30449 - MATHEMATICS - MODULE 2 (APPLIED MATHEMATICS)
Course offered to incoming exchange students
Department of Decision Sciences
SIMONE CERREIA VIOGLIO
Suggested background knowledge
Mission & Content Summary
MISSION
CONTENT SUMMARY
- 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.
Intended Learning Outcomes (ILO)
KNOWLEDGE AND UNDERSTANDING
- 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.
APPLYING KNOWLEDGE AND UNDERSTANDING
- 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.
Teaching methods
- Face-to-face lectures
- Online lectures
- Exercises (exercises, database, software etc.)
DETAILS
Teaching and learning activities for this course consist of (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.
Assessment methods
Continuous assessment | Partial exams | General exam | |
---|---|---|---|
|
x | x |
ATTENDING AND NOT ATTENDING STUDENTS
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.
Teaching materials
ATTENDING AND NOT ATTENDING STUDENTS
-
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.