ECE 3337 Hebert
Schaum's Complex variables
chapters/sections that we will cover.


Chapter 1 Complex Numbers
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Real number system
graphical representation of real numbers
complex number system
fundamental operations with complex numbers
absolute value
axiomatic foundations of the complex number system
graphical representation of complex numbers
polar form of complex numbers
de moivres theorem
roots of complex numbers
euler's formula
polynomial equations
the nth roots of unity
vector interpetation of complex numbers
point sets

Chapter 2 Functions, limits, and continuity
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variables and functions
single and multiple valued functions
transformations
the elementary functions
limits
theorems on limits
infinity
continuity
continuity in a region

Chapter 3.  Complex differentiation and the cauchy-riemann equations
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derivatives
analytic functions
cauchy-riemann equations
harmonic functions
rules for differentiation
derivatives of elementary functions
l'hopitals's rule
singular points

Chapter 4. Complex integration and cauchy's theorem
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complex line integrals
real line integrals
connection between real and complex line integrals
properties of integrals
change of variables
simply and multiply connected regions
convention regarding traversal of a closed path
cauchy's theorem. The cauchy-goursat theorem
integrals of special functions
some consequences of cauchy's theorem

Chapter 5.  Cauchy's integral formula and related theorems
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cauchy's integral formula