MATHEMATICAL ANALYSIS III

Study of the theory of functions of a complex variable and the Integral Transforms. The student will also develop the ability to apply the concepts learned to the resolution of problems and non-trivial exercises.

Complex numbers and the complex plane. Functions on the complex plane. Continuous functions. Holomorphic functions. Integration along curves. Goursat’s theorem. Cauchy’s integral formulas. Morera’s theorem. Power series. Analyticity of power series. Laurent series. Singular points. Laurent expansions and the residue theorem. Residue calculus. Zeros and poles. The Fourier Transform. The Laplace Transform. The Zeta Transform. Distributions. Limits of Distributions. The Fourier Transform of a Tempered Distribution.

Di Fazio G., Frasca M. Metodi Matematici per l’Ingegneria,, Monduzzi Editoriale.