Lecturer: Simona Fornaro  

Course name: Mathematical analysis 1
Course code: 500115
Degree course: Ingegneria Edile-Architettura
Disciplinary field of science: MAT/05
L'insegnamento costituisce attività di base per: Ingegneria Edile-Architettura
University credits: ECTS 6
Course website: n.d.

Specific course objectives

The aim of this course is to give the base knowledge of differential and integral calculus for univariate real functions, of numerical sequences and series, and of ordinary differential equations.

Course programme

Preliminaries
Set theory, mathematical logic, real numbers. Complex numbers: algebraic, trigonometric, and exponential form. Operations on complex numbers; algebraic equations on the complex field.

Functions of one variable
Real numbers. Function definition, properties, graph. Invertible functions. Even, odd, periodic functions. Elementary functions.

Limits and continuity
Limits of real sequences. Monotone sequences. Limits of functions. Continuous functions and their properties. Discontinuities.

Differential calculus
Derivative and primitive of a function; properties and theorems. Indefinite integral.

Applications of derivatives
Taylor approximation. Finding extrema of functions. De l'Hopital rule

Series
Definition, properties, and basic examples. Convergence tests. Absolute and simple convergence.

Integrals
Definite integral: definition, properties and applications. Theorems of integral calculus. Computing integrals. Improper integrals

Introduction on differential equations
Ordinary differential equations: a) first order linear b) first order with separable variable c) second order linear and with constant coefficients

Course entry requirements

Entry requirements are the ones of the university admission

Course structure and teaching

Lectures (hours/year in lecture theatre): 60
Practical class (hours/year in lecture theatre): 20
Practicals / Workshops (hours/year in lecture theatre): 0

Suggested reading materials

M. Bramanti, C.D. Pagani, S. Salsa. Analisi Matematica 1. Zanichelli.

Testing and exams

The final exam consists in a written test and an oral examination on the course topics