Continuum Mathematics
A.Y. 2018/2019
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
Lesson period: First semester
Assessment methods: Esame
Assessment result: voto verbalizzato in trentesimi
Single course
This course cannot be attended as a single course. Please check our list of single courses to find the ones available for enrolment.
Course syllabus and organization
Single session
Lesson period
First semester
ATTENDING STUDENTS
Course syllabus
NON-ATTENDING 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_Digitale_18-19.html
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_Digitale_18-19.html
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_Digitale_18-19.html
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_Digitale_18-19.html
MAT/01 - MATHEMATICAL LOGIC
MAT/02 - ALGEBRA
MAT/03 - GEOMETRY
MAT/04 - MATHEMATICS EDUCATION AND HISTORY OF MATHEMATICS
MAT/05 - MATHEMATICAL ANALYSIS
MAT/06 - PROBABILITY AND STATISTICS
MAT/07 - MATHEMATICAL PHYSICS
MAT/08 - NUMERICAL ANALYSIS
MAT/09 - OPERATIONS RESEARCH
MAT/02 - ALGEBRA
MAT/03 - GEOMETRY
MAT/04 - MATHEMATICS EDUCATION AND HISTORY OF MATHEMATICS
MAT/05 - MATHEMATICAL ANALYSIS
MAT/06 - PROBABILITY AND STATISTICS
MAT/07 - MATHEMATICAL PHYSICS
MAT/08 - NUMERICAL ANALYSIS
MAT/09 - OPERATIONS RESEARCH
Practicals: 48 hours
Lessons: 64 hours
Lessons: 64 hours
Professors:
Garbagnati Alice, Maggis Marco, Rondi Luca
Professor(s)
Reception:
On appointment
Department of Mathematics, office number 1038