OVERVIEW

The aim of the course is to provide the basic elements of integral calculus for functions of one variable, of the theory of ordinary differential equations and of differential calculus for functions of several variables, and of numerical series.

AIMS AND CONTENT

LEARNING OUTCOMES

The module provides an introduction to integral calculus, to series, to ordinary differential equations and to the theory of functions of several variables.

AIMS AND LEARNING OUTCOMES

The main expected learning outcomes are

• the knowledge of the analytical and geometrical meaning of integral calculus and numerical series.
• the knowledge of the basic tools of differential calculus for functions of several variables
• the knowledge of the basic methods for solving ordinary differential equations
• the ability to solve exercises, discussing the reasonableness of the results

PREREQUISITES

Contents of the course Mathematical Analysis 1A.

TEACHING METHODS

Lecture classes and exercise classes.

Students having disabilities or Specific Learning Disorders can request suitable aids for the examinations. Such aids will be defined according to specific needs, together with the Referent for the Polytechnic School of the Committe for the inclusion of Students with Disabilites and with SLD. Students in such conditions are invited to get in touch (via e-mail) with the Teacher a sufficient time before the examination, inserting in copy the Referent for the Polytechninc School

1) for Electrical Engineering prof. Silvana Dellepiane - silvana.dellepiane@unige.it

2) for Chemical Engineering and Civil, Construction and Environmental Engineering prof. Federico Scarpa - federico.scarpa@unige.it

(https://unige.it/en/commissioni/comitatoperlinclusionedeglistudenticondisabilita.html), without sending any document about their disabilites.

SYLLABUS/CONTENT

Integral calculus and series.  Definite and indefinite integrals. Improper integrals. Numerical series and convergence criteria.

Functions of several variables. Continuity, directional and partial derivatives, gradient.  Differentiability and tangent plane. Level sets. Local minima and maxima: second order derivatives and the Hessian. Schwarz theorem.

Differential equations. Separation of variables.  Linear differential equations: solving methods. Systems of differential equations. Existence and uniqueness for the Cauchy problem. General solution for systems of linear equations.

RECOMMENDED READING/BIBLIOGRAPHY

Specific guidelines on the reference bibliography will be provided by the professor at the beginning of the course.

In general, lecture notes and the materials available for download from the course webpage are sufficient for exam preparation. More specifically, the following materials may be useful:

• Professor Maurizio Romeo's theory handouts, available for free download from the course's AulaWeb page;
  Worksheets containing links to webpages with various solved exercises, available for free download from the course's AulaWeb page;
• Worksheets containing links to webpages with various solved exercises, available for free download from the course's AulaWeb page;
• C. Canuto, A. Tabacco, Analisi Matematica 1, 4a edizione, Springer-Verlag Italia, 2014;
• C. Canuto, A. Tabacco, Analisi Matematica 2, 2a edizione, Springer-Verlag Italia, 2014.
• M. Baronti, M., F. De Mari,  R. van der Putten, I. Venturi,  Calculus Problems, Springer International Publishing Switzerland, 2016.

TEACHERS AND EXAM BOARD

LESSONS

LESSONS START

Class schedule at https://corsi.unige.it/corsi/11879/studenti-orario

Class schedule

The timetable for this course is available here: Portale EasyAcademy

EXAMS

EXAM DESCRIPTION

The exam consists of

• Written exam
• Oral test

To enroll the exam you must register by the deadline on the website https://servizionline.unige.it/studenti/esami/prenotazione

ASSESSMENT METHODS

Written exam. This part includes open questions and exercises. It is aimed to verify the knowledge of the main tools of  calculus that have been introduced through the course. The written exam consists of exercises with several questions of different difficulty.   The student must be able to solve the exercises correctly and to justify the necessary steps to obtain the final result, and to use the correct formalism.

Oral test. It is aimed at verifying the logical/deductive reasoning skills and consists of an oral test on the topics covered in the lectures, with particular focus on the correct statement of the theorems, the proofs of the results discussed during the lectures, and the solution to exercises. In particular, the student's logical/deductive ability and the degree of understanding of the concepts are assessed.

FURTHER INFORMATION

Ask the professor for other information not included in the teaching schedule.