50188 - QUANTITATIVE METHODS - PREPARATORY

The precourse presents basic elements of Calculus which are required in the study of mathematics and statistics oriented to legal, economic and financial applications. It rests on certain knowledge, which should be in possession of all admitted students, on the basis of ministerial programs. Since such knowledge is often absent, Bocconi offers this precourse in which these themes are concisely presented or for revision or for the first introduction. Therefore, the main goato provide each incoming student with the necessary knowledge base to follow with successful course of "Quantitative Methods"

• Somme di numeri reali. Famiglia di insiemi. Fattoriale di un intero positivo.
• Nozione di funzione reale di una variabile reale. Grafico di funzione. Funzioni definite a tratti. Algebra delle funzioni.
• Proprietà delle funzioni. Funzioni elementari.
• Funzione composta. Funzione inversa. Nozione elementare di continuità.
• Derivata prima. Derivate elementari. Equazione della retta tangente. Algebra delle derivate.
• Derivata di una funzione composta. Punti stazionari. Monotonia e derivabilità. Primo test di riconoscimento dei punti stazionari.
• Derivata seconda. Concavità/convessità di una funzione e derivata seconda. Secondo test di riconoscimento dei punti stazionari.
• Primitiva di una funzione. Primitive di funzioni elementari. Metodi di integrazione indefinita: scomposizione.
• Metodi di integrazione indefinita: sostituzione, per parti. Nozione di vettore. Nozione di matrice. Algebra delle matrici.
• Matrici quadrate notevoli. Sottomatrici principali di Nord-Ovest. Calcolo del determinante di una matrice quadrata di secondo e terzo ordine. Minori principali di Nord-Ovest.

•    Describe the main properties and notions about functions.
•    Reproduce the correct procedure to find stationary points and recognize their nauture.
•    Select the convenient method to find an antiderivative.

• Face-to-face lectures

     Traditional whiteboard lessons with slide support projected into the classroom.

     The assesment is included in the Quantitative Methods Course. 

All teaching material will be available on Bboard classes at the beginning of the preparatory course.

The precourse presents basic elements of Calculus which are required in the study of mathematics and statistics oriented to legal, economic and financial applications. It rests on certain knowledge, which should be in possession of all admitted students. Since such knowledge is often missing, Bocconi offers this precourse in which the notions are concisely presented both for a revision and for a first introduction. Therefore, the main goal is to provide each incoming student with the necessary knowledge that will allow them to follow with success the course of "Quantitative Methods".

• Set Theory elements. Numbers: sum of real numbers, factorial.
• Functions; real functions of one real variable; the graph of a function.
• Functions properties; maxima and minima. Elementary functions. Piecewise functions.
• Composition of functions. Inverse function. Continuous functions.
• Derivatives. Elementary derivatives. The tangent line. Algebra of derivatives. The chain rule.
• Stationary points. Monotonicity and derivatives. First order test for maxima and minima.
• Second order derivative; concavity/convexity test. Second order test for maxima and minima.
• Antiderivative of a function. Elementary antiderivatives. Indefinite integral and its properties.
• Integral calculus methods; decomposition, by parts and change of variable.
• Vectors and matrices. Matrix calculus.
• Square matrices; determinant of a square matrix of order two and three.
• Minors of a square matrix, North-West minors.

• Describe the main properties and notions about functions.
• Reproduce the correct procedure to find stationary points and recognize their nature.
• Select the convenient method to find an antiderivative.

•  Apply differential calculus to argue the behavior of a function.
•  Compute antiderivates by choosing the convenient method.
•  Solve basic problems of unconstrained optimization.
•  Compute the determinant and the minors of a square matrix.

• Face-to-face lectures

     Traditional whiteboard lessons with slide support projected into the classroom.

     The assesment is included in the Quantitative Methods Course. 

All teaching material will be available on Bboard classes at the beginning of the preparatory course.