Didattica

Tutoring: Mathematics (Economics)

This course is designed for first year Master's degree students in Economics and Finance (Economics curriculum) at the Department of Economics and Management “Marco Fanno”, University of Padua.

This course offers a review of the main concepts in Calculus to follow better the Mathematics for Economics course in MEF. This course gives students skills for implementation of the mathematical knowledge and expertise to the problems of economics.

Participation in the course is voluntary. However, it is strongly suggested for students that during their previous studies never took a course in Mathematics for Economics or passed a Math exam with equivalent grade less than 90/100. This course is not for credit and under no circumstances it can considered a substitute for all or part of the course Mathematics for Economics

 

Required Materials
All materials and exercises will be made available by the teacher, through the publication in the Moodle page of the course.

 

Prerequisites
Its prerequisites are both the knowledge of the single variable calculus and the foundations of linear algebra including operations on matrices, the main concepts of differentiation, gradient and Hessian.

 

Course Objectives
At the completion of this course, students will be able to:
1. Solve problems of constrained and unconstrained optimization.
2. Apply Dini implicit function theorems
3. Solve systems of differential equations and find their equilibrium points;
4. Use Kuhn-Tucker conditions for solving various economic problems.
5. Apply the necessary conditions of the Pontryagin Theorem for some optimal control problems.

 

Schedule and daily learning goals
This review course lasts 10 weeks for a total of 20 hours, with 2 hours a week in 1 meeting per week.

-       4 hours on vector algebra

-       4 hours on multivariable calculus

-       4 hours on Differential equations

-       8 hours on various topics in advanced mathematics that may require special attention, among which Dynamic Optimization.

 

Lecture 01: 26 September 2022 from 17.00 to 19.00

TITLE “Operations with matrices and Linear systems”

Lecture 02: 3 October 2022 from 17.00 to 19.00
TITLE “Eigenvalues and eigenvectors”;

Lecture 03: 10 October 2022 from 17.00 to 19.00
TITLE “Stationary Points, Unconstrained optimization, Total Derivatives with solutions”;

Lecture 04: 24 October 2022 from 17.00 to 19.00

TITLE “Implicit differentiation, Implicit functions Theorem (Dini)”;

Lecture 05: 7 November 2022 from 17.00 to 19.00
TITLE “Optimization with inequality and mixed constraints (Kuhn-Tucker)”;

------------ skip 17 October --------- on demand --------

Lecture 06: 14 November 2022 from 17.00 to 19.00
TITLE “Differential equations”;

Lecture 07: 21 November 2022 from 17.00 to 19.00
TITLE “System of differential equations, equilibrium points”;

Lecture 08: 28 November 2022 from 17.00 to 19.00
TITLE “Optimal control Pontryagin Maximum Principle”.

Lecture 09: 5 December 2022 from 17.00 to 19.00
TITLE “Optimal control Hamilton Jacoby Bellman equation”.

Lecture 10: 12 December 2022 from 17.00 to 19.00
TITLE “Optimal control review”. TITLE “Resolution of the exam template”

 

Additionally 10 hours of consultations “on demands” are planned. This schedule can be flexible but the approximate hours are below:

Consultation  1, 10 October 2022 from 19.00 to 20.00 (1 hours)

Consultation  2, 17 October 2022 from 17.00 to 18.00 (1 hours)

Consultation  3, 24 October 2022 from 19.00 to 20.00 (1 hours)

Consultation  4, 7 November 2022 from 19.00 to 20.00 (1 hours)

Consultation  5, 14 November 2022 from 19.00 to 20.00 (1 hours)

Consultation  6, 21 November 2022 from 19.00 to 20.00 (1 hours)

Consultation  7, 28 November 2022 from  19.00 to 20.00 (1 hours)

Consultation  8, 12 December 2022 from 19.00 to 20.00 (1 hours)

Consultation  9, 19 December 2022 from 17.00 to 19.00 (2 hours)

 

Lessons will be held online on Zoom - Moodle page

Teacher: Soloviova Mariia
E-Mail: mariiasoloviova93@gmail.com

For further information:
Segreteria didattica Dipartimento di Scienze Economiche e Aziendali "M. Fanno"
Via Ugo Bassi, 1 Padova - tel. 049 827 1230
didattica.economia@unipd.it