Unit CALCULUS I

Course
Industrial engineering
Study-unit Code
GP004983
Curriculum
In all curricula
Teacher
Ilaria Mantellini
Teachers
  • Ilaria Mantellini
  • Loris Faina (Codocenza)
Hours
  • 51 ore - Ilaria Mantellini
  • 30 ore (Codocenza) - Loris Faina
CFU
9
Course Regulation
Coorte 2020
Offered
2020/21
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.
Reference texts
Bramanti, Pagani, Salsa: Matematica: Calcolo infinitesimale e algebra lineare, Zanichelli Alternative texts: Anichini-Conti: Analisi matematica 1, Pearson Notes supplied by the teacher.
Educational objectives
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, tutorials, some PC-aided sessions.
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 3 hours, consists of technical questions with free answer, about the main themes of the course: sequences of series, 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 40 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.
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