MATHEMATICAL ANALYSIS 1
Stampa
Enrollment year
2021/2022
2021/2022
Regulations
DM270
MAT/05 (MATHEMATICAL ANALYSIS)
Department
DEPARTMENT OF ELECTRICAL,COMPUTER AND BIOMEDICAL ENGINEERING
Course
INDUSTRIAL ENGINEERING
Curriculum
PERCORSO COMUNE
Year of study
Period
1st semester (27/09/2021 - 21/01/2022)
ECTS
9
Lesson hours
83 lesson hours
Language
Italian
Activity type
WRITTEN AND ORAL TEST
Teacher
GIANAZZA UGO PIETRO (titolare) - 9 ECTS
Prerequisites
Mathematics: all the prerequisites required for enrollment in the Faculty of Engineering
Learning outcomes
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 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.
Teaching methods
Lectures (hours/year in lecture theatre): 45
Practical class (hours/year in lecture theatre): 38
Practicals / Workshops (hours/year in lecture theatre): 0