OVERVIEW

In addition to what was covered in the course of Mathematical Model Mod. 1, the aim of the teaching is to provide basic knowledge of integral calculus for functions of a single variable and an introduction to ordinary differential equations and systems of differential equations. These are essential topics in Mathematical Analysis, such as differential and integral calculus for functions of a single variable, which are fundamental for understanding the subjects covered in subsequent courses."

AIMS AND CONTENT

LEARNING OUTCOMES

The course provides the first tools of mathematical modeling: integral calculus: Riemann integral, improper integrals, ordinary differential equations: separable variables, first-order linear equations with continuous coefficients, linear equations of order n with constant coefficients, systems of linear differential equations.

AIMS AND LEARNING OUTCOMES

The knowledge of mathematical basic tools useful in physical problems modelling.  The skill of setting up and solving problems by using intuitive and deductive reasoning as well as recognizing and using the suitable mathematical tools in solving problems in a physical setting.

At the end of the course the student will be able

1. to state the concepts ( theorems and definitions ) introduced during the course ( f.i. Infimum and Supremum of a set, derivative, integral, line integral, Existence and Uniqueness theorems for differential problems );

2. to give physical and geometric interpretation of the basic concepts of Mathematical Analysis;

3. to set up problem solving with an intuitive approach;

4. to select the suitable mathematical tools in problem solving;

5. to solve problems with deductive reasoning.

PREREQUISITES

The contents of Mathematical Methods Mod.1 and Linear Algebra and Geometry.

TEACHING METHODS

The course consists of 60 hours of lectures and practices. In the lectures the topics of the syllabus are explained with definitions and theorems and some proofs which can be useful for the comprehension of the topics and to develop the logical and deductive skills. Every theoretical topic is explained with easy examples and some exercises. In the practices, many exercises are solved with the aim of going into the knowledge of theoretical topics treated in the lectures and preparing the student for the exam. Several intermediate tests are provided.

Students  have several exercises at their disposal on Aulaweb.

Students with SLD, disability or other regularly certified special educational needs are advised to contact the professor and the University referent at the beginning of the course to agree on teaching methods that, in compliance with the course objectives, take into account the individual learning requirements.

SYLLABUS/CONTENT

L’Hopital’s rule.  Antiderivative. Riemann integrals. Mean value integrals. Fundamental theorem and formula of integrals calculus. Integration formulas. Integral functions. Improper integrals. Ordinary differential equations. Cauchy problem : existence and unicity theorems and resolution methods in some special cases : separation variable equation. Linear Differential Equations.  Structure of the set of solutions of a linear differential equations in the homogeneous and non homogeneous.  First orderl inear differential equatios with continuous coefficient. Metods  for solving linear differential equations with constant coefficients. Systems of linear differential equations. Lagrange formula.                                                                                

RECOMMENDED READING/BIBLIOGRAPHY

Theory

T. Apostol : Calculus - John Wiley & Sons Inc, 1967

Exercises

M. Baronti – F. De Mari – R. van der Putten – I. Venturi : Calculus Problems. Springer 2016

TEACHERS AND EXAM BOARD

LESSONS

Class schedule

The timetable for this course is available here: Portale EasyAcademy

EXAMS

EXAM DESCRIPTION

The exam consists of a written test lasting two to three hours. The written exam includes two open-ended questions, and during the exam, students are allowed to consult notes and texts, use calculators, but cannot use laptops or smartphones.

There are two in-progress tests scheduled during the lecture period, which, if passed, replace the written exam.

Students with certification of DSA, disabilities, or other special educational needs are advised to contact the instructor and the university contact person at least 15 days before each exam session to agree on exam arrangements that, while respecting the course objectives, take into account individual learning methods.

To participate in an exam session, students must register within the deadline on the website: https://servizionline.unige.it/studenti/esami/prenotazione

ASSESSMENT METHODS

The aim of the examination is verifying the skills acquired by the student.

The aim of the written examination is verifying the skills acquired by the student. The problems proposed in the examination call for the choice and the application of suitable mathematical tools, besides their solution needs the skill of constructing a logical connection applying theoretical topics treated. The student must solve the exercises justifying the most important passages recalling theorems and definitions and underlying the physical and geometric interpretation of the problem.

The final evaluation depends also on the quality of the written exposition and on the ability of reasoning.