Unit MATHEMATICS 2
- Course
- Chemistry
- Study-unit Code
- GP000254
- Curriculum
- In all curricula
- Teacher
- Paola Rubbioni
- Teachers
-
- Paola Rubbioni
- Hours
- 42 ore - Paola Rubbioni
- CFU
- 6
- Course Regulation
- Coorte 2023
- Offered
- 2023/24
- Learning activities
- Base
- Area
- Discipline matematiche, informatiche e fisiche
- Academic discipline
- MAT/05
- Type of study-unit
- Obbligatorio (Required)
- Type of learning activities
- Attività formativa monodisciplinare
- Language of instruction
- italian
- Contents
- Numerical series. Curves and line integrals. Differential calculus for functions of several variables. Double integrals. Differential forms. Differential equations.
- Reference texts
- M. Bramanti; C. D. Pagani; S. Salsa; Analisi Matematica 2, Zanichelli Ed., 2009
C. Canuto; A. Tabacco; Analisi matematica 2, Pearson, 2021 - Educational objectives
- knowledge of the methodological and operational aspects of the arguments and ability to use this knowledge in order to describe and solve problems
- Prerequisites
- In order to understand and know how to apply the topic of this course it is important to have followed and possibly passed the exam of the course Mathematics I.
- Teaching methods
- Lectures on all the topics of the course.
In addition to a detailed theoretical presentation, the relative exercises will also be carried out for each topic that will serve as a model for those proposed in the exams.
To support teaching, the Geogebra software and the OneNote and Drawboard applications will be used. - Other information
- During the written test it is allowed to use: textbook; handwritten cards with their personal notes inserted in a price list; draft sheets; pens, pencils, ruler, ...
However, it is not possible to keep with you: bags or backpacks; smartphones or notebooks or calculators or other similar devices; books other than textbooks.
For communications and teaching material, reference is made to the UniStudium platform. - Learning verification modality
- The verification of the profit is divided into a calculus test and a theoretical test. In the first test the student must perform some exercises to verify the knowledge and skills related to the calculation. In the second test the acquisition of the method, of the language and of the fundamental theoretical knowledge of the subject is verified; this test, lasting one hour, consists of three questions relating to statements and proofs of theorems, definitions, examples and counterexamples on the topics of the program.
Students with disabilities and / or SLDs can take advantage of compensations and dispensatory measures: the student can choose whether to take the two written tets using one third more time or one third less exercises.
For information on support services for students with disabilities and / or DSA visit http://www.unipg.it/disabilita-e-dsa - Extended program
- 1. Numerical series.
Definitions and first examples. Series with non-negative terms. Series with terms of variable sign.
2. Infinitesimal calculus for curves
Vector-valued functions: limits, continuity, differentiability. Simple, closed, plane, Cartesian, polar curves. Regular curves, length of a curve arc and line integrals of I type.
3. Differential calculus for functions in several variables.
Limits and continuity, topological properties of continuous functions. Partial derivatives, differentiability and linear approximation. Higher order derivatives and free optimization. Constrained ends.
4. Integral calculus for functions in two variables and vector fields
Double integrals on regular domains. Vector fields and line integrals of the II type, conservative fields and irrotational fields, Gauss-Green formulas.
5. Differential equations
First order differential equations with separable and linear variables. The Cauchy Problem. Linear second order differential equations with constant coefficients. - Obiettivi Agenda 2030 per lo sviluppo sostenibile
- Quality education