Notes for the course in Mathematics freely available on the Moodle page of the course.
Learning Objectives
Knowledge and comprehension of the mathematical formalism relevant to the characterizing courses of the cursus studiorum.
Ability on applying the knowledge and comprehension on mathematica tools to describe and solve problems.
Autonomy of judgement on critical evaluation of a mathematical text, on selecting a proper path to the solution of problems, and on the verification of achieved results.
Comunicative skills on translating data described in current Italian language into mathematical formalism and viceversa.
Ability on learning concepts of modern mathematics such as differential and integral calculus.
Prerequisites
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.
Further information
Every student in need of specific auxiliary support can request it by email to the professor.
Type of Assessment
Mandatory written exam. It consists on a multiple choice test. Each correct answer adds three points to the final score, while unanswered or wrong answers do not add nor subtract points from the score. The mark of the written test corresponds to the final score when there are up to 10 correct answers. With 11 or 12 correct answers, the proposed mark of the written exam is thirty cum laude.
The oral exam can be requested by both the professor and the candidate; each such request must be granted.
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.