#
Mathematics

A.Y. 2018/2019

Learning objectives

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.

Expected learning outcomes

Undefined

**Lesson period:**
First semester

**Assessment methods:** Esame

**Assessment result:** voto verbalizzato in trentesimi

Course syllabus and organization

### Single session

Responsible

Lesson period

First semester

**Course syllabus**

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.

**Website**

MAT/01 - MATHEMATICAL LOGIC

MAT/02 - ALGEBRA

MAT/03 - GEOMETRY

MAT/04 - MATHEMATICS EDUCATION AND HISTORY OF MATHEMATICS

MAT/05 - MATHEMATICAL ANALYSIS

MAT/06 - PROBABILITY AND STATISTICS

MAT/07 - MATHEMATICAL PHYSICS

MAT/08 - NUMERICAL ANALYSIS

MAT/09 - OPERATIONS RESEARCH

MAT/02 - ALGEBRA

MAT/03 - GEOMETRY

MAT/04 - MATHEMATICS EDUCATION AND HISTORY OF MATHEMATICS

MAT/05 - MATHEMATICAL ANALYSIS

MAT/06 - PROBABILITY AND STATISTICS

MAT/07 - MATHEMATICAL PHYSICS

MAT/08 - NUMERICAL ANALYSIS

MAT/09 - OPERATIONS RESEARCH

Practicals: 32 hours

Lessons: 56 hours

Lessons: 56 hours

Professor(s)