
Course unit
MATHEMATICS
SCN1036023, A.A. 2016/17
Information concerning the students who enrolled in A.Y. 2016/17
ECTS: details
Type 
ScientificDisciplinary 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 
Hours of Individual study 
Shifts 
Practice 
7.0 
70 
105.0 
No turn 
Lecture 
8.0 
64 
136.0 
No turn 
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 nonnegative / 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 threedimensional 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. RouchÃ©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) 


