This course is designed for 1st year Master's degree students of Economics and Finance (Economics Curriculum) at the Department of Economics and Management “Marco Fanno”, University of Padova.

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
The teacher will publish all materials and exercises 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 (with exercises)
-       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, October, 4, from 2.30 to 4.30 pm
TITLE “Operations with matrices and Linear systems”

Lecture 02, October, 11, from 2.30 to 4.30 pm
TITLE “Eigenvalues and eigenvectors”;

Lecture 03, October, 18, from 2.30 to 4.30 pm
TITLE “Implicit differentiation, Implicit functions Theorem (Dini)”;

Lecture 04, October, 25, from from 2.30 to 4.30 pm
TITLE “Optimization with inequality and mixed constraints (Kuhn-Tucker)”;

Lecture 05, November, 8, from from 2.30 to 4.30 pm
TITLE “Differential equations”;

Lecture 06, November, 15, from from 2.30 to 4.30 pm
TITLE “System of differential equations, equilibrium points”;

Lecture 07, November, 22, from from 2.30 to 4.30 pm
TITLE “Optimal control Pontryagin Maximum Principle”.

Lecture 08, November, 29, from from 2.30 to 4.30 pm
TITLE “Optimal control Hamilton Jacoby Bellman equation”.

Lecture 09, December, 6, fromfrom 2.30 to 4.30 pm
TITLE “Optimal control review”.

Lecture 10, December, 13, from 2.30 to 4.30 pm
TITLE “Resolution of the exam template”.

Lessons will be held online through Zoom platform

Teacher: PhD Zormpas Dimitrios
Email: dimitrios.zormpas@unipd.it

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