Course 2024-2025 a.y.

30449 - MATHEMATICS - MODULE 2 (APPLIED MATHEMATICS)

Department of Decision Sciences

Course taught in English
code 30448 Mathematics - Module 1 (Theory and methods) and code 30449 Mathematics - Module 2 (Applied mathematics) are respectively the first and the second module of the course code 30447 Mathematics

Class timetable
Exam timetable
Go to class group/s: 13
BESS-CLES (9 credits - II sem. - OB  |  SECS-S/06)
Course Director:
SIMONE CERREIA VIOGLIO

Classes: 13 (II sem.)
Instructors:
Class 13: MAURO D'AMICO


Suggested background knowledge

A review of differential calculus and linear algebra is suggested.

Mission & Content Summary

MISSION

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.

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

At the end of the course student will be able to...
  • 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

At the end of the course student will be able to...
  • 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

  • Lectures
  • Practical Exercises

DETAILS

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.

Assessment methods

  Continuous assessment Partial exams General exam
  • Written individual exam (traditional/online)
   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.
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