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Politecnico di Torino
Academic Year 2009/10
03BNXFP, 03BNXFO, 03BNXGG
Mathematics
1st degree and Bachelor-level of the Bologna process in Technology And International Business - Torino/Parigi
1st degree and Bachelor-level of the Bologna process in Technology And International Business - Torino/Barcellona
1st degree and Bachelor-level of the Bologna process in Technology And International Business - Torino/Athlone
Teacher Status SSD Les Ex Lab Tut Years teaching
Lucia Umberto ORARIO RICEVIMENTO A2 ING-IND/10 89 23 0 0 3
SSD CFU Activities Area context
FIS/01
MAT/06
2
8
A - Di base
A - Di base
Fisica e chimica
Matematica, informatica e statistica
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

. Rouchè-Capelli'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 non-inertial 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.

Programma provvisorio per l'A.A.2005/06
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