


Politecnico di Torino  
Academic Year 2009/10  
03BNXFP, 03BNXFO, 03BNXGG Mathematics 

1st degree and Bachelorlevel of the Bologna process in Technology And International Business  Torino/Parigi 1st degree and Bachelorlevel of the Bologna process in Technology And International Business  Torino/Barcellona 1st degree and Bachelorlevel of the Bologna process in Technology And International Business  Torino/Athlone 





Objectives of the course
This course gives the students the basic mathematical tools required to study subjects with a scientific and statistic content. Using mathematics and statistics, the students are enabled to solve problems in a logic and exact way. Besides lectures, practicals are arranged. The professor provides the students with lecture notes.
This course also gives the students the main tools to understand mechanics and the skills to apply mathematical abstract models and concepts to real scientific problems. 
Syllabus
Matrix calculus
. Definition of a matrix . Operations of matrix . Transformations . Reductions . Characteristic . Determinant . Inversion Linear systems . Linear equations . Solutions, compatibility and incompatibility . Matrix of the systems and of coefficient . Reduced lienar system and its solution . Elimination method . Resolution of general linear systems . RouchèCapelli's theorem Plane analytical geometry . Line . Conic section . Circumference . Parabola . Ellipse . Hyperbola Fundamentals of probability and statistics Fundamentals of combinatorial analysis . Tartaglia's triangle . Fundamental rule of calculus . Newton's binomal . Ordered combination with repetition . Ordered combination without repetition . Unordered combination with repetition . Unordered combination without repetition . Permutations Fundamentals of probability theory . Definition of probability; comparison among different definitions . Events . "Conditioned" probability  Bayer's theorem Introduction to Descriptive statistics . Population, parameters, random standard . Absolute and relative frequency . Frequency distribution . Graphical representation of frequency distribution . Cumulative and ogive distributions . Variables . Average, deviation, variance, mode, median Financial mathematics . Index and logarithms  Arithmetic and geometric progressions . Simple interest and discount . Compund interest and discount . Depreciation  Remaining debt  Mortgage loan  Depreciation funds . 1D motion, trajectory, motion's laws, x(t), speed and acceleration . Exercises on rectilinear uniform motion and uniformed accelerated motion . Acceleration in 3D and in curvilinear motion; vectors . Uniform circular motion, speed and angular velocity . Sum of vectors; forces; weight force and constraining force . Frictional force, static and dynamic friction; elastic force . Exercises on forces and on vectors . Work and kinetic energy . Conservative and dissipative forces; energy conservation . Inertial and noninertial systems; relative motion; fictitious forces . Quantity of motion; conservation of the quantity of motion . Exercises on forces and on dynamics' laws . Simple harmonic motion; period and frequence; equation of motion . Torque; dyad of parallel forces . Moment of inertia; equations of translational and rotatory motion 
Laboratories and/or exercises
Trainings besides lectures are arranged.

