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.
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