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.

AIMS AND CONTENT

LEARNING OUTCOMES

The course 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
• 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.

As part of the innovation learning project (adopted by the Bachelor Degree Course in Mechanical Engineering), novel tools will be used for the active learning of students. The goal is to increase students' skills via interactive, experience-based, learning methodologies (e-learning, teamwork, etc.) for enhanced participation, using an advanced level of communication that makes the student more aware and autonomous

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

• 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

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.