Course 2020-2021 a.y.

• Differential calculus for functions of n real variables: partial derivatives, first order and second order differential.
• Implicit functions.
• Unconstrained optima. Constrained optima: classical programming and differentiable non linear programming.
• Dynamical systems: ordinary differential equations, finite difference equations. Glossary and properties.
• Solving separable and linear autonomous equations.
• Stability: the linear autonomous case, linearization method in the non linear autonomous case. One dimensional autonomous systems: phase diagram, stair step and cobweb diagrams.

• Recognize the mathematical model and its main properties.
• Identify a model and the assumptions that must hold in order that the model may be correctly applied.
• Reproduce the correct procedures  for solving a static optimization problem, for assessing the asymptotic behavior of a dynamical system or for finding its trajectories.

• Apply the learned calculus methods to  solve an optimization problem, to analyze the asymptotic behavior of a dynamical system, to compute the solutions of a differential/difference equation.
• Demonstrate the main properties of a model.
• Formulate in a proper way the assumptions which are required to apply the mathematical tool.

• Face-to-face lectures
• Online lectures
• Exercises (exercises, database, software etc.)

Teaching and learning activities for this course are divided into (1) face-to-face-lectures and/or online lectures, (2) in class exercises.  

1. During the lectures convenient examples and applications allow students to identify the quantitative patterns and their main logical-mathematical properties.
2. The in class exercises allow students to properly apply the analytical tools in practice.

Each student can choose:

(a) whether to take a single final exam (Long Test). The Long Test is worth 100% of the final grade;

(b) or whether to do 4 assignments plus a final exam (Short Test). Each assignment is worth 10% of the final grade (40% in total) and the Short Test is worth the 60% of the final grade. 

Both the Short and the Long tests are online individual exams consisting of closed answers questions aimed to assess the students' ability to:

• Choose the correct mathematical tools to solve optimization problems and differential/difference equation;
• Apply in a proper way the learned calculus methods.
• Recognise the connection between the main concepts and their properties.

Each assignment consists of open-answers questions aimed to assess students’ ability to:

• Apply the analytical  tools in order  to solve optimization problems and differential/difference equations.
• Describe the notions and the methods learned.
• Justify in a proper manner the achieved conclusions.

• E. CASTAGNOLI, M. MARINACCI, E. VIGNA, Principles of Mathematics and Economics, Milano, dispense Egea, 2013, (ISBN 978-88-6407-192-3).
• E. CASTAGNOLI, M. CIGOLA (2019), Static Optimization, PDF available on Bboard.
• M. CIGOLA, L. PECCATI (2019), Dynamical Systems, PDF available on Bboard.
• Past written exams with solutions, PDF available on Bboard.