MATHEMATICAL METHODS FOR CLIMATE CHANGE ANALYSIS

This course will provide the formal tools to reason about time varying systems in real world phenomena, with particular focus on enviromental and economic quantities dynamics due to climate change. Most of the course will be devoted to certainty condition, and the Students will have to consider the ability to represent and elaborate the typical mathematic tool like linear algebra, differential equations and system. In a final part, possibly even elements of bifurcation and chaos will be explained, given that this non linear part has received particular attention in envirnmental science.

a) Knowledge and understanding:
a.1) Ability to understand the concept of dynamic change
a.2) Ability to think formally about dynamic relationships
a.3) Ability to recognize and use the most important items in dynamis systems, both in the discrete and in the continuous case

b) Applying knowledge and understanding:
b.1) Ability to deal with linear algebra.
b.2) Ability to manipulate and use differential equations and finite difference equation.
b.3) Ability to build formal dynamica models and solving the related problems.

c) Making judgements
c.1) Ability to evaluate dynamic properties of a system..

Basic mathematics and calculus (functions, derivatives, optimization, integral, vector, matrices and systems of linear equations)
It is remarkable that Students cannot ignore fundamental of calculus, included complex numbers, vectors and matrices.. Thus the Students are strongly encouraged in a summer preparation (before the course starting), reviewing in particular the element of basic calculus (functions, derivatives, optimization, complex numbers, vectors and matrices)

Complex numbers, vectors and matrices, eigenvalues and eigenvectors
Differential equations and systems
Equilibra and stability of dynamic systems
Element of non linear dynamics and of chaos theory

Required readings
Material distributed by the Lecturer during the seminars and some recommended books (which will be specified during the course)

Recommended readings
Some books will be recommended during the course

Tests during the course. Final exam or in alternative (at least in part) Student's presentation.

Traditional with slides. Student's presentation.

Attendance is required. Daily preparation is also required; in every lesson the Students will be asked for exercises assigned in the previous lessons; this will constitute part of the exam. The arguments in the first part (Basic calculus) together with “Complex numbers”, “Vectors and Matrices” will be ONLY briefly resumed, being supposed acquainted in basic academic courses.

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This subject deals with topics related to the macro-area "Climate change and energy" and contributes to the achievement of one or more goals of U. N. Agenda for Sustainable Development