Unit CALCULUS II
- Course
- Industrial engineering
- Study-unit Code
- GP004984
- Curriculum
- In all curricula
- Teacher
- Ilaria Mantellini
- Teachers
-
- Ilaria Mantellini
- Loris Faina (Codocenza)
- Hours
- 51 ore - Ilaria Mantellini
- 30 ore (Codocenza) - Loris Faina
- CFU
- 9
- Course Regulation
- Coorte 2019
- Offered
- 2019/20
- Learning activities
- Base
- Area
- Matematica, informatica e statistica
- Academic discipline
- MAT/05
- Type of study-unit
- Obbligatorio (Required)
- Type of learning activities
- Attività formativa monodisciplinare
- Language of instruction
- Italian
- Contents
- Generalized integral, series of functions, functions of several variables, differential equations, multiple integrals, line integrals, surface integrals
- Reference texts
- -Notes of the teacher
-C. Bardaro Elementi di Analisi Matematica 2- Galeno Ed.¿
C. Vinti Lezioni di Analisi Matematica, Volume 2 - Galeno Ed.¿ - Educational objectives
- The purpose of this course is to teach basic concepts and give the student methods to elaborate them in order to describe and use models in several applied areas of Engineering.
- Prerequisites
- It is obligatory to pass the exam of Calculus I, and it is advisable to be acquainted with Analytiic Geometry.
- Teaching methods
- Lessons in classroom, exercises
- Other information
- Reception: Tuesday 9-10
- Learning verification modality
- A written test of about three hours; if sufficient, a subsequent oral exam.¿The test consists of questions to be solved in open form, about the main themes of the course.
This test is intended to assess the candidate's ability to identify the most suitable tools for solving the various questions, the ability to use them correctly, and the consistency and clarity in drawing up the appropriate conclusions in an exhaustive manner. The oral exam, in the case of passing the written test, consists of a further exercise consisting in the resolution of a linear differential equation, and, in case of a positive result, of an interview of about 40 minutes, which usually begins with the discussion of the written test, and is mainly aimed at clarifying whether and to what extent the candidate is able to express himself clearly and consistently on the main theoretical issues, and has understood the usefulness in resolving concrete problems. For information on support services for students with disabilities and / or DSA visit the page http://www.unipg.it/disabilita-e-dsa - Extended program
- Generalized Riemann Integral, sequences and series of functions, power series, Fourier series. Limit theorems for integrals and derivatives.¿Functions of several variables: continuity, differentiability, maxima and minima. Implicit functions. Ordinary differential equations: existence and uniqueness theorems for the first order, theory of linear equations, methods of solutions.¿Integration in two dimensions or more: Fubini's theorem, change of variables, applications. Differential forms, line integrals and Gauss-Green formulas.¿Surface integrals: area, tangent plane, divergence theorem, Stoke's theorem, and applications.