CODE  56594 

ACADEMIC YEAR  2022/2023 
CREDITS 

SCIENTIFIC DISCIPLINARY SECTOR  MAT/05 
LANGUAGE  Italian 
TEACHING LOCATION 

SEMESTER  Annual 
PREREQUISITES 
Propedeuticità in uscita
Questo insegnamento è propedeutico per gli insegnamenti:

TEACHING MATERIALS  AULAWEB 
OVERVIEW
The course "Mathematical Analysis I" aims to provide students with some basic mathematical tools, both theoretical and computational, useful for engineering and applicationoriented topics of all the next courses.
The course will be focused on functions of one and several real variables, on the related differential and integral calculus, on the resolution of ordinary differential equations and numerical series.
AIMS AND CONTENT
LEARNING OUTCOMES
The course introduces general mathematical notions and tools at the basis of engineering modeling, related to the study of the functions of one or more real variables. In particular, the concept of limit and continuity, the differential and integral calculus, also of functions of several real variables, the resolution of ordinary differential equations, the analysis of curves and surfaces, and the study of the convergence of numerical series.
AIMS AND LEARNING OUTCOMES
The "Mathematical Analysis I" course aims at giving basic mathematical tools necessary to the studies in the engineering field.
At the end of the lessons the student will have acquired sufficient theoretical knowledge:
 to identify, understand, formulate and solve general engineering problems related to mathematically modeled quantitie using appropriate analytical methods;
 to combine notions of theory into practice to solve basic model engineering problems;
 to be able to autonomously learning new mathematical tools useful for engineering applications, throughout the entire working life;
 to analyze and model geometric and physical objects related to functions of one or more real variables, and to calculate quantities associated with them;
 to apply mathematical resolution tools in the context of the differential calculation of the functions of one or more real variables;
 to apply mathematical resolution tools in the context of the integral calculation of the functions of one real variable;
 to compute the maximum and minimum unconstrained values of functions of one and several variables, useful in application areas of optimization;
 to analyze and model geometric objects related to curves, and calculate associated quantities;
 to understand and solve simple models related to ordinary differential equations, through which physical phenomena of engineering interest are represented;
 to know the concept of numerical series and to evaluate their convergence, useful in the approximate calculation of quantities in the numericalcomputational field.
PREREQUISITES
Elementary algebra: literal calculus, polynomials, equations and inequalities, trigonometry.
TEACHING METHODS
72 hours of theoretical lessons, 48 hours of classroom practices. During the theoretical lessons the definitions and the theorems will be presented with many examples and applications. During the other part of the course many exercises will be solved.
In addition, a tutor will solve some exercises in extra (optional) lesson hours.
SYLLABUS/CONTENT
The teaching program includes both theoretical study and practical resolution of exercises in the following topics:
 Sets, logic, real numbers, infimum and supremum
 Functions of one real variable, elementary functions, limits, infinitesimals and infinities, continuous functions, derivable functions, differentiable functions. Taylor’s formula, expansion of elementary functions.
 Primitives and indefinite integrals, methods of indefinite integration, definite integrals, fundamental theorem of integral calculus.
 Functions of several variables (scalar and vectorial fields), limits and continuity. Directional derivatives. Differentiable functions. Necessary and sufficient conditions for differentiability. Derivatives of composite functions. Derivatives of higher order, Schwarz Theorem and Taylor polynomial in several variables. Unconstrained maxima and minima of scalar fields, necessary and sufficient conditions, Hessian matrix.
 Differential equations of the first order, with separable variables, linear, homogeneous, Bernoulli and Riccati types. Existence and uniqueness theorem (hints) for the Cauchy’s problem. Linear differential equations. Linear differential equations of higher order with constant coefficients, homogeneous and nonhomogeneous,
 Improper integrals of one variable.
 Numerical series. Convergence criteria for constant sign numerical series. Numerical alternating series and absolutely convergent series. Function series. Uniform (hints) and total convergence. Power series.
RECOMMENDED READING/BIBLIOGRAPHY
Handouts: "MATHEMATICS I" and "MATHEMATICS II" by prof. Maurizio Romeo, downloadable for free from the web page of the course.
Sheets containing links to web pages with different solved exercises, downloadable for free from the web page of the course.
Workbook: Laura Recine  Maurizio Romeo, Esercizi di analisi matematica  Volume II, Maggioli Editore.
P. Marcellini – C. Sbordone: Calcolo, Liguori Editore, Napoli, or any other good text of mathematical analysis.
M.Baronti – F.De Mari – R.Van Der Putten – I.Venturi: Calculus Problems, Springer
TEACHERS AND EXAM BOARD
Ricevimento: By appointment via email.
Exam Board
CLAUDIO ESTATICO (President)
MARCO BARONTI (President Substitute)
ULDERICO FUGACCI (President Substitute)
LESSONS
LESSONS START
Class schedule
The timetable for this course is available here: Portale EasyAcademy
EXAMS
EXAM DESCRIPTION
The final exam consists of a written test and an oral exam. The student must obtain an evaluation of at least 16/30 in the written test to access the oral exam, in both the two parts related to the two semesters.
Students with DSA certification ("specific learning disabilities"), disability or other special educational needs are advised to contact the teacher at the beginning of the course to agree on teaching and examination methods that, in compliance with the teaching objectives, take account of individual learning arrangements and provide appropriate compensatory tools.
ASSESSMENT METHODS
The exam consists of a written test and an oral test.
The written test consists in solving exercises concerning the arguments of the course. The written test must be passed before attending the oral examination and can be taken both in previous sessions and in the same session in which the student intends to attend the oral examination.
Only students who have previously passed the written test with a grade greater than or equal to 16/30 can access the oral exam.
Exam schedule
Data appello  Orario  Luogo  Degree type  Note 

16/01/2023  09:00  GENOVA  Scritto  
23/01/2023  09:00  GENOVA  Orale  
06/02/2023  09:00  GENOVA  Scritto  
15/02/2023  09:00  GENOVA  Orale  
14/06/2023  09:00  GENOVA  Scritto  
19/06/2023  09:00  GENOVA  Orale  
14/07/2023  09:00  GENOVA  Scritto  
19/07/2023  09:00  GENOVA  Orale  
08/09/2023  09:00  GENOVA  Scritto  
14/09/2023  09:00  GENOVA  Orale 
FURTHER INFORMATION
Attendance is not compulsory but strongly recommended to all students.