Continuum mathematics

A.y. 2018/2019
12
Max ECTS
112
Overall hours
SSD
MAT/01 MAT/02 MAT/03 MAT/04 MAT/05 MAT/06 MAT/07 MAT/08 MAT/09
Language
Italian
Learning objectives
Fornire gli strumenti base, sia dal punto di vista concettuale che del calcolo, indispensabili per poter seguire con profitto un corso universitario a carattere scientifico. Fornire conoscenze propedeutiche ad altri corsi base del cdl.
Expected learning outcomes
Undefined
Course syllabus and organization

Single session

Lesson period
First semester
ATTENDING STUDENTS
Course syllabus
Real numbers and real functions.
The set of real numbers. Maximum, minimum, supremum, infimum. Elementary properties of functions. Elementary functions. Basics of combinatorics. Complex numbers.

Limits of sequences.
Definitions and first properties. Bounded sequences. Operations with limits. Comparison theorems. Monotone sequences. Undetermined forms. Special limits.

Limits of functions and continuous functions.
Definition and first properties of limits of functions and of continuous functions. Kind of discontinuities. Limits and continuity of the composition of functions. Some important theorems on continuous functions.

Derivatives and study of functions.
Definition of derivatives. Computation of derivatives. Theorems of Fermat, Rolle, Lagrange and Cauchy and their consequences. Second and higher order derivatives. Applications to the study of functions. L'Hôpital theorem and Taylor formula.

Integration
Definite integrals and methods of exhaustion. Definition of integrable functions and classes of integrable functions. Properties of the definite integrals. Indefinite integrals. Fundamental theorem of integral calculus. Integration methods. Integration by parts and by substitution. Integration of rational functions.

The detailed program may be found on the web page of the course: https://sites.unimi.it/rondi/did/Matematica_Continuo_Comunicazione_Digi…
NON-ATTENDING STUDENTS
Course syllabus
Real numbers and real functions.
The set of real numbers. Maximum, minimum, supremum, infimum. Elementary properties of functions. Elementary functions. Basics of combinatorics. Complex numbers.

Limits of sequences.
Definitions and first properties. Bounded sequences. Operations with limits. Comparison theorems. Monotone sequences. Undetermined forms. Special limits.

Limits of functions and continuous functions.
Definition and first properties of limits of functions and of continuous functions. Kind of discontinuities. Limits and continuity of the composition of functions. Some important theorems on continuous functions.

Derivatives and study of functions.
Definition of derivatives. Computation of derivatives. Theorems of Fermat, Rolle, Lagrange and Cauchy and their consequences. Second and higher order derivatives. Applications to the study of functions. L'Hôpital theorem and Taylor formula.

Integration
Definite integrals and methods of exhaustion. Definition of integrable functions and classes of integrable functions. Properties of the definite integrals. Indefinite integrals. Fundamental theorem of integral calculus. Integration methods. Integration by parts and by substitution. Integration of rational functions.

The detailed program may be found on the web page of the course: https://sites.unimi.it/rondi/did/Matematica_Continuo_Comunicazione_Digi…
MAT/01 - MATHEMATICAL LOGIC - University credits: 0
MAT/02 - ALGEBRA - University credits: 0
MAT/03 - GEOMETRY - University credits: 0
MAT/04 - MATHEMATICS EDUCATION AND HISTORY OF MATHEMATICS - University credits: 0
MAT/05 - MATHEMATICAL ANALYSIS - University credits: 0
MAT/06 - PROBABILITY AND STATISTICS - University credits: 0
MAT/07 - MATHEMATICAL PHYSICS - University credits: 0
MAT/08 - NUMERICAL ANALYSIS - University credits: 0
MAT/09 - OPERATIONS RESEARCH - University credits: 0
Practicals: 48 hours
Lessons: 64 hours
Professors: Garbagnati Alice, Maggis Marco, Rondi Luca