Theory of function of one complex variable, and applications to calculus. Fourier transform and Laplace transform. Introduction to Partial Differential Equations. The aim is to provide the students with basic tools for addressing scientific issues which can be formalized in the language and methods of complex analysis and functional transforms.
Functions of one complex variable. Holomorphic functions. Cauchy-Riemann equations. Cauchy's integral formula. Analiticity of holomorphic functions and applications. Laurent series. Calculus of residues. Fourier transform. Laplace transform. Applications to ordinary differential equations and to to partial differential equations.
|H. F. Weinberger||A first course in partial differential equations: with Complex Variables and Transform Methods||Dover||1995||978-0486686400|
|John H. Mathews, Russel W. Howell||Complex Analysis for Mathematics and Engineering (Edizione 6)||Jones & Bartlett||2010||978-1449604455|
The final exam consists of a written test followed, in case of a positive result, by an oral test. The written test consists of some exercises on the program.
The oral test will concentrate mainly but not exclusively on the theory.
The written part of the exam is aimed to verify the ability to solve problems related to the course program, to possess adequate analysis, synthesis and abstraction capacity, starting from requests formulated in natural or specific language.
The oral part is aimed to verify the ability to produce rigorous proofs as well as analysis, synthesis and abstraction abilities. The mark gained in the oral exam (in the interval -5, +5) will be added to the written test mark to obtain the final grading.
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