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Introduction to complex variable functions and Fourier and Laplace transforms. |
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Real functions in one and several variables. |
- Analytic functions: derivatives, the Cauchy-Rieman equations. Definite integrals, the Cauchy theorem. Residues, the residue theorem, the Cauchy integral formula. Taylor and Laurent series.
- Distribution theory: introduction, Dirac distribution, convolution product for functions and distributions.
- Fourier transform of functions and distributions: properties of the transformation and of its inverse.
- Laplace transform: range, elementary properties. Applications to the solution of linear differential systems
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