Notes for the course in Mathematics freely available on the Moodle page of the course.
Learning Objectives
Learning of the mathematical formalism relevant to the characterizing courses of the cursus studiorum.
Learning Objectives - Part B
Learning of the mathematical formalism relevant to the characterizing courses of the cursus studiorum.
Prerequisites
Arithmetics of real numbers.
Notions of synthetic geometry.
Notions of literal calculus.
Prerequisites - Part B
Arithmetics of real numbers.
Notions of synthetic geometry.
Notions of literal calculus.
Teaching Methods
Frontal lessons complemented with recorded videos available on the Moodle platform.
Teaching Methods - Part B
Frontal lessons complemented with recorded videos available on the Moodle platform.
Further information
Every student in need of specific auxiliary support can request it by email to the professor.
Further information - Part B
Every student in need of specific auxiliary support can request it by email to the professor.
Type of Assessment
Mandatory written and oral examen.
Type of Assessment - Part B
Mandatory oral and written exam with exercise of excel.
Course program
Real numbers and algebraic laws: powers of ten; percent and proportions; means.
Algebraic expressions: verification of correctness; ste of variability; subordinate expressions; conditions for existence; domain; transformation of an expression.
Euclidean distance: Cartesian coordinates on a straight line, on a plane, on the space; Pythagoras theorem and calculus of distance.
Angles: not oriented and oriented; sine, cosine, tangent, cotangent, and their inverse of the measure of an angle; polar coordinates.
Straight lines on a plane: how to determine the cartesian equation.
Vectors, scalar product, sum of vectors, product of a scalar times a vector, canonical writing of a vector; orthogonal projection of a vector; cross product.
Equations and inequalities: techniques to solve them; determination of the sign of expressions.
Asymptotes and continuity: notion of limit; operations with limits.
Differential calculus: de l'Hospital theorem; monotonicity and sign of first derivative; second derivative and convexity; theorems on differentiable functions; critical points.
Integral calculus: definite, indefinite, improper integral and techniques of computation.
Course program - Part B
Real numbers and algebraic laws: powers of ten; percent and proportions; means.
Algebraic expressions: verification of correctness; ste of variability; subordinate expressions; conditions for existence; domain; transformation of an expression.
Euclidean distance: Cartesian coordinates on a straight line, on a plane, on the space; Pythagoras theorem and calculus of distance.
Angles: not oriented and oriented; sine, cosine, tangent, cotangent, and their inverse of the measure of an angle; polar coordinates.
Straight lines on a plane: how to determine the cartesian equation.
Vectors, scalar product, sum of vectors, product of a scalar times a vector, canonical writing of a vector; orthogonal projection of a vector; cross product.
Equations and inequalities: techniques to solve them; determination of the sign of expressions.
Asymptotes and continuity: notion of limit; operations with limits.
Differential calculus: de l'Hospital theorem; monotonicity and sign of first derivative; second derivative and convexity; theorems on differentiable functions; critical points.
Integral calculus: definite, indefinite, improper integral and techniques of computation.
The relative and absolute referement of celle in Excel, numerical tratement of data, tables. Formulas and funciotns. graphics, ricerca obiettivo , maximum and minimum problems.