Mathematical Methods for Engineering

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Mathematical Methods for Engineering

Credits

6

Prerequisites

Mathematical Analysis 2.

Examination method

Passing an oral exam.

Learning
objectives

The course aims to provide an introduction to the theory of partial differential equations of mathematical physics. Students learn methods for the study of well-posed problems relating to such equations.

Contents

Complex numbers. Elementary functions in the complex field, power series. Analytic functions and Cauchy-Riemann conditions. Line integrals of functions of a complex variable. Taylor series expansion. Laurent series expansion. Residues and applications to the computation of integrals. Fourier series; pointwise convergence and mean-square convergence. Fourier transform: definition and formal properties; inverse transform. Distributions and derivatives in the sense of distributions. Poisson formula and Fourier transform of periodic signals. Unilateral and bilateral Laplace transform: definition; notable examples of Laplace transforms; formal properties; inverse transform. Use of the unilateral Laplace transform in linear differential models.