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Viser: Problems and Theorems in Analysis I Series. Integral Calculus. Theory of Functions
Problems and Theorems in Analysis I Series. Integral Calculus. Theory of Functions
(2021)
om ca. 10 hverdage
Detaljer om varen
- 1. Udgave
- Udgiver: (Oktober 2021)
- ISBN: 9783540636403
Part.- 1 Complex Numbers and Number Sequences.- Regions and Curves. Working with Complex Variables.- Location of the Roots of Algebraic Equations.- Zeros of Polynomials, Continued. A Theorem of Gauss.- Sequences of Complex Numbers.- Sequences of Complex Numbers, Continued: Transformation of Sequences.- Rearrangement of Infinite Series.- 2 Mappings and Vector Fields.- The Cauchy-Riemann Differential Equations.- Some Particular Elementary Mappings.- Vector Fields.- 3 Some Geometrical Aspects of Complex Variables.- Mappings of the Circle. Curvature and Support Function.- Mean Values Along a Circle.- Mappings of the Disk. Area.- The Modular Graph. The Maximum Principle.- 4 Cauchy's Theorem * The Argument Principle.- Cauchy's Formula.- Poisson's and Jensen's Formulas.- The Argument Principle.- Rouche's Theorem.- 5 Sequences of Analytic Functions.- Lagrange's Series. Applications.- The Real
Part of a Power Series.- Poles on the Circle of Convergence.- Identically Vanishing Power Series.- Propagation of Convergence.- Convergence in Separated Regions.- The Order of Growth of Certain Sequences of Polynomials.- 6 The Maximum Principle.- The Maximum Principle of Analytic Functions.- Schwarz's Lemma.- Hadamard's Three Circle Theorem.- Harmonic Functions.- The Phragmén-Lindelöf Method.- Author Index.