First cycle
degree courses
Second cycle
degree courses
Single cycle
degree courses
School of Science
Course unit
SCN1036023, A.A. 2016/17

Information concerning the students who enrolled in A.Y. 2016/17

Information on the course unit
Degree course First cycle degree in
SC1157, Degree course structure A.Y. 2014/15, A.Y. 2016/17
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Number of ECTS credits allocated 15.0
Type of assessment Mark
Course unit English denomination MATHEMATICS
Department of reference Department of Chemical Sciences
Mandatory attendance
Language of instruction Italian
Single Course unit The Course unit can be attended under the option Single Course unit attendance
Optional Course unit The Course unit can be chosen as Optional Course unit

Teacher in charge ROBERTO BERTELLE

Course unit code Course unit name Teacher in charge Degree course code

ECTS: details
Type Scientific-Disciplinary Sector Credits allocated
Basic courses MAT/01 Mathematical Logic 3.0
Basic courses MAT/02 Algebra 4.0
Basic courses MAT/03 Geometry 4.0
Basic courses MAT/05 Mathematical Analysis 4.0

Course unit organization
Period First semester
Year 1st Year
Teaching method frontal

Type of hours Credits Teaching
Hours of
Individual study
Practice 7.0 70 105.0 No turn
Lecture 8.0 64 136.0 No turn

Start of activities 01/10/2016
End of activities 20/01/2017
Show course schedule 2019/20 Reg.2014 course timetable

Examination board
Examination board not defined

Prerequisites: None
Target skills and knowledge: Basic mathematical knowledge for degree courses in scientific disciplines.
Examination methods: Written with possible oral
Assessment criteria: The formal correctness and any creativity in solving exercises related to the course content is evaluated
Course unit contents: Basics. Real numbers. Inequalities. Elements of trigonometry. Exponential and logarithmic functions. Summations. Factorial. Binomial coefficients. Newton's binomial formula.
Real functions of a real variable. Successions. Limits. Continuous functions. Derived. Tangent line to the graph of a function. Fundamental theorems of differential calculus. Maximum and minimum relative and absolute. Trigonometric functions, exponential and logarithmic. Study of a function. Definite and indefinite integrals. Volumes of solids of revolution. Lengths of function graphs. Integrals.
Numerical series. General notions. Geometric series. Harmonic series. Telescopic series. Series in terms non-negative / positive. Convergence criteria. Convergence for series in terms of alternating signs. Taylor series and Maclaurin. Approximations.
Hints on complex numbers. Gauss plane. Trigonometric representation of complex numbers. Euler formulas. Outline of trigonometric and exponential functions in the complex field.
Differential equations. First order differential equations, linear and with separable variables. Models described by linear differential equations of the first order. Second order linear differential equations with constant coefficients. Applications: simple harmonic motion, harmonic motion with viscosity, harmonic motion with sinusoidal external force. Resonance.
Vectors and analytic geometry of three-dimensional space. Vectors in the plane and in space. Scalar product, vector product, mixed product and their geometrical interpretation. Parametric and Cartesian equations of lines and planes in three dimensional space. Angles and distances.
Elements of linear algebra. Vector spaces. Linear dependence. Bases of a vector space. Matrices and linear transformations. Determinants. Linear systems. Rouché-Capelli theorem. Eigenvectors and eigenvalues. Diagonalization.
Functions of several variables. Limits. Continuity. Partial derivatives. Differentiability. Tangent planes. Contour lines. Directional derivative. Gradient vector. Maxima and minima. Saddle points. Constrained maxima and minima.
Planned learning activities and teaching methods: Lecture and classroom exercises
Additional notes about suggested reading: The reference texts will be communicated at the beginning of the course.
Handouts prepared by the teachers, integrative exercises and tasks resloved will be given.
Textbooks (and optional supplementary readings)