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
ELECTRONIC AND COMPUTER 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
FORNARO SIMONA (titolare) - 9 ECTS
Prerequisites
Entry requirements are the ones of the university admission
Learning outcomes
The aim of this course is to give the basic knowledge of differential and integral calculus for real-valued functions of one real variable, of numerical sequences and series, of complex numbers and of ODEs. In general, there will be much emphasis on the comprehension of the definitions and the principal results. Only few proofs will be treated in full details. There will be several examples and exercises. At the end of the course, the students should be able to do computations on limits, derivatives, graphs of functions, integrals, differential equations and series and have a deep knowledge of the mail notions.
Course contents
1. Basic properties of numerical sets and in particular of the real numbers (total ordered field, continuity axiom). The field of complex numbers: algebraic and trigonometrical form, exponential form.
2. Functions: definition, properties, graphs. Invertible functions. Even, odd, periodic functions. Elementary functions and their graphs. Limits of functions. Continuous functions and their properties. Discontinuities and their classification. Global properties of continuos functions. Sequences and numerical series: definition, properties, and convergence criteria.
3. Derivative of a function; applications to Geometry and Physics. Basic rules for computing derivatives. Principal theorems. Higher order derivatives;
Taylor approximation; Graph of a function; extremal points of functions; De l'Hopital rule.
4. Definite integral: definition, properties and applications to Geometry and Physics. Fundamental Theorems on integral calculus. Computing integrals. Improper integrals.
5. Differential equations
Introduction to ordinare differenti equations; the Cauchy problem. First order linear differential equations. Second order linear differential equations 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