Unit MATHEMATICS 2
- Course
- Chemistry
- Study-unit Code
- GP000254
- Curriculum
- In all curricula
- Teacher
- Tiziana Cardinali
- Teachers
-
- Tiziana Cardinali
- Hours
- 42 ore - Tiziana Cardinali
- CFU
- 6
- Course Regulation
- Coorte 2024
- Offered
- 2024/25
- 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
- 1) C. CANUTO, A. TABACCO; Analisi matematica 2, Pearson, 2021
o le edizioni precedenti:
C. CANUTO, A. TABACCO Analisi Matematica II, Springer-Verlag , 1nd 2008 o 2nd Ed., 2014
o la versione in inglese:
1)' C. CANUTO, A. TABACCO Mathematical Analysis II, Springer-Verlag , 2nd Ed., 2015
Altri testi consigliati:
M. BRAMANTI, C.D. PAGANI, S. SALSA, Analisi matematica 2, Zanichelli, 2009. - Educational objectives
- The course represents the second Mathematics course and examines the basic elements relating to the differentiation and integration of the functions of two variables, the study of numerical series, ordinary differential equations and the basic elements relating to conservative fields and their integration.
The aim of the course is to enable the student to process the concepts acquired in order to be able to use them to interpret and describe some problems of applied sciences.
At the end of the course students should:
- having acquired the properties of continuity, differentiability, optimization and integration (both on domains and on curves) for functions of two variables;
- have acquired the main elements on the study of conservative fields and their integration on curves.
- have acquired the first knowledge of ordinary differential equations and numerical series;
- possess computational skills for solving exercises on the course topics.
- know how to explain the properties presented in the course with appropriate language.
- understand the procedures that allow you to apply the contents of the course with other disciplines, in particular Chemistry.
- acquire an analytical method in tackling problems and exercises
- think critically and express mathematical concepts precisely in writing
- know how to apply the knowledge acquired during the course in other situations and disciplines.
The skills set out are in my opinion essential to be able to address the objectives set by the Course in Chemistry. - 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.
The arguments presented are accompanied by examples and counterexamples in order to achieve a good understanding of the definitions and statements of the theorems.
A strategy used as a support to teaching is the tutoring activity carried out by a capable and deserving student, as established by the Intercourse Council. In additional hours to the lessons, the capable and deserving student will carry out, under the guidance of the teacher, further exercises in preparation for the exemption tests and the exams.
To support teaching, slides created by the teacher and the Goodnotes application will be used. - Other information
- During the written test the use of: textbook is permitted; 4 or 5 handwritten cards with your personal notes; 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 text books.
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
"In the event that the student intends to advance the examination in a year to the one scheduled in the study plan, it is recommended to attend the lecture series and
to take the examination in the first useful call after the said lectures are finished, thus respecting the
semester of the teaching schedule."
For communications and teaching material, please refer 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
"In the event that the student intends to advance the examination in a year to the one scheduled in the study plan, it is recommended to attend the lecture series and
to take the examination in the first useful call after the said lectures are finished, thus respecting the
semester of the teaching schedule."
Exam Commission:
T.Cardinali, I.Benedetti (A.Boccuto, R.Filippucci, P.Rubbioni, A. Sambucini, E.Vitillaro). - 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