


Politecnico di Torino  
Academic Year 2012/13  
02NNDLX, 02NNDMQ Complex analysis and introductory statistics 

1st degree and Bachelorlevel of the Bologna process in Electrical Engineering  Torino 1st degree and Bachelorlevel of the Bologna process in Mathematics For Engineering  Torino 





Subject fundamentals
Complex variable functions and distributions are a prerequisite for the study of the Fourier and Laplace transforms. These transforms are an important tool in the differential equation development, in the electrical circuits and in the signal theory. All these topics will be dealt with in the first part fo the course.
Probability and Statistics are fundamental tools for Electrical Engineers dealing with random systems and wanting to analyse experimental or observational data. In the second part of the course, elementary probability calculus will be taught together with some statistical techniques. 
Expected learning outcomes
The student will be able to compute modulus and argument of a complex variable function and to use residue theory to compute line integrals in the complex field. The student will be enabled to compute Fourier and Laplace transforms of some important functions and distributions using the transform properties.
The student will learn the fundamental notions of Probability from a mathematical point of view,calibrated on his/her former education. The student will learn how to draw reliable conclusions based on probability, in addition to data. Appropriate statistical software will be discussed. 
Prerequisites / Assumed knowledge
The complete program of the current courses of Mathematical Analysis (I and II) and Geometry (including Linear Algebra) or equivalent education.

Contents
The four credits in Complex Analysis will be approximately equally distributed as follows:
•Fourier series in the complex frame and analytic functions, Cauchy theorems and Laurent series •Residues and partial fraction decomposition by residue method •Distributions, derivatives and generalized distributional limits and the transform definition of distributions •Fourier and Laplace transform properties The four credits in Probability and Statistics will be approximately equally distributed as follows: •Elementary probability and its calculus •Random variables, expected values, error propagation •Estimation and Regression •Applications in probabilistic systems. reliability, quality control 
Delivery modes
Traditional exercise sessions will complement lectures, whereas appropriate statistical software will be indicated in one or two computer sessions.

Texts, readings, handouts and other learning resources
The following textbook or something equivalent will be used:
Athanasios Papoulis: The Fourier Integral and its Applications. McGrowHill, New York 1962. Sheldon Ross Probability and Statistics for Engineers and Scientists. Wiley 2004. 
Assessment and grading criteria
The exam is written and will be typically made up of four problems: two in complex Analysis, one in Probability, one in Statistics and some multiple choice test. The oral exam will be a check of the written exam and, when necessary, a discussion of it.

