MATEMATICA A - L

The course aims to deepen the basic knowledge and to get student achieve adequate logic and mathematical skills for them to be capable to analyze and set up mathematical models with a particular focus on the ones dealing with the physical sciences or biology or chemistry

The course is held in the classroom by frontal type lessons

Module 1. Set theory
Axioms of operations ordering and completeness of real numbers
Sets; definition, representation, operation
Relations: definition, relations of ordering, relations of equivalence, quotient set.
Numerical sets. Non completeness of Q
Maggioranti, minoranti, estremo inferiore, estremo superiore, massimo, minimo di un insieme.

Modulo 2. Theory of functions
Functions: definition, domain, codomain. injectivity, surjectivity, bijectivity of a function. Composition of functions, inverse functions, monotonic functions. Maximum and minimum relative and absolute of a function. The cartesian plane, representation of elementary functions (polynomial, esponentil, logaritmic, goniometric).

Module 3: Limits and derivatives
Limits f successions and functions. The concept of limit. Limit of a succession. Teroems on limits of successions.
Limits of functions: definition and teorems on limits of functions. Continuous functions and fundamental teorems; discontinuous functions.
The derivative of a function: Definition and fundamental teorems (Lagrange, Rolle, Cauchy e De Hopital). Graphic of a function.

Module 4: Integrals and differential equations
Integrals. mention of measure theory; indefinite integrals; Integrals of elementary functions; Methods of integation. Definition of definite integral, Teorems on integrals;
Differential equations. Differential equation of first order and of second order. Elementary differential models of biology and physics.

• Elementi di Analisi Matematica uno. (versione semplificata per i nuovi corsi di laurea), P. Marcellini, C. Sbordone, ed. LIGUORI
• Slides del corso a cura del docente