نظرة عامة على البرنامج

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Program Overview

The University of Genoa offers a comprehensive program in Mathematical Analysis 1B, providing students with fundamental elements of integral calculus for functions of one variable, differential calculus for functions of multiple variables, and the theory of ordinary differential equations.

Objectives and Contents

Formative Objectives

The primary objective of this course is to provide students with the first tools of mathematical modeling, including integral calculus, series, ordinary differential equations, and the basic theory of functions of multiple variables.

Detailed Formative Objectives and Learning Outcomes

The main learning outcomes expected from this course include:

• Knowledge of the analytical and geometric meaning of integral calculus
• Knowledge of the fundamental tools of differential calculus for functions of multiple variables
• Knowledge of the main methods for solving ordinary differential equations
• Ability to solve exercises, discussing the reasonableness of the results obtained

Prerequisites

Students are required to have completed the contents of the Mathematical Analysis 1A course.

Teaching Methods

Lectures and exercises will be held in person. Through the teaching innovation project, innovative tools will be used to promote active student learning. The goal is to increase student competence through new learning methodologies, from e-learning to team work, through experiences that enhance student participation and make them more aware and autonomous.

Program/Content

Calculus and Numerical Series

• Indefinite and definite integrals
• Improper integrals
• Numerical series and convergence criteria

Functions of Multiple Real Variables

• Continuity, directional and partial derivatives, gradient
• Differentiability and tangent plane
• Level sets
• Free maxima and minima: second derivatives and Hessian criterion
• Schwarz's theorem

Differential Equations

• Equations with separable variables, linear equations: solution methods
• Systems of differential equations
• Existence and uniqueness for the Cauchy problem
• General integral for linear systems

Texts/Bibliography

• C. Canuto, A. Tabacco, Mathematical Analysis 1, 4th edition, Springer-Verlag Italia, 2014
• C. Canuto, A. Tabacco, Mathematical Analysis 2, 2nd edition, Springer-Verlag Italia, 2014
• M. Baronti, F. De Mari, R. van der Putten, I. Venturi, Calculus Problems, Springer International Publishing Switzerland, 2016

Teachers and Commissions

• Marco Baronti
• Laura Capelli

Examination Commission

• Marco Baronti (President)
• Laura Capelli
• Andrea Bruno Carbonaro (Supplementary President)
• Simone Di Marino (Supplementary President)
• Claudio Estatico (Supplementary President)
• Edoardo Mainini (Supplementary President)

Lessons

Lesson Schedule

The schedule for this course can be found on the EasyAcademy Portal.

Exams

Examination Methods

The exam consists of:

• Written test
• Oral test

Assessment Methods

• Written test: This part includes open questions and exercises. It is aimed at verifying the mastery of calculation techniques and knowledge of the main calculation tools introduced in the course.
• Oral test: The oral test is aimed at verifying the logical/deductive reasoning abilities and is constituted by a discussion on the topics covered in the course, with attention to the correct statement of theorems and demonstrations, as well as the execution of exercises.

Exam Calendar

Exam Date	Time	Location	Type	Notes
17/06/2025	14:00	Genoa	Written Analysis 1B with online acceptance
16/07/2025	14:00	Genoa	Written Analysis 1B with online acceptance
05/09/2025	14:00	Genoa	Written Analysis 1B with online acceptance