DALMINE
Overview
Date/time interval
Syllabus
Course Objectives
In order to know the potential and limitations of the tools described above, the student will also have a full awareness of their theoretical foundations and will express them with adequate command of the language.
Course Prerequisites
1. Plane Euclidean geometry: in particular, triangle criteria for equality and similarity, Euclid and Pythagoras theorems, elementary properties of polygons and circles. One-to-one correspondence between real numbers and points on a line; intervals, half line; Cartesian plane; distance between two points in the place: Elementary locus in the plane: line (parallelism and orthogonality conditions), circle. ellipse, parabola and hyperbole. 2. Powers with integer exponent, properties of powers, polynomials: divisibility, Ruffini rule, roots, factorization. Powers with rational and real exponent, graphics and main properties. Exponential functions: its graphic and its main properties. Logarithms, its graphic and main properties. 3. Equations and Inequalities of first and second degree. System of equations and inequalities. 4. Irrationals equations and inequalities, Equations and Inequalities with Exponentials, Logarithm and absolute value. 5. Trigonometry: measure of angles in radiant, fundamental identity Graphics of sine, cosine and tangent. Equations and Inequalities with trigonometric functions
Teaching Methods
The teaching is composed by lectures (60 hours), exercises and tutoring (36 hours) . In all activities the student is encouraged to participate with suggestions and proposals.
Assessment Methods
- Mastery of the methods and techniques developed
- Awareness of their theoretical foundations
- Appropriateness of the language used.
Only students who succeeded the entrance test in mathematics (OFA) can access the exam.
The exam consists of two parts, one practical and one theoretical, both mandatory.
The practical part is a written test, consisting of 4/6 exercises. Each exercise will be given a grade specified at the beginning of the exam.
The theoretical part is a written test too, is held immediately after the practical test, and in any case it consists of 3/4 questions in which the knowledge of definitions, examples, statements of theorems, proofs is assessed. The relevance of the answer to the question, the ability to synthesize, the property of language are also taken into consideration. The commission also reserves the right to hear from any student after the correction of the written tests, in case it deems it necessary to acquire further evaluation elements.
Students who are enrolled in the first year in the current academic year can replace the exam with two ongoing tests. Students who still have the mathematics OFA to complete will be allowed to take the first ongoing test. The first ongoing test is held in the middle of the course, and concerns the first half of the program. The second concerns the second part of the program (including the prerequisites contained in the first part) and is held in conjunction with the first complete winter session.
The two ongoing tests have the same modality as the complete test. The second test is accessed with a minimum score of 15 in the first test.
In the first winter session, the student who has passed the first ongoing test is free to decide whether to take the second ongoing test or the complete test.
Contents
2. Sequences and limits.
3. Series.
4. Limits and continuity of functions.
5. Derivative.
6. Antiderivatives and definite integrals.
7. Generalized integrals