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Course 2019-2020 a.y.


Department of Decision Sciences

For the instruction language of the course see class group/s below

Go to class group/s: 23

BIG (I sem. - P)
Course Director:

Classes: 23 (I sem.)

Class group/s taught in English

Mission & Content Summary

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 15 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.


Online part:

  • 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.
  • 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.
  • First and second degree inequalities. Higher degree inequalities. Fractional inequalities. Systems of inequalities. Equations and inequalities with terms in absolute value.

Classroom part:

  • Summation symbol and remarkable sums.
  • Real functions of one real variable: definition, graph, examples. Composite function. Inverse function. Elementary functions and their graphs: linear, affine linear, quadratic, power, exponential, logarithmic functions. Piecewise defined functions. Transformation of elementary functions.
  • Behaviour of elementary functions at the boundary of their domain. Hierarchy of infinite functions.
  • Exponential equations and inequalities. Properties of logarithms. Logarithmic equations and inequalities. Solution to equations and inequalities by graphical methods.
  • Difference quotient, derivative. Derivatives of elementary functions. Algebra of derivatives. Chain rule. Equation of the tangent line. Stationary points. Derivative and monotonicity. Second derivative. Convex and concave functions.
  • Graph of a function: domain, behaviour at the boundary, zeros (or x-intercepts), y-intercept, sign, monotonicity, points of maximum and minimum, concavity and convexity.
  • Antiderivatives of elementary functions. Integration methods: decomposition, substitution, by parts.

Teaching methods
  • Face-to-face lectures
  • Online lectures

Online lectures: the first part of the preparatory course takes place online, on the Bboard teaching platform.

Assessment methods
  Continuous assessment Partial exams General exam
  • Included in the assessment procedures for code 30319
  •   x x

    Teaching materials
    • Online part: all teaching materials are available on the Bboard platform.
    • Classroom part: teaching materials prepared by the instructor.
    Last change 27/05/2019 11:32