MATHEMATICS
Academic year and teacher
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- Versione italiana
- Academic year
- 2022/2023
- Teacher
- CINZIA BISI
- Credits
- 6
- Didactic period
- Primo Semestre
- SSD
- MAT/02
Training objectives
- The main objective of the course is to provide students with the basics of the Differential and Integral Calculus for real functions of one real variable, relating to items on the "course programme".
At the end of the course students will be able to study certain types of real functions of one real variable (rational, exponential and logarithmic) and to calculate simple areas bounded by curves and straight lines. Prerequisites
- Elementary algebra. Elements of Euclidean geometry of the plane. Elements of trigonometry. First elements of mathematical logic: concepts of definition, theorem, proof, role of examples and counterexamples.
Course programme
- The course includes 48 hours of teaching between lessons and exercises. The topics covered in the course are as follows.
* Elements of descriptive statistics: frequencies, data representation, position indexes (mean and median), dispersion indices (variance and standard deviation) (4 hours).
* Notion of real functions of a real variable (3h). Theory of limits (3h). Continuous functions (2h). Fundamental limits (2h). Comparison between infinities and comparison between infinitesimals (2h).
* Differentiable functions (3h). Continuity of differentiable functions (1h). Derivatives of elementary functions (3h). Rules of derivation (4h). Fundamental theorems of differential calculus (4h). Relative and absolute maxima and minima of a function (2h). Study of the graph of a function (4h).
* Indefinite integral: calculation of primitives (2). Methods of indefinite integration (4h). Riemann definite integral of a continuous function over an interval (2h). Fundamental theorem of integral calculus (2h). Area calculation (1h). Didactic methods
- Lectures to introduce the theoretical concepts. Exercises related to the application of these concepts.
Learning assessment procedures
- The aim of the exam is to verify the level of achievement of the previously indicated educational objectives.
The exam is written and consists of 16 multiple choice exercises.
The 16 multiple choice questions concern the whole program and have only one correct answer (which is worth 2 points) .
The not given answer is worth 0 and the wrong answer is worth -0.5.
The total exam grade is the arithmetic sum of the score obtained in each exercise. The score 32 corresponds to 30 cum Laude and the exam is sufficient with score 17,5.
The teacher will provide the right integer approximation for the final score when the total score is not an integer.
Please note that enrollment in the written exam is mandatory, as is the presentation of a valid identity document at the beginning of the exam. Reference texts
- The textbook of the course is
Title:
METODI MATEMATICI PER LE SCIENZE APPLICATE.
Authors: C. Bisi, R. Fioresi.
Editors : CEA Zanichelli.
Published from October 2022.
