Complex Analysis

Additional Info

  • ECTS credits: 6
  • Semester: 2
  • University: University of L'Aquila
  • Prerequisites:

     

    Knowledge of all topics treated the Mathematical Analysis courses in the first and second year: real functions of real variables, limits, differentiation, integration; sequences and series of funcions; ordinary differential equations

  • Objectives:

     

    Knowledge of basic topics of complex analysis: elementary functions of complex variable, differentiation, integration and main theorems on analytic functions . Ability to use such knowledge in solving problems and exercises

  • Topics:

     

    - Complex numbers. Sequences. Elementary functions of complex numbers. Limits, continuity. Differentiation. Analytic functions. Harmonic functions.
    - Contour integrals. Cauchy's Theorem. Cauchy's integral formula. Maximum modulus theorem. Liouville's theorem. Morera's theorem.
    - Series representation of analytic functions. Taylor's theorem. Laurent's series and classification of singularities.
    - Calculus of residues. The residue theorem. Application in evaluation of integrals on the real line and Principal Value. The logarithmic residue, Rouche's theorem.
    - Fourier transform for L^1 functions. Applications. Fourier transform for L^2 functions. Plancherel theorem.
    - Laplace transform and applications.

  • Books:

     

    - J.E. Marsden, M.J. Hoffman, Basic complex analysis , Freeman New York.
    - W. Rudin, Real and complex analysis , Mc Graw Hill.

Read 1164 times Last modified on Tuesday, 19 May 2020 14:09