30122 - PRECORSO DI MATEMATICA / MATHEMATICS - PREPARATORY COURSE
Per la lingua del corso verificare le informazioni sulle classi/
For the instruction language of the course see class group/s below
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Class group/s taught in English
Lezioni della classe erogate in presenza
The aim of the preparatory course in mathematics is to consolidate some topics in pre-undergraduate mathematics, in order to help students begin their university studies with comfort and competence. In university courses, these topics are considered as known and are not repeated. The preparatory course is a blended learning course, that is it is partly online and partly in person. The online part is accessible from the summer that precedes the first year of university studies. The classroom part deals with different topics with respect to the online part, consists of a 12 hours course and it is entirely delivered during the Welcome Week of the first year. It is preferable that students complete the online part before the beginning of the classroom part. The knowledge of the content delivered in both the online and classroom parts are integral in helping students earn high marks on the first exams in mathematics, which are part of their plan of study.
- Sets. Operations with sets. Number sets. Representation of number sets on the line.
- Powers with integer exponents. Roots. Powers with rational exponents and with real exponents.
- Number systems.
- Polynomial algebra.
- First and second degree equations. Higher degree equations. Fractional equations. Systems of equations.
- Cartesian coordinates in the plane. Straight lines. Parabolas. Other curves.
- Elements of trigonometry.
- First and second degree inequalities. Higher degree inequalities. Fractional inequalities. Systems of inequalities. Equations and inequalities with terms in absolute value.
- Introduction to proofs. Connectives, quantifiers. Demonstration techniques: direct, contrapositive and indirect (or by contradiction). Principle of induction.
- Real functions of one real variable: definition, graph, examples. Surjective, injective, bijective functions. Composite function. Inverse function. Bounded and unbounded functions. Increasing and decreasing functions. Global extrema of a function. Concave and convex functions. Operations with functions (sum, difference, product and quotient). Linear combination of functions. Odd and even functions. Periodic functions. Elementary functions and their graphs: constant, linear, affine linear, power, exponential and logarithm. Piecewise defined functions. Elementary notion of continuity.
- Derivative. Derivatives of elementary functions. Algebra of derivatives. Chain rule. Equation of the tangent line. Stationary points. Second derivative.
- Face-to-face lectures
- Online lectures
Online lectures: the first part of the preparatory course takes place online, on the Bboard teaching platform.
|Continuous assessment||Partial exams||General exam|
Assessment is included in the first year, first semester Mathematics course, with the methods used for that course.
- Online part: all teaching materials are available on the Bboard platform.
- Classroom part: teaching materials prepared by the instructor.