30449 - MATHEMATICS - MODULE 2 (APPLIED MATHEMATICS)
Course taught in English
Go to class group/s: 13
A review of one variable differential calculus, integral calculus, linear algebra and complex numbers is suggested.
Modeling in applied science always requires mathematical and statistical tools. In particular, Economic Theory makes a large use of some classical mathematical topics such as Mathematical Programming and Dynamical Systems. The development of technology has increased computing power making manageable and convenient the use of many mathematical techniques. Notwithstanding, the implementation and the comprehension of any model needs the knowledge of the available tools. The course goal is providing the main mathematical and analytical tools which are used in models applied to Economics and Decision Theory.
- 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.
- During the lectures convenient examples and applications allow students to identify the quantitative patterns and their main logical-mathematical properties.
- The in class exercises allow students to properly apply the analytical tools in practice.
|Continuous assessment||Partial exams||General exam|
The exam is written. Each student can choose whether to take:
General Exam: a single final exam (labelled with I). The General Exam consists of open answer questions and is worth 100% of the final grade;
Partial Exam: 2 partial written exams (labelled with I) plus 2 online tests. Each partial written exam is worth 34% of the final grade (68% in total). Each online test consists of closed answer questions and is worth the 16% of the final grade (32% in total).
Both the General and the Partial written exams consists of open answer 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.
The online tests consist of closed answer questions and aim 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.
- 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.