Continuous mathematics
A.Y. 2018/2019
Lesson for
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.
Course structure and Syllabus
Active edition
Yes
Responsible
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
ATTENDING STUDENTS
Syllabus
NONATTENDING STUDENTS
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…
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… Lesson period
First semester

Lesson period
First semester
Professor(s)
Reception:
Thursday 11am12 noon and 2pm4pm or by appointment
room 2051 (attic), Dipartimento di Matematica