Mathematics

The course provides the basic principles of mathematical analysis, numerical methods, and linear algebra so that the quantitative behaviour of environmental phenomena and corresponding mathematical models.can be studied and interpreted. Main topics: sets and real numbers; functions (definition, graph, composite function and inverse function, monotonicity, convexity); elementary functions (polynomials, exponentials, logarithms, sine, cosine and tanget, their properites and graphs); limits (definition, main properties, calculus of limits); continuity (definition, discontinuity and continuity points, uniform continuity, the Weierstrass, Heine-Cantor, zeros and Darboux theorems); derivatives ( definition, geometric meaning, derivatives of elementary functions, rules to comoute derivatives); Rolle theorem, Lagrange theorem and its corollaries. Taylor's and Mac Laurin's formulas. Properties of functions and their graphs: increasing and decreasing, conditions for the existence of local maximum and minimum; convexity and asymptotes. Integrability (definition, properties of the definite integral, sufficient conditions for integrability, mean value and the fundamental theorem of calculus, primitive functions, indefinite integrals, integration rules. Basic linear algebra: real vector spaces, linear transformation and matrices. Solution of linear equations systems.