The objective of this course is to give students an understanding of basic calculus as well as to enable them to approach problems from a mathematical perspective.
teacher profile teaching materials
- Inf and Sup, min and max. Theorem of completeness of R. The absolute value of a real number.
- Real function in one real variable. Image and pre-image. Lecture of a graph.
- Composition, translation and absolute value. Injective, surjective, bijective, inverse functions. Symmetries.
- monotonicity, injectivity and related theorems. Lower and upper bounds of functions, local and global extrema.
- basic functions and their inverse (power, exp, logarithm, trigonometric)
- R^2 as a vector space. The scalar product and euclidean plane
- sequences in R: theorems of uniqueness of limit, sign permanence, limit of monotonic sequences, Bolzano-Weierstrass theorem
- equivalence of sequences and properties
- proof of sin(a_n)/a_n —1 when a_n–0.
- o and O
- limit of a functions and related theorems
- continuous functions, theroem of existence of seros, Darboux, sign permanence
- derivative of a function and geometric interpretation. Derivation rules
- characterization of monotonic and convex functions through their derivatives
- primitives and integration
- Riemann integral: construction and example of integrable functions. The fundamental theorem of calculus
- bascs of ODE
- Elementi di Matematica, Marcellini-Sbordone, Luguori ed. (ATTENZIONE: questo testo non copre tutto il programma)
– Elementi di Calcolo, Marcellini-Sbordone, Luguori ed. (più completo)
Ontherwise any book of Basic Calculus will be fine.
Notes of the project Matematica Assistita - Ariel (Univeristà degli Studi di Milano) download at URL : matematicaassistita.ariel.ctu.unimi.it/ : register as Utente Esterno -- Contenuti -- scegliere l'Argomento
Programme
- The real field R and its subsets N, Z and Q. Intervals: upper a and lower bounds.- Inf and Sup, min and max. Theorem of completeness of R. The absolute value of a real number.
- Real function in one real variable. Image and pre-image. Lecture of a graph.
- Composition, translation and absolute value. Injective, surjective, bijective, inverse functions. Symmetries.
- monotonicity, injectivity and related theorems. Lower and upper bounds of functions, local and global extrema.
- basic functions and their inverse (power, exp, logarithm, trigonometric)
- R^2 as a vector space. The scalar product and euclidean plane
- sequences in R: theorems of uniqueness of limit, sign permanence, limit of monotonic sequences, Bolzano-Weierstrass theorem
- equivalence of sequences and properties
- proof of sin(a_n)/a_n —1 when a_n–0.
- o and O
- limit of a functions and related theorems
- continuous functions, theroem of existence of seros, Darboux, sign permanence
- derivative of a function and geometric interpretation. Derivation rules
- characterization of monotonic and convex functions through their derivatives
- primitives and integration
- Riemann integral: construction and example of integrable functions. The fundamental theorem of calculus
- bascs of ODE
Core Documentation
Recommended Texts (in italian)- Elementi di Matematica, Marcellini-Sbordone, Luguori ed. (ATTENZIONE: questo testo non copre tutto il programma)
– Elementi di Calcolo, Marcellini-Sbordone, Luguori ed. (più completo)
Ontherwise any book of Basic Calculus will be fine.
Notes of the project Matematica Assistita - Ariel (Univeristà degli Studi di Milano) download at URL : matematicaassistita.ariel.ctu.unimi.it/ : register as Utente Esterno -- Contenuti -- scegliere l'Argomento
Type of delivery of the course
lectures with chalk and blackboardAttendance
it is not mandatory to attend the class, but strongly recommended for the understanding.Type of evaluation
Written and oral examination. If the written score >= 24/30, then the oral part can be skipped. two Mid term written test. If the score >= 24/30 one can skip the final oral test. Passing the final part (oral)/confirm the written score within the winter session (Jan or feb) is mandatory for those who pass the mid term tests.