# Ingegneria Meccanica | OFA - MATEMATICA

## Ingegneria Meccanica OFA - MATEMATICA

cod. OFA0612301

#### OFA - MATEMATICA

OFA0612301 | |

DIPARTIMENTO DI INGEGNERIA INDUSTRIALE | |

EQF6 | |

MECHANICAL ENGINEERING | |

2022/2023 |

YEAR OF COURSE | |

YEAR OF DIDACTIC SYSTEM 2018 | |

AUTUMN SEMESTER |

SSD | CFU | HOURS | ACTIVITY | |
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NN | 0 | 60 | LESSONS |

Objectives | |
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Educational Objectives: expected learning outcomes and competence to be acquired The course aims at recovering the basic mathematical knowledge that students should have acquired in high school and on which they were found lacking, based on the results of the entrance test. Knowledge and understanding Ability to understand and formalize simple mathematical problems. Applying knowledge and understanding Being able to recognize and solve simple equations and inequalities, as well as problems of analytic geometry and trigonometry. Making judgement Being able to understand which mathematical techniques are suitable for solving a problem. Communication skills Being able to explain the method used to solve a problem. Learning skills Being able to extend applied methods to more complex problems. |

Prerequisites | |
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For a successful achievement of the set objectives, the student is required to have basic mathematical knowledge, relating to topics covered in middle school. |

Contents | |
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PolynomialsMonomials, normal form, operations with monomials. GCD and LCM of monomials. Polynomials, normal form. Complete, homogeneous, ordered polynomials. Operations with polynomials. Division between polynomials in one variable. Ruffini's theorem and Ruffini's rule. Notable products. Decomposition of polynomials. EquationsIdentities and equations. Determined, indeterminate, impossible equations. Equivalent equations. Principle of addition and multiplication. 1st degree equations. Fractional equations. Literal equations. RadicalsDefinition of radical. Properties of radicals. Reduction to the same index. Rationalization methods. Equations of 2nd degree and higher degreeEquations of 2nd degree. Sum and product of the solutions. Relationship between roots and coefficients. Rule of Decartes. Biquadratic equations. Equations of degree higher than the second that can be solved with the use of Ruffini's rule or through special replacements. Real numbersIntroduction to real numbers. Geometric representation. Completeness of the real line. Power with real exponent. Exponentials and logarithmsDefinition of exponential and logarithm, their properties, elementary exponential and logarithmic equations. Analytic geometryThe Cartesian plane. The point, length of a segment or distance between two points. Midpoint. Equation of the line. Equation of the circumference. Lines tangent to a circle from a point. Equation of the ellipse, of the hyperbola, of the equilateral hyperbola referred to its asymptotes. Equation of the parabola. Tangent lines to a conic. TrigonometryAngles, radians. Elementary goniometric functions: sine, cosine, tangent. Fundamental relationships. Important trigonometry angles. Reflections, shifts and periodicity. Angle sum and difference identities, double-angle formulas, half-angle formulas, Werner formulas, prosthaphaeresis formulas. Elementary trigonometric equations. Inequalities1st degree, 2nd degree, fractional, irrational inequalities. |

Teaching Methods | |
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Teaching includes theoretical lessons, during which the topics of the course will be presented through lectures and classroom exercises. The exercises will provide the main tools necessary for solving exercises relating to the contents of the theoretical teaching. |

Verification of learning | |
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The exam aims at assessing the knowledge and the ability to understand the concepts presented during the lessons and the ability to apply such knowledge. The exam is divided into two selective written tests, the first in the middle of the course, the second at the end of the course itself. The written tests propose simple exercises based on the topics presented during the lessons. The final evaluation is expressed as “passed / failed”. |

Texts | |
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Any high-school mathematics book that contains the topics described in “Course content”. |

BETA VERSION Data source

**ESSE3**[Ultima Sincronizzazione: 2023-03-29]