dz
C
is a multiple of the contour integral around
ELEC3002/ELEC7005 Lecture 3
Singularities in complex analysis. Integration.
(sections 1.5 and 1.6 in James)
Complex 3/1
ITEE
Singularities, zeros and residues
A singularity is a point in the complex plane where the function f(z) ceases to be analy
ELEC3002/ELEC7005 Lecture 1
Complex Analysis (Chapter 1 in Glyn James)
This lecture covers section 1.2 A/Prof. Nick Shuley, Room 73535
complex 1/1
ITEE
What in this section?
All about the use of complex analysis and its application to Electrical