First cycle
degree courses
Second cycle
degree courses
Single cycle
degree courses
School of Engineering
MATHEMATICAL ENGINEERING
Course unit
ANALYTICAL AND STOCHASTIC MATHEMATICAL METHODS FOR ENGINEERING
INP5070357, A.A. 2017/18

Information concerning the students who enrolled in A.Y. 2017/18

Information on the course unit
Degree course Second cycle degree in
MATHEMATICAL ENGINEERING (Ord. 2017)
IN2191, Degree course structure A.Y. 2017/18, A.Y. 2017/18
N0
bring this page
with you
Degree course track Common track
Number of ECTS credits allocated 12.0
Type of assessment Mark
Course unit English denomination ANALYTICAL AND STOCHASTIC MATHEMATICAL METHODS FOR ENGINEERING
Department of reference Department of Civil, Environmental and Architectural Engineering
Mandatory attendance No
Language of instruction English
Branch PADOVA
Single Course unit The Course unit can be attended under the option Single Course unit attendance
Optional Course unit The Course unit can be chosen as Optional Course unit

Lecturers
Teacher in charge GIORGIA CALLEGARO MAT/06
Other lecturers PAOLO GUIOTTO MAT/05

ECTS: details
Type Scientific-Disciplinary Sector Credits allocated
Core courses MAT/05 Mathematical Analysis 6.0
Core courses MAT/06 Probability and Mathematical Statistics 6.0

Mode of delivery (when and how)
Period First semester
Year 1st Year
Teaching method frontal

Organisation of didactics
Type of hours Credits Hours of
teaching
Hours of
Individual study
Shifts
Lecture 12.0 96 204.0 No turn

Calendar
Start of activities 02/10/2017
End of activities 19/01/2018

Syllabus
Prerequisites: None
Target skills and knowledge: Objective
Introduce the students to the basic knowledge of mathematical and probability tools for engineers.
Outcomes
A student who has met the objectives of the course will have a comprehensive knowledge of :
• Basic mathematical tools of functional analysis and measure theory
• Basic concepts of probability
Examination methods: Final examination based on: written examination.
Assessment criteria: Critical knowledge of the course topics. Ability to present the studied material.
Course unit contents: 1. Lebesgue Measure and Integral — Lebesgue measure and integral on R^d, limit theorems, dependence by parameters, reduction formula and change of variables. Introduction to abstract measure and integral.
2. Normed spaces — Concept of norm; uniform, L^1 and L^p norms; sequences, limits, completeness and Banach spaces. Concept of scalar product and Hilbert space; the space L^2; separable spaces and concept of orthonormal base.
3. Fundamentals of Complex Analysis — Power series in C and elementary analytic functions; concept of holomorphic function, Cauchy-Riemann equations, analyticity of holomorphic functions; isolated singularities; residue theorem and applications.
4. Introduction to Fourier Analysis — Fourier series: Euler formulas, convergence and sum (point-wise, uniform, L^2). Fourier transform: L^1 definition, convolution and approximate units, inversion formula. Schwarz functions and L^2 Fourier transform. Applications.
5. Introduction to probability — probability spaces, axioms of probability, conditional probabilities, independence of events.
6. Random variables (discrete and continuous) — definition, expectation and moments. Examples of random variables and applications, with a focus on Gaussian random variables.
7. Random vectors.
8. Characteristic function.
9. Convergence of random variables: weak, in probability, in L^p, almost sure.
10. The law of large numbers and the central limit theorem with applications.
11. Conditional expectation.
12. Martingales in discrete time.
Planned learning activities and teaching methods: Lectures supported by exercises.
Additional notes about suggested reading: Lecture notes relative to the Analytical Methods part will be provided.
See the reference book below for the Probability part.
Textbooks (and optional supplementary readings)
  • Sheldon Ross, A first course in Probability. --: Pearson, 1976. Ninth edition Cerca nel catalogo