Complex analysis

by Tokiou Narusawa

It is Complex Analysis that I was specializing in university era and mathematical foundation theory. In the United States, I heard that I will study at a graduate school. Certainly, in mathematics, together with multivariate analysis functions, we enter the most difficult field. Knowledge in most fields of mathematics is necessary.
● Complex Analysis
- Chapter 1 Complex Numbers
- Algebra of complex numbers
- Arithmetic operation
- square root
- justification
- conjugate complex number, absolute value
- Inequality
- Complex numbers and geometric explanations
- Geometric explanation of additive and multiplicative
- Binomial equation
- Analytic geometry
- Spherical display
- Chapter 2 Complex Functions
- Introduction of concept of analysis function
- Limit and continuity
- Analysis function
- polynomial
- rational function
- Basic properties of the serial number
- Sequence
- Series
- uniform convergence
- Ordinal number
- Abel's continuity theorem
- Exponential function and trigonometric function
- Phase set phase
- Sets and elements
- Distance space
- Connectivity
- Compact
- Continuous function
- Phase space
- isometric
- Curve and closed curve
- conformal mapping
- length and area
(I contradict the general relativity of Einstein.)
-1 order conversion
-1 order conversion group
- anharmonic ratio
Symmetry
- Oriented circle
- Yen of the circle
- Basic conformal mapping
- Use contour lines
- Basic mapping
- Primary Riemann surface
- Complex integral
- Line integral
- Curve with length
- Line integral as a function of the curve
- Cauchy's theorem for a rectangle
- Cauchy's theorem for a disc
- Cauchy's integral formula
- Exponent of points on closed curves
- Integral formula
- higher order derivatives
- Local properties of analytic functions
- removable singularity
- Zero and Poles
- Local mapping
- Principle of maximum value
- General form of Cauchy's theorem
- Chain and cycle
- Single connection
- Homology
- General form of Cauchy's theorem
- Proof of Cauchy's theorem
- Complete differentiation locally
- Multiple connection area
- Residue analysis
- residue theorem
- Principle of argument
- Calculation of definite integral
- Harmonic function
- Definitions and basic properties
- the nature of the mean
- Poisson's formula
- Schwarz's theorem
- Principle of mirror image
- Series expansion and infinite product expansion
- Weierstrass's theorem
- Taylor expansion
( Fourier series)
- Laurent series
- Partial fraction and factorization
- Infinite product
- Basic product
- Gamma function
- Stirling's formula
- Align function
- Official official
- Hadamard's theorem
- Riemann's zeta function
- Development by product
Connection of - ζ (s) to all planes
- Function Equation
- Zero of Zeta function
- Normal group
- Continuous
- Normality and compact
- Alzera's theorem
- Analysis function family
- Classical definition
- Chapter 6 Conformal Map and Dirichlet Problem
- Definition of Riemann map
- Theorem and proof
- Behavior at boundary
- Application of the principle of mirror image
- Analysis curve
- conformal mapping of polygons
- Behavior in the corner
- Schwarz-Kristoffiff's official
- Rectangular mapping
- Schwarz's triangle function
- Standard mapping of multiple connection regions
- harmonic measure
- Green function
- parallel ridge line area
- Elliptic function
- Single period function
- Display by exponential function
- Fourier expansion
- finite order function
- Double period function
- periodic addition group
- Unimodular transformation
- Standard basis
- General Properties of Elliptic Functions
- Weierstrass's theory
- Weierstrass's ρ function (p function)
- Functions ζ (z) and σ (z)
- Differential equation
- Modular function λ (t)
Conformal mapping by -λ (t)
- Chapter 8 Global Analysis Function
- Analytical connection
- Weierstrass's theory
- Buds and layers

13 pages, Kindle Edition

Published December 6, 2017