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chapter 1 complex numbers and functions of a complex variable
��1.1 complex numbers and its four fundamental operations
��1.2 geometric representation of complex numbers
��1.3 complex conjugates
��1.4 powers and roots
��1.5 riemann sphere and infinity
��1.6 complex number sets
��1.7 functions of a complex variable
��exercise 1
chapter 2 analytic functions
��2.1 the concept of analytic function
��2.2 necessary and sufficient conditions of analytic functions
��2.3 elementary functions
��exercise 2
chapter 3 complex integrals
�� 3.1 the concept of complex integral
�� 3.2 cauchy integral theorem
�� 3.3 cauchy integral formula
�� 3.4 analytic functions and harmonic functions
�� exercise 3
chapter 4 series
�� 4.1 series of complex numbers and series of complex functions"
�� 4.2 power series
�� 4.3 taylor series
4.4 laurent series
�� exercise 4
chapter 5 residues
�� 5.1 isolated singularities
�� 5.2 residues
�� 5.3 application of residues in evaluating definite and improper integrals
�� exercise 5
chapter 6 conformal mappings
��6.1 the concept of conformal mapping
��6.2 fractional linear transformations
��6.3 condition of uniqueness
��6.4 some important fractional linear transformations
��6.5 mapping by some elementary functions
��exercise 6
chapter 7 fourier transform
��7.1 fourier integral and fourier integral theorem
��7.2 fourier transform and inverse fourier transform
��7.3 unit impulse functions
��7.4 generalized fourier transform
��7.5 the properties of fourier transform
��7.6 convolution
��exercise 7
chapter 8 laplace transform
��8.1 the concept of laplace transform
��8.2 the properties of laplace transform
��8.3 inverse laplace transform
��8.4 application of laplace transform
��exercise 8
answers to selected exercises
��exercise 1
��exercise 2
��exercise 3
��exercise 4
��exercise 5
��exercise 6
��exercise 7
��exercise 8
bibliography
appendix
index
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