30122 - PRECORSO DI MATEMATICA / MATHEMATICS - PREPARATORY COURSE
Department of Decision Sciences
For the instruction language of the course see class group/s below
GUIDO OSIMO
Class group/s taught in English
Mission & Content Summary
MISSION
CONTENT SUMMARY
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:
- Real functions of one real variable: general concepts and examples. Composite and inverse functions. Graph of a function. Graphs of elementary functions: linear, power, exponential, and logarithmic functions. Piecewise-defined functions and their graphs. Transformations of elementary functions.
-
Exponential equations and inequalities. Properties of logarithms. Logarithmic equations and inequalities.
-
More on functions: increasing/decreasing, concave/convex, and bounded functions. Global and local extrema of a function.
-
Behavior of elementary functions at the boundaries of the domain. Hierarchy of infinite functions.
-
Graph of a function: domain, behavior at the boundaries, zeros (or x-intercepts), y-intercept, sign, monotonicity, points of maximum and minimum, concavity and convexity.
-
Summation symbol and remarkable sums. Summation properties.
-
Limits: an intuitive idea.
-
Basic language and examples of differential and integral calculus.
Intended Learning Outcomes (ILO)
KNOWLEDGE AND UNDERSTANDING
APPLYING KNOWLEDGE AND UNDERSTANDING
Teaching methods
- Face-to-face lectures
- Online lectures
DETAILS
Online lectures: the first part of the preparatory course takes place online, on the Bboard teaching platfor
Assessment methods
Continuous assessment | Partial exams | General exam | |
---|---|---|---|
|
x | x | x |
ATTENDING AND NOT ATTENDING STUDENTS
Assessment is included in the first year, first semester mathematics course, with the methods used for that course.
Teaching materials
ATTENDING AND NOT ATTENDING STUDENTS
- Online part: all teaching materials are available on the Bboard platform.
- Classroom part: teaching materials prepared by the instructor.