Description: Basic treatment includes existence theorem for solutions of differential systems where data is analytic, holomorphic functions, Cauchy's integral, Taylor and Laurent expansions, more. Exercises. 1973 edition. CHAPTER I. POWER SERIES IN ONE VARIABLE I. Formal power series 2. Convergent power series 3. Logarithmic and exponential functions 4. Analytic functions of one variable Exercises CHAPTER II. HOLOMORPHIC FUNCTIONS; CAUCHY'S INTEGRAL I. Curvilinear integrals; primitive of a closed form 2. Holomorphic functions; fundamental theorems Exercises CHAPTER III. TAYLOR. AND LAURENT EXPANSIONS I. Cauchy's inequalities; Liouville's theorem 2. Mean value property and the maximum modulus principle 3. Schwarz' lemma 4. Laurent's expansion 5. Introduction of the point at infinity. Residue theorem 6. Evaluation of integrals by the method of residues Exercises CHAPTER IV. ANALYTIC FUNCTIONS OF SEVERAL VARIABLES; HARMONIC I. Power series in several variables 2. Analytic functions 3. Harmonic functions of two real variables 4. Poisson's formula; Dirichlet's problem 5. Holomorphic functions of several complex variables Exercises "CHAPTER V. CONVERGENCE OF SEQUENCES OF HOLOMORPHIC OR MEROMORPHIC FUNCTIONS ; SERIES, INFINITE PRODUCTS ; NORMAL FAMILIES" I. Topology of the space C(D) 2. Series of meromorphic functions 3. Infinite products of holomorphic functions 4. Compact subsets of H(D) Exercises CHAPTER VI. HOLOMORPHIC TRANSFORMATIONS I. General theory ; examples 2. "Conformal representation ; automorphisms of the plane, the Riemann sphere, the open disc" 3. Fundamental theorem of conformal representation 4. Concept of complex manifold ; integration of differential forms 5. Riemann surfaces Exercises CHAPTER VII. HOLOMORPHIC SYSTEMS OF DIFFERENTIAL EQUATIONS I. Existence and uniqueness theorem 2. Dependence on parameters and on initial conditions 3. Higher order differential equations Exercises SOME NUMERICAL OR QUANTITATIVE ANSWERS TERMINOLOGICAL INDEX NOTATIONAL INDEX
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EAN: 9780486685434
UPC: 9780486685434
ISBN: 9780486685434
MPN: N/A
Number of Pages: 240 Pages
Language: English
Publication Name: Elementary Theory of Analytic Functions of One or Several Complex Variables
Publisher: Dover Publications, Incorporated
Item Height: 0.5 in
Subject: Functional Analysis, Complex Analysis
Publication Year: 1995
Features: New Edition
Type: Textbook
Item Weight: 10.2 Oz
Subject Area: Mathematics
Item Length: 8.5 in
Author: Henri Cartan
Series: Dover Books on Mathematics Ser.
Item Width: 5.4 in
Format: Trade Paperback
