Syllabus
EN
IT
Attendance is not compulsory but highly recommended
Prerequisites
Being able to solve first and second order equations, inequalities, fractional inequalities, exponential, logarithmic and trigonometric inequalities.
Basic knowledge of properties of exponential, logarithmic and trigonometric functions.
Basic knowledge of properties of exponential, logarithmic and trigonometric functions.
Program
Basic properties of functions.
Set theory. Set Operations: union, intersection, difference, complement. Intuitive construction of number sets.
Real valued functions.
Linear, quadratic and polynomial functions. Exponential, Logarithmic and Trigonometric functions. Domain, Range of a function. Increasing, decreasing and monotonic functions.
Injective, surjective functions. The inverse function.
Sequences.
Definition of limit of a sequence, uniqueness of the limit of a sequence (with proof), monotonic sequences. Existence of the limit of a monotonic and bounded sequence. Comparison Theorem (with proof). Notable limits.
Series.
Definition and examples. Conditions for convergence of geometric series (with proof).
Limit of real functions of one real variable.
Definition. Uniqueness of the limit. Comparison Theorem.
Continuity: definition and main theorems. Characterization of the discontinuity points of a function: jumps and removable and essential discontinuities.
Derivative of a real functions of one real variable.
Necessary condition for differentiability (with proof).
Maxima and minima of a function: necessary and sufficient conditions.
Tangent line and 1st order Taylor approximation.
Convex and concave functions. Second-order conditions for maxima and minima.
Set theory. Set Operations: union, intersection, difference, complement. Intuitive construction of number sets.
Real valued functions.
Linear, quadratic and polynomial functions. Exponential, Logarithmic and Trigonometric functions. Domain, Range of a function. Increasing, decreasing and monotonic functions.
Injective, surjective functions. The inverse function.
Sequences.
Definition of limit of a sequence, uniqueness of the limit of a sequence (with proof), monotonic sequences. Existence of the limit of a monotonic and bounded sequence. Comparison Theorem (with proof). Notable limits.
Series.
Definition and examples. Conditions for convergence of geometric series (with proof).
Limit of real functions of one real variable.
Definition. Uniqueness of the limit. Comparison Theorem.
Continuity: definition and main theorems. Characterization of the discontinuity points of a function: jumps and removable and essential discontinuities.
Derivative of a real functions of one real variable.
Necessary condition for differentiability (with proof).
Maxima and minima of a function: necessary and sufficient conditions.
Tangent line and 1st order Taylor approximation.
Convex and concave functions. Second-order conditions for maxima and minima.
Books
Lorenzo Peccati, Sandro Salsa, Annamaria Squellati. Mathematics for economics and business.
Bibliography
Knut Sydsæter, Peter Hammond, Arne Strøm, Essential Mathematics for Economic Analysis
Carl P. Simon, Lawrence Blume, Mathematics for Economists
Carl P. Simon, Lawrence Blume, Mathematics for Economists
Teaching methods
Lectures and exercise sesssions
Exam Rules
Mathematics is a single corse split in two modules. After the final exam only one grade will be registered.
The exam consists of a set of exercises and theoretical questions on the material covered during the course.
The exam is passed if the mark is grater than or equal to 18/30.
Every result of the exam will be registered, including "fail".
Students are allowed to reject a mark greater or equal to 18 only once and re-take the exam. In the case, at the second time the grade will be registered.
The exam consists of a set of exercises and theoretical questions on the material covered during the course.
The exam is passed if the mark is grater than or equal to 18/30.
Every result of the exam will be registered, including "fail".
Students are allowed to reject a mark greater or equal to 18 only once and re-take the exam. In the case, at the second time the grade will be registered.
Attendance Rules
Attendance is not compulsory but highly recommended