Mathematics

A.Y. 2018/2019
9
Max ECTS
88
Overall hours
SSD
MAT/01 MAT/02 MAT/03 MAT/04 MAT/05 MAT/06 MAT/07 MAT/08 MAT/09
Language
Italian
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
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.
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
Practicals: 32 hours
Lessons: 56 hours
Professor(s)
Reception:
on appointment
office 2099