Analise Complexa
Informações Gerais
Informações Gerais
Horários:
Segunda-Feira : 17:00h - 18:50h Sala do Vasco
Quarta-Feira: 15:00h - 17:00h Sala do Vasco
Sexta-Feira: 17:00h - 18:50h Sala do Vasco
Calendário
Calendário
Provas: (sob reserva de modificações)
Primeira prova P1:
Segunda prova P2:
Terceira prova P3:
Revisão:
Provas P1: A ser determinado
Provas P2: A ser determinado
Provas P3: A ser determinado
Material de apoio
Material de apoio
E. M. Stein and R. Shakarchi, Complex analysis, Princeton Lectures in Analysis, 2, Princeton University Press, Princeton, NJ, 2003.
J. B. Conway, Functions of one complex variable, Springer-Verlag, New York, 1973.
Listas de Exercícios:
Listas de Exercícios:
Incluso nas notas de aula
Pre-requisitos: Curso de Espaços Métricos e Análise no Rn, ajuda muito.
Holomorphic functions and Analytic functions 1 - The extended plane and its spherical representation (The Riemann sphere) 2 - Power Series and Holomorphic functions
Integration along curves 3 - Riemann Stieltjes complex integrals 4 - Rectifiable path, complex integral over rectifiable path, Local existence of primitives
Cauchy’s Theorem and Its Applications 5 - Cauchy-Goursat theorem, evaluation of some integrals 6 - Cauchy’s integral formulas 7 - Cauchy's Theorem general I 8 - Elliptic regularity and Analytic continuation 9 - Uniform limit of holomorphic functions and Schwarz reflection principle 10 - Winding number (index of curves) 11 - Jordan curve theorem (optional)
Meromorphic Functions Zeros of Holomorphic functions Singularities and meromorphic functionsThe residue formulaThe complex logarithmFourier series and harmonic functionsPaley-Wiener theoremAnalytic maps and M\"obius transforms
Entire Functions
Notas de Aula
Holomorphic functions and Analytic functions 1 - The extended plane and its spherical representation (The Riemann sphere) 2 - Power Series and Holomorphic functions Notas de Aula
Integration along curves 3 - Riemann Stieltjes complex integrals 4 - Rectifiable path, complex integral over rectifiable path, Local existence of primitives
Cauchy’s Theorem and Its Applications 5 - Cauchy-Goursat theorem, evaluation of some integrals 6 - Cauchy’s integral formulas 7 - Cauchy's Theorem general I 8 - Elliptic regularity and Analytic continuation 9 - Uniform limit of holomorphic functions and Schwarz reflection principle 10 - Winding number (index of curves) 11 - Jordan curve theorem (optional)
Meromorphic Functions Zeros of Holomorphic functions Singularities and meromorphic functionsThe residue formulaThe complex logarithmFourier series and harmonic functionsPaley-Wiener theoremAnalytic maps and M\"obius transforms
Entire Functions
Bibliografia indicada
Bibliografia indicada
E. M. Stein and R. Shakarchi, Complex analysis, Princeton Lectures in Analysis, 2, Princeton University Press, Princeton, NJ, 2003.
J. B. Conway, Functions of one complex variable, Springer-Verlag, New York, 1973.
T. W. Gamelin, Complex analysis, Undergraduate Texts in Mathematics, Springer-Verlag, New York, 2001.
Terence Tao: Analysis II, 3rd edition, Texts and Readings in Mathematics, Hindustan Book Agency, Springer 2015.