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Functions of a Complex Variable by Francis B Hildebrand with Selected Chapters from Richard Courant's The Theory of Functions of a Complex Variable.

Topics in the theory of analytic functions of a complex variable, including residue calculus, conformal mapping, and applications.

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A complex number \$\\alpha\$ is an expression of the form \$\\alpha=a+i b\$, where \$a\$ and \$b\$ are real numbers and \$i\$ is the imaginary unit, satisfying the equation
$
i^{2}=-1.
$
We speak of $a$ as the real part of \$\\alpha\$ and of \$b\$ as the imaginary part of \$\\alpha\$, and write
$
\\alpha=a+i b: \\quad a=\\Re(\\alpha), \\quad b=\\Im(\\alpha) .
$
In the same way, we may consider a complex variable \$z=x+i y\$, where \$x\$ and \$y\$ are real variables.

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This is a test.

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Functions of a Complex Variable

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