#
Mathematics

A.Y. 2019/2020

Learning objectives

The main objective of the course is to provide students with the basics of the Differential and Integral Calculus for real functions of a real variable and of Linear Algebra

Expected learning outcomes

At the end of the course the student will be able to study some types of real functions of real variables (rational functions, exponential and logarithmic functions) and calculate simple limits and areas delimited by curves and lines. He will be able to draw the graph of these functions and calculate the required areas. He will know the principles underlying linear equation systems and will be able to solve simple systems of linear equations and calculate real eigenvalues and eigenvectors of a real and symmetric matrix. Will develop skills to be able to address the scientific subjects of the course of study.

**Lesson period:** First semester
(In case of multiple editions, please check the period, as it may vary)

**Assessment methods:** Esame

**Assessment result:** voto verbalizzato in trentesimi

Course syllabus and organization

### Unique edition

Responsible

Lesson period

First semester

**Course syllabus**

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.

**Prerequisites for admission**

Required by entrance test. Elementary algebra: monomials, polynomials and their operations. Trigonometry: sine, cosine and tangent functions; their properties and relationships; goniometric circle. Geometry: equations of line, circumference, ellipse, parabola, hyperbola. Exponential functions and logarithms.

**Teaching methods**

Lecture-style instruction

**Bibliography**

G. Aletti, G. Naldi, L. Paeschi, Calcolo differenziale e algebra lineare - McGraw-Hill Education (Italy) srl

**Assessement methods and criteria**

The exam consists of a written test made by both multiple choice questions and open ones. The comprehension of the contents and the ability to solve mathematical problems will be evaluated. The test lasts according with the number and the structure of the assigned exercises, but not more than three hours. There are no intermediate tests. The results will be communicated through the UNIMIA portal.

MAT/01 - MATHEMATICAL LOGIC - University credits: 0

MAT/02 - ALGEBRA - University credits: 0

MAT/03 - GEOMETRY - University credits: 0

MAT/04 - MATHEMATICS EDUCATION AND HISTORY OF MATHEMATICS - University credits: 0

MAT/05 - MATHEMATICAL ANALYSIS - University credits: 0

MAT/06 - PROBABILITY AND STATISTICS - University credits: 0

MAT/07 - MATHEMATICAL PHYSICS - University credits: 0

MAT/08 - NUMERICAL ANALYSIS - University credits: 0

MAT/09 - OPERATIONS RESEARCH - University credits: 0

MAT/02 - ALGEBRA - University credits: 0

MAT/03 - GEOMETRY - University credits: 0

MAT/04 - MATHEMATICS EDUCATION AND HISTORY OF MATHEMATICS - University credits: 0

MAT/05 - MATHEMATICAL ANALYSIS - University credits: 0

MAT/06 - PROBABILITY AND STATISTICS - University credits: 0

MAT/07 - MATHEMATICAL PHYSICS - University credits: 0

MAT/08 - NUMERICAL ANALYSIS - University credits: 0

MAT/09 - OPERATIONS RESEARCH - University credits: 0

Practicals: 32 hours

Lessons: 56 hours

Lessons: 56 hours

Educational website(s)

Professor(s)

Reception:

on appointment

office 2099