Complex Functions Examples Collection

The theory of complex functions is a large field in the mathematics studies. SPE, scientific pdf ebooks presents here a plethore of complex ebooks to download for free. It consists on 9 scientific pdf ebooks. You can find it as a collection here. Please share it and leave a comment if you find it interesting. Good lecture!

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Introduction 1 
Some necessary theoretical results 2 
Topological concepts 3 
Complex Functions 4 
Limits 5 
Line integrals 6 
Differentiable and analytic functions; Cauchy-Riemann’s equations 7 
The polar Cauchy-Riemann’s equations 8 
Cauchy’s Integral Theorem 9 
Cauchy’s Integral Formula 10 
Simple applications in Hydrodynamics
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Some practical formulas in the applications of the calculation of residues 1.1 
Trigonometric integrals 1.2
Improper integrals in general 1.3 
Improper integrals, where the integrand is a rational function 1.4 
Improper integrals, where the integrand is a rational function time a  trigonometric function 1.5 
Cauchy’s principal value 1.6 
Sum of some series
2.  Trigonometric integrals
3.  Improper integrals in general
4.  Improper integral, where the integrand is a rational function 
5.  Improper integrals, where the integrand is a rational function times a  trigonometric function
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Rules of computation of residues
2  Residues in nite singularities
3  Line integrals computed by means of residues
4  The residuum at ∞
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Introduction 
1.  Some necessary theoretical results 
2.  Polynomials 
3.  Fractional functions 
4.  The exponential function and the logarithm function 
5.  Trigonometric and hyperbolic functions
6.  Harmonic functions
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Introduction 
1.  The complex numbers 
2.  Polar form of complex numbers 
3.  The binomial equation 
4.  Equations of second degree 
5.  Rational and multiple roots in polynomials 
6.  Symbolic currents and voltages 
7.  Geometrical point sets
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Introduction 
1.  Some theoretical background 
2.  Laurent series 
3.  Fourier series 
4.  Laurent series solution of dierential equations 
5.  Isolated boundary points
6.  The conditions around the point at infinity
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Introduction 
1.  Some simple theoretical results concerning power series 
2.  the Theory of Complex Functions and Simple Fourier series 
3.  Power series 
4.  Analytic functions described as power series 
5.  The power series method  and Linear differential equations
6.  The classical differential equations 
7. Some more difficult differential equations
8.  Zeros of analytic functions 
9.  Fourier series 
10.  The maximum principle
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Introduction 
1.  Some theoretical background 
1.1  The Laplace transform
1.2  The Mellin transform
1.3  The z-transform
1.4  Linear difference equations of second order and of constant  coefficients
2.  The Laplace transform 
3.  The Mellin transform
4.  The 3-transform 
5.  The Fourier transform 
6.  Linear difference equations 
7.  Distribution theory
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Introduction 
1. Some theoretical background 
1.1  The argument principle
1.2  Stability criteria
1.3  Inverse functions
2.  The argument variation 
3.  Stability criteria
4.  The innitely-valued function log z
5.  The many-valued functions az and za 
6.  The Arcus Functions and the Area Functions 
7.  The inverse of an algebraic expression 
8.  Simple example of potential flows
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Complex Functions Examples Collection

Keywords: maths, mathematics, complex, complex functions