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Course 2020-2021 a.y.

30449 - MATHEMATICS - MODULE 2 (APPLIED MATHEMATICS)

BESS-CLES
Department of Decision Sciences

Course taught in English

Go to class group/s: 13

BESS-CLES (9 credits - II sem. - OB  |  SECS-S/06)
Course Director:
MARGHERITA CIGOLA

Classes: 13 (II sem.)
Instructors:
Class 13: MARGHERITA CIGOLA


Suggested background knowledge

A review of one variable differential calculus, integral calculus, linear algebra and complex numbers 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
  • 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.

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.
  • 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.
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 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 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.

Assessment methods
  Continuous assessment Partial exams General exam
  • Written individual exam (traditional/online)
  • x   x
  • Individual assignment (report, exercise, presentation, project work etc.)
  • x    
    ATTENDING AND NOT ATTENDING STUDENTS

    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.

    Teaching materials
    ATTENDING AND NOT ATTENDING STUDENTS
    • 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.
    Last change 09/12/2020 17:24