Unit CALCULUS I
- Course
- Industrial engineering
- Study-unit Code
- GP004983
- Curriculum
- In all curricula
- Teacher
- Ilaria Mantellini
- Teachers
-
- Ilaria Mantellini
- Hours
- 81 ore - Ilaria Mantellini
- CFU
- 9
- Course Regulation
- Coorte 2022
- Offered
- 2022/23
- Learning activities
- Base
- Area
- Matematica, informatica e statistica
- Academic discipline
- MAT/05
- Type of study-unit
- Obbligatorio (Required)
- Type of learning activities
- Attività formativa monodisciplinare
- Language of instruction
- Italian
- Contents
- Set theory and functions. Sequences, limits. Continuity and related theorems. Series: theory and criteria. Differentiation: calculus for basic maps, theorems, search for maxima and minima. Study of functions, Taylor series. Integration: theory and calculus. Primitive mappings, fundamental formula of integral calculus.
- Reference texts
- Notes supplied by the teacher.
For exercises and related topics
Bramanti, Pagani, Salsa: Matematica: Calcolo infinitesimale e algebra lineare, Zanichelli
Notes supplied by the teacher. - Educational objectives
- Students acquire the basic mathematical knowledge to face the science subject taught in the graduate program. For the positive exit of the final written test, it is required that the student can recognize, in the various problems, the most suitable tools among those studied, and is able to use them properly, finding the correct conclusions coherently. In order to superate the oral test, the student is requested to properly and precisely express the theoretical topics studied, distinguishing surely their main aspects, also by means of relevant examples.
- Prerequisites
- Basic notions from Algebra, Geometry, Analytic Geometry, and trigonometric, exponential and logaritmic functions. A preliminary course is given on these topics during the month of September, before the beginning of the lessons.
- Teaching methods
- Lectures and tutorials.
- Other information
- It is advisable to attend the preliminary course, held in September, before the beginning of the regular courses.
- Learning verification modality
- Written test, and, if positive, subsequent oral examination. The exam consists of two tests: the first one is written, the second one is oral. The first test, during 1,5 hours, consists of technical questions with free answer, about the main themes of the course: studies of functions, integration. This test aims to evaluate the attitude of the student to find the right tools to solve each problem, his/her skillness in using them properly, and coherence and precision in describing the conclusions obtained. The second test, subject to the positive result of the first one, is a discussion of about 30 minutes, usually beginning with the revision of the written test, and aims to clarify if and to what extent the student can properly and coherently express the main theoretical results, and clearly knows their utility in the solution of concrete problems.
- Extended program
- Short survey of the topics discussed in the preliminary course: set theory, ordering, functions, monotonicity, cardinality. Elements of Combinatorics. Sequences: monotonicity, extrema, limits. Limits of functions: theory and calculus. Infinitesimals, continuity, and related theorems. Series: general theory, criteria, applications. Differentiation: geometric and analytic aspects, calculus with elementary functions. Theorems on differentiation, local maxima and minima, monotonicity test, and so on. De L'Hospital rule, higher order derivatives, study of functions. Taylor formulas and series. Integration: varifold meanings, theory and calculus. Primitive functions, integral function, fundamental formula, and applications.