Unit MATHEMATICS 1
- Course
- Chemistry
- Study-unit Code
- GP000253
- Curriculum
- In all curricula
- Teacher
- Danilo Costarelli
- Teachers
-
- Danilo Costarelli
- Hours
- 63 ore - Danilo Costarelli
- CFU
- 9
- Course Regulation
- Coorte 2022
- Offered
- 2022/23
- 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
- Sets, upper and lower extremes, Topology, numerical sequences, elementary functions.
Limits, continuity and differential calculus for real functions of one variable.
Riemann Integral.
Basic notions of geometry and linear algebra with the ultimate aim of giving the general algorithm of resolution of a linear system. - Reference texts
- 1) C. Vinti, Lezioni di Analisi Matematica 1.
2)Bramanti, Pagani, Salsa, Analisi Matematica 1.
Additional teaching materials (as the pdf files of the lessons) will be uploaded on unistudium. - Educational objectives
- The course aims to provide students with the basics of Calculus and Linear Algebra. At the end of the course the student must: have acquired the notions of limit, derivative, integral; be able to carry out the complete study of a function of one variable; know how to calculate simple Riemannian integrals; knowing how to solve a linear system; know how to expose and discuss the definitions and theorems presented in class.
- Prerequisites
- First and second degree equations and inequalities, rational, irrational, transcendent. Elements of analytical geometry.
- Teaching methods
- Face-to-face lessons on all the topics of the course.
In addition to a detailed theoretical presentation, for each topic will also be carried out the related exercises that will be of the same type to those proposed in the examination. - Other information
- During the written test the use of: textbooks, smartphones or notebooks or calculators or other similar devices is not allowed.
For communications and any additional material, reference is made to the Unistudium platform. - Learning verification modality
- The final exam consists of a written and a oral test. The written exam will have a duration of 90 minutes, and the student should show that he can solve the practical exercises (3 exercises). During the oral exam, the student should show to know the main theoretical notions studied during the course.
For information on support services for students with disabilities and / or DSA visit http://www.unipg.it/disabilita-e-dsa - Extended program
- Basic concepts on sets; elementary logic; real numbers; definitions of upper and lower extremes of a set. topology.
Functions of one variable: generality and elementary functions; composition of functions and inverse functions.
Limits and continuity: numerical sequences; limits of functions, continuity, asymptotes; limit's calculus; global properties of continuous functions.
Differential calculus for functions of one variable: derivative of a function; rules for the computation of the derivatives; the theorem of the mean value and its consequences; second derivative; study of the graph of a function.
Riemann Integral: integral of a function; properties of the integral; the fundamental theorem of integral calculus; computation of indefinite and defined integrals.
Elements of geometry and linear algebra: vector spaces; matrices; linear systems; eigenvalues and eigenvectors.