Energy Engineering

Bidimensional and tridimensional geometry. lines, planes, conics, quadrics. Alignment and complanarity in connection to geometrical vectors. Sets. Vector spaces. Subspaces. Matrices. Analysis of geometrical entities with the aid of analytic geometry. Dimension, linear dependence, generators and bases. orthogonality. Intersection and sum of subspaces. Linear applications, eigenvectors, diagonalisation. Change of coordinates. Rotations and translations. Reduction of a conic to canonical form. Invariants for conics and quadrics. Brief introduction to curves.

The literal calculation. Notable products. Decomposition of polynomials. Ruffini's theorem. Division between polynomials. Analogies between integers and polynomials. Irreducible polynomials. Algebraic equations. First degree inequalities. The Cartesian plan. The line. The conics (outline). Equations of the conics. The parable. Second level inequalities. Intersection between curves. Equation systems. Tangent line. Vectors and operations between vectors and on vectors (outline). Algebraic inequalities of a higher degree. Equations and rational inequalities. Irrational equations and inequalities. Overview of set theory. Overview of the logic of the propositions. Required, sufficient, necessary and sufficient conditions. Demonstration for absurd. The form of x. Equations and inequalities with the modules, also making use of graphic resolution. Power function with some graphs. Rules of powers. Exponential function. Exponential equations and inequalities. The logarithm and its basic properties. Graph of the logarithm. Logarithmic equations and inequalities. Overview of the inverse function. The trigonometric functions. The inverse trigonometric functions. Trigonometric equations and inequalities.

A. Vietri, Itinerario di geometria e algebra lineare, ed. CISU (reprint of 2017, revised). Recommended reading for additional exercises: S. Capparelli, A. Del Fra: Geometria, ed. Esculapio. M. Bordoni: Geometria I modulo, Geometria II modulo, ed. Esculapio. G. Vaccaro, A. Carfagna, L. Piccolella: Lezioni di geometria e algebra lineare, ed. Zanichelli. Recommended reading for further details: S. Capparelli, A. Del Fra: Geometria, ed. Esculapio. M. Bordoni: Geometria I modulo, Geometria II modulo, ed. Esculapio. G. Vaccaro, A. Carfagna, L. Piccolella: Lezioni di geometria e algebra lineare, ed. Zanichelli.

Frontal lessons with alternating introduction of new topics, review and exercises. Counseling in the study. Use of email to solve exercises or for general questions related to the course. Remote lessons simultaneously with frontal lessons if required.

Not compulsory (4 lectures per week, each one of two hours, plus two hours of tutoring).

In order to make the written test, students must be in possession of an identity document; protocol sheets can be carried. You should justify the answers (not in the case of questions V / F or numeric response) and write neatly, with clarity, using a sheet or at most two. High up on the first page, you must write the name, then leaving a space of a few lines for evaluation. It will be delivered only fair copy (Part II) together with the text of the examination with answers to any questions (Part I) written directly on the sheet of the exam paper, so do not transcribe it on the fair copy. It will not be possible to make use of books or notes, or other sources. During the test, you'll tell the teacher, at any time, you want to cancel deliveries, leaving only the text sheet of the exam to the teacher. The examination will be recorded as "Rinuncia" on Infostud. The calculator is not recommended: what is preferable (and often more comprehensible) is an algebraic type response, symbolic or otherwise, instead of an approximation from a systematic and superficial use of the calculator, which generally does not provide the precise solution. The test duration is 2 hours and 40 minutes. In the correction phase and evaluation, each exercise of Part II is associated with a score that is the sum of the scores of the various questions. The questions V / F and numeric (Part I) are administered only in appeals of January and February; These questions require an extreme mastery, since a wrong answer results in a decrease of the vote. I suggest to consider above all free exercises and subsequently the questions of Part I (the overall score of Part I questions is lower than that of the exercises of Part II - at most half). Students will have to book via Infostud and print sheet that they will bring the day of the oral examination (provided they have passed the written test). Without the reservation it will not be possible for the student to have a receipt. The statement of results and the schedule of the oral exams are posted on the course web-page, after the correction of written tests (about a week after the test, in January and February, a little less in the other cases). The oral test can provide more precise information on the preparation and the ability of the candidate (thanks to the performance of basic or more complex exercises, and sometimes through proof of theorems in accordance with the level of the written test). The more the written test is close to the minimum threshold (usually between 15 and 16), the more important the oral exam in the final outcome. At the beginning of the oral exam, the written test is analized and the first interview questions are asked, in this regard. Then further questions are made, with no connection with the written test. As for the written test, you need an identity card (also a driving licence). With rare exceptions, the oral examination should be performed in the same session of the written test. There are 5 calls (during the months of January, February, June, July, September); you can participate in any appeal, without exception. For "fuori-corso", "ripetenti" or "part-time" students, two further appeals are available ("appelli straordinari").

Frontal lessons with alternating introduction of new topics, review and exercises. Counseling in the study. Use of email to solve exercises or for general questions related to the course. Remote lessons simultaneously with frontal lessons if required.