ID:
500115
Duration (hours):
83
CFU:
9
SSD:
ANALISI MATEMATICA
Year:
2025
Overview
Date/time interval
Primo Semestre (29/09/2025 - 16/01/2026)
Syllabus
Course Objectives
The course is aimed at providing the basic knowledge of sequences, series, calculus (differential, integral) for real functions of one real variable, together with an introduction to ordinary differential equations. Lectures will be mainly focused on the comprehension of notions (definitions, results), although some proofs (not too many, actually) will be given with full details. Many examples and exercises will be presented througout the course. By the end of the course the students are expected to be able to correctly handle limits, derivatives, function graphs, integrals, series, differential equations, and the corresponding theoretical results.
Course Prerequisites
Mathematics: all the prerequisites which are required for the enrollment in the Faculty of Engineering
Teaching Methods
Lectures (hours/year in lecture theatre): 45 Practical classes (hours/year in lecture theatre): 38 Practicals / Workshops (hours/year in lecture theatre): 0
Assessment Methods
The exam consists of a written examination and an optional oral examination: the written examination lasts two hours an thirty minutes, and is further divided into two parts: eight exercises with free answers (first part) and eight multiple-choice theoretical questions (second part). For each question, among the four given answers, only one is correct. Written and optional oral examinations should be passed within the same session. The oral examination is based on definitions, examples and counterexamples, theorems (some, although few, with proofs).
Texts
1) M. Bramanti, C.D. Pagani e S. Salsa. Analisi Matematica 1, C.E. Zanichelli, Bologna, 2008-2009. 2) M. Bramanti, C.D. Pagani e S. Salsa, Analisi matematica 2, C. E. Zanichelli, Bologna, 2008-2009. 3) S. Salsa e A. Squellati, Esercizi di Analisi Matematica 1 - Seconda edizione, Zanichelli 4) S. Salsa e A. Squellati, Esercizi di Analisi Matematica 2, Zanichelli 5) C. Marcelli, Analisi matematica 1 - Esercizi con richiami di teoria, Pearson 6) C. Canuto, A. Tabacco, Palestra di Analisi matematica 1 - Quesiti, test ed esercizi svolti, Pearson
Contents
1. Preliminaries. Recalls and complements on: set theory, mathematical logic, real numbers. Complex numbers: algebraic, trigonometric, and exponential form. Operations on complex numbers; algebraic equations in the complex field. 2. Functions, Limits, Continuity. Sequences and Series. Functions: definitions, graphs; invertible functions; odd and even functions; monotone functions; periodic functions; operations on functions; nested functions. Elementary functions and corresponding graphs. Limits of functions: definitions, operations on limits. Continuous functions. Discontinuity points and their classification. Global properties of continuous functions. Limits of real sequences. Real series: definitions and basic examples; series with positive terms (and convergence tests); absolute and simple convergence. 3. Differential Calculus in one real variable and Applications. Derivative of a function: definition and properties, applications in Geometry and Physics. Derivation rules and calculus. Fundamental theorems of differential calculus. Higher order derivatives. Study of the graph of a function: extrema, monotonicity, convexity. De l'Hopital rules. 4. Integral Calculus. Definite integrals: definitions and basic properties, applications in Geometry and Physics. Primitives and indefinite integrals. Fundamental theorems of integral calculus. Integration techniques. Generalized integrals. 5. Ordinary Differential Equations. Introduction to ordinary differential equations. The Cauchy problem. Separation of variables. Linear ordinary differential equations of the first order. Linear ordinary differential equations of the second order with constant coefficients.
Course Language
Italian
More information
Students in the categories identified by the project on innovative teaching will have the opportunity to hold receptions even at special times and to view the teacher's lecture notes for the 2022-23 academic year.
Degrees
Degrees
INDUSTRIAL ENGINEERING
Bachelor’s Degree
3 years
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