MATHEMATICAL ANALYSIS 1
Stampa
Enrollment year
2021/2022
Academic year
2021/2022
Regulations
DM270
Academic discipline
MAT/05 (MATHEMATICAL ANALYSIS)
Department
DEPARTMENT OF CIVIL ENGINEERING AND ARCHITECTURE
Course
BUILDING ENGINEERING AND ARCHITECTURE
Curriculum
PERCORSO COMUNE
Year of study
Period
1st semester (27/09/2021 - 21/01/2022)
ECTS
6
Lesson hours
60 lesson hours
Language
Italian
Activity type
WRITTEN AND ORAL TEST
Teacher
ROCCA ELISABETTA (titolare) - 6 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 and of complex numbers. There will be several examples and exercises.
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.

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.

3. Derivative of a function; applications to Geometry and Physics. Basic rules for computing derivatives. Principal theorems. Higher order derivatives;
Taylor approximation; extremal points of functions; De l'Hopital rule.

4. Sequence and limits. Numerical series: definition, properties, and convergence criteria.

5. Definite integral: definition, properties and applications. Theorems on integral calculus. Computing integrals. Improper integrals.
Teaching methods
Lectures (hours/year in lecture theatre): 37
Practical class (hours/year in lecture theatre): 23
Practicals / Workshops (hours/year in lecture theatre): 0
Reccomended or required readings
M. Bramanti, C.D. Pagani, S. Salsa, Analisi Matematica 1, Zanichelli, Bologna, 2009.
M. Bramanti, Esercitazioni di Analisi Matematica 1, Ed. Esculapio, Bologna, 2011.
Assessment methods
The final exam consists in a written test and an oral examination on the course topics. For more detailed information see http://matematica.unipv.it/rocca/
Further information
The final exam consists in a written test and an oral examination on the course topics. For more detailed information see http://matematica.unipv.it/rocca/
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