Course 2022-2023 a.y.

• Implicit functions.
• Constrained optima; classical programming and differentiable non linear programming.
• Integral Calculus
• Complex Numbers
• Eigendecomposition of a square matrix. Power and exponential matrices,
• 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. Autonomous systems of dimension 1; phase and stairstep diagrams.

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

• Apply the learned calculus methods to solve an optimization problem, to compute integrals, 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 consist of (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.

The exam is written. Each student can choose whether to take:

General Exam: a single final exam (labelled with S). The General Exam is worth 100% of the final grade.

Partial Exam:  2 partial written exams (labelled with I). Each partial written exam is worth 50% of the final grade (100% in total). 

Both the General and the Partial written exams consists of open answer questions which aim to assess the students’ ability to:

• Apply in a proper way the learned calculus methods in order to compute integrals, to solve optimization problems and differential/difference equations.
• Describe the notions and the methods learned.
• Justify in a proper manner the achieved conclusions.

• Recognise and demonstrate the connections between the main concepts and their properties.

• S. CERREIA-VIOGLIO, M. MARINACCI, E. VIGNA, Principles of Mathematics and Economics, draft version (March 2022). Available on BBoard in PDF format.

• R. K. SUNDARAM, A First Course in Optimization Theory, Cambridge University Press, 1996, ISBN: 978052149770.

• M. CIGOLA, L. PECCATI (2019), Dynamical Systems, PDF available on Bboard.
• Past written exams with solutions, PDF available on Bboard.