Corso di laurea in Fisica

This course provides the fundamentals of Mathematical Analysis of functions of one real variable that are necessary for the understanding of the main scientific disciplines, with a special attention to the physical sciences.

Knowledge and understanding

Knowledge of the differential and integral calculus for functions of one real variable.

Applying knowledge and understanding

At the end of the course students must be able to solve exercises and problems using the tools of fundamental calculus (in particular: calculate the limits of sequences and functions, study the qualitative graph of a function, solve integration problems of elementary character, solve some simple differential equations). They also should be able to state, and prove in some cases, the basic theorems of Mathematical Analysis.

The hours indicated in the official calendar as "Tutoraggio di Analisi1" will be held in the presence of proff. Capietto (50 hours) and Zucco (22 hours) and by collaborating students (34 hours). The proff. Capietto and Zucco will examine the more complex contents carried out remotely by prof. Boscaggin, will hold guided exercises and will answer questions and requests for clarification / insights. Collaborating students will be available for clarification on the exercises assigned weekly in preparation for the written test. Each contribution will be (for the first 3 weeks) held 4 times; in this way the contribution provided will be identical for the groups A1, A2, B1, B2. Starting from the fourth week, if it is possible (on the basis of the evolution of the sanitary situation and the number of freshmen attending the hours in the presence) we could move to 3 groups, in order to be able to deal with a greater number of topics.
The contributions provided in the presence (and the timing with which they will be deployed) are strictly connected to the lessons and exercises held remotely by proff. Boscaggin and Zucco. These contents, carried out remotely and uploaded at the Moodle page of the course, will contain all the program required for the exam.
For any clarification, freshmen are invited to contact anna.capietto@unito.it, alberto.boscaggin@unito.it, davide.zucco@unito.it

The evaluation procedures consist of a final exam whose details are described in the slot Modalità e programma d'esame of the Moodle page of this course. It is recommended to read carefully the content of that page.
 
No intermediate checks are planned.

If necessary, exams will take place remotely. Details shall be available as soon as possible.

Tutoring during term time. See the slot Tutorato of the Moodle page of this course.

Students who, for valid reasons, cannot access the Physics department, will be able to attend (upon request) Webex sessions for clarifications.

The detailed program will be posted at the Moodle page  of the course.

Elementary logic concepts. Propositional calculus and quantifiers. Real
numbers. The notion of function and elementary functions.Limits of
sequences and of functions.Pointwise continuity and continuity in
intervals. Derivatives and differential calculus theorems.Maxima and
minima.Graphs of functions.Taylor formula.Integral calculus: primitives,
definite integrals, Fundamental theorem of calculus.Improper integrals:
convergence criteria.Complex numbers.First order differential equations:
solvability of linear equations and of equations with separable variables.
Second order linear differential equations with constant coefficients.
Initial value problems.

Official text: Analisi Matematica - Dal Calcolo all'analisi - Vol.1
Authors: M. Conti, D. Ferrario, S. Terracini, G.Verzini
Editor: Apogeo

Exercises:

M. Badiale, P. Caldiroli, S. Coriasco, Esercizi di Analisi Matematica, Aracne Ed.

P. Marcellini, C. Sbordone, Esercitazioni di Matematica, Vol. 1, Liguori

Any detail and teaching material can be found at Moodle page of this course