Allow the acquisition of the method deductive logic and provide the basic mathematical tools of the calculation of differential and integral. Each topic will be introduced and strictly the treaty, carrying, sometimes, detailed demonstrations, and also doing large reference to physical meaning, geometric interpretation and application number. Proper methodology and a reasonable skill in the use of the concepts of calculation and its entirety and differential results will put in grade students in principle to face so easy application more topics that will take place in the following courses.
scheda docente
materiale didattico
Analisi matematica I Pagani-Salsa
Esercitazioni di Matematica Marcellini-Sbordone
Programma
Numerical sets (N, Z, Q and R), axiomatic construction of R, construction of N and principle of induction, complex numbers; elements of topology in R and Bolzano-Weierstrass theorem; real functions of real variable, limits of functions and their properties, limits of sequences, notable limits, the Napier number; continuous functions and their properties; derivative of functions and their properties, the fundamental theorems of differential calculus (Fermat, Rolle, Cauchy, Lagrange, de l'Hopital, Taylor's formula), convex / concave functions; function graph; Riemann integration and properties, integrability of continuous functions, fundamental theorem of integral calculus, integration by substitution and by parts, integration rules; numerical series, simple and absolute convergence, convergence criteria for series with positive terms and for series with any terms; Taylor series; improper integrals.Testi Adottati
Analisi matematica I Marcellini-SbordoneAnalisi matematica I Pagani-Salsa
Esercitazioni di Matematica Marcellini-Sbordone
Bibliografia Di Riferimento
"Funzioni Algebriche e Trascendenti", B. Palumbo, M.C. Signorino, editore Accademica "Analisi Matematica", M. Bertsch, R. Dal Passo, L. Giacomelli, editore MCGraw-Hill "Esercizi di Analisi Matematica", S. Salsa, A. Squellati, editore Zanichelli "Esercizi e complementi di Analisi Matematica: vol. 1", E. Giusti, editore Bollati BoringhieriModalità Erogazione
The course includes lectures and exercises. Attendance is not mandatory but strongly recommended. during the COVID-19 emergency we will follow the regulation of ’art.1 del Decreto Rettorale n°. 703 del 5 maggio 2020Modalità Frequenza
OptionalModalità Valutazione
The written exam is aimed at evaluating the student's ability to perform exercises also of a theoretical nature. It lasts two hours and consists of a first part with four multiple choice questions and a second part with an open question. The student can be exempted from the written exam if he passes an intermediate written test on the first part of the course and a final one on the second part of the course, each lasting two hours, structured in a similar way to what is described above. In the first session, the student will have the opportunity to recover one of the two intermediate tests. After passing the written examination, there is an oral discussion which is relevant for the grade attribution