Mathematical Methods for Engineering

Credits

Prerequisites

Mathematical Analysis 2.

Scientific-disciplinary sector (SSD)

MAT/05 Mathematical Analysis.

Examination method

Oral exam.

Learning
objectives

Acquisition and operational awareness of the fundamental concepts and results of complex analysis, Fourier analysis and differential equations, with a view to their main applications.

Syllabus

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.

Expected learning
outcomes

On completion of the course, students must demonstrate that they

know and understand the fundamental concepts and results of complex analysis;
can apply the knowledge acquired to the study of applied models in physics and engineering;
can communicate ideas and solutions clearly, rigorously and effectively to both specialist and non-specialist audiences;
can identify the most appropriate methods to analyse and solve a problem relating to the course topics and interpret the results correctly.

Learning outcomes
to be assessed

Command of the knowledge acquired, confidence in using the notions acquired in applied models.

Mathematical Methods for Engineering