- Docente: Nicola Arcozzi
- Credits: 9
- SSD: MAT/05
- Language: Italian
- Moduli: Nicola Arcozzi (Modulo 1) Francesca Colasuonno (Modulo 2)
- Teaching Mode: Blended Learning (Modulo 1) Traditional lectures (Modulo 2)
- Campus: Bologna
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Corso:
First cycle degree programme (L) in
Civil Engineering (cod. 8888)
Also valid for First cycle degree programme (L) in Environmental Engineering (cod. 9198)
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from Feb 22, 2024 to Jun 07, 2024
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from Feb 20, 2024 to May 31, 2024
Learning outcomes
At the end of the course, the student has a practical and theoretical knowledge of basic concepts and tools in differential and integral calculus in several variables, and in probability theory.
Course contents
Integrational Elements of Mathematical Analysis (60h)
- Review of series and improper integrals.
- Differential equations
Separable differential equations; Linear equations of the first order; Linear equations with constant coefficients of the second order. - Curves
Vector-valued functions: limits and continuity; Regular curves and vector differential calculus; Length of a curve; Line integrals of the first kind. - Functions of several variables
Limits: Calculation of limits; Continuity and theorems on continuous functions.
Differential calculus: Partial derivatives and directional derivatives; Tangent plane; Differentiability conditions; Second-order derivatives, Hessian matrix, and Taylor's formula. - Maxima and minima of functions in several variables.
Free optimization: Fermat's theorem; Study of the nature of critical points: sufficient conditions of the second order.
Constrained optimization: Lagrange multiplier theorem. - Double and triple integrals
Coordinate transformations in the plane and in space.
Simple domains; Reduction theorems; Change of variables. - Vector fields
Line integrals of the second kind, work and line integrals along a closed curve; Irrotational fields and conservative fields.
Elements of Probability Calculation (30h)
- Probability spaces
Measure of probability; Conditional probability and Independence, Partition Equation, Bayes' formula; Combinatorics. - Discrete models
Discrete random variables and main distributions: Bernoulli, binomial, geometric, and Poisson distribution; Cumulative distribution function; Expected value; Variance. - Continuous models
Absolutely continuous random variables; Density and Cumulative distribution function; Expected value; Variance. Examples: uniform, normal, and exponential random variables.
Readings/Bibliography
- Analisi Matematica 2. Teoria con esercizi svolti
Autrice: Francesca G. Alessio
Editore: Esculapio
Anno edizione: 2020
- Analisi matematica 2
Autori: Marco Bramanti, Carlo D. Pagani, Sandro Salsa
Editore: Zanichelli
Anno edizione: 2009
- Esercizi di Analisi matematica 2
Autori: Sandro Salsa, Annamaria Squellati
Editore: Zanichelli
Anno edizione: 2011
- Introduzione alla probabilità - con elementi di statistica, 2a edizione
Autore: Paolo Baldi
Editore: McGrawHill
Anno edizione: 2012
Teaching methods
Lectures and exercise sessions. A third of the lectures will be delivered online, with the use of specific software.
Assessment methods
The exam has practical part, and a more theoretical part. both in the form of a written test. The theoretical part will be shortly discussed with the instructors.
Teaching tools
Supplementary material will be made available on Virtuale.
Office hours
See the website of Nicola Arcozzi
See the website of Francesca Colasuonno