00674 - Mathematics

Learning outcomes

Upon completion of the course, students will have acquired the fundamental knowledge of mathematical analysis, linear algebra, and analytic geometry of the plane. They will be able to study functions of one variable, solve linear systems using matrix methods, and apply double integrals to the computation of areas, centroids, and moments of inertia.

Course contents

Linear Algebra: vectors in the plane; matrices; determinants and inverse matrices; systems of linear equations; substitution method and Gaussian elimination.

Analytic Geometry of the Plane: equation of a line; Cartesian and parametric equations of the circle and the parabola.

Functions of One Variable: elementary and trigonometric functions (fundamental trigonometric identities and elementary trigonometric equations); limits and continuity; remarkable limits and indeterminate forms. Derivative and its geometric interpretation; derivatives of elementary and trigonometric functions; differentiation rules (linearity, product rule, quotient rule, and chain rule). Function analysis: monotonicity, local maxima and minima, concavity and convexity, qualitative graph sketching.

Applications of Derivatives: Rolle's Theorem, the Mean Value Theorem, and L'Hôpital's Rule.

Indefinite and Definite Integrals: antiderivatives and integration techniques (substitution and integration by parts); the Fundamental Theorem of Calculus.

Differential Equations: introduction to second-order homogeneous differential equations.

Functions of Several Variables: graphical representation; partial derivatives; double integrals and applications (area of a domain, centroid, moments of inertia).

Readings/Bibliography

For a review of trigonometry, the following textbook is recommended:

• Bergamini, Barozzi, Trifone, Matematica.blu 2.0, Zanichelli Editore, or any other high-school trigonometry textbook.

A useful reference textbook, which does not replace the need for comprehensive lecture notes, is:

• M. Bramanti, C. D. Pagani, S. Salsa, Matematica: calcolo infinitesimale e algebra lineare, 2nd ed., Zanichelli, 2004.

A valuable resource for practice exercises is:

• S. Salsa, A. Squellati, Esercizi di matematica: calcolo infinitesimale e algebra lineare. Vol. 1, Zanichelli, 2001.

Teaching methods

Face-to-face classroom lectures, active student participation, and homework assignments.

Assessment methods

USE OF AI DURING THE EXAM

AI can be a useful tool to support individual study through in-depth insights, summaries, and self-assessment activities. However, regarding the assessment of learning, the use of AI during in-person exams is prohibited. Any use constitutes a violation of academic integrity

 

Final written examination. The assessment consists of problem-solving exercises and theoretical questions designed to evaluate the achievement of the intended learning outcomes in terms of knowledge and skills. At the discretion of the examination board, and in order to safeguard candidates, a discussion of the written examination may take place.

 

Students with Specific Learning Disorders (SLD) or temporary or permanent disabilities are advised to contact the University Office responsible well in advance, at the following address: (https://site.unibo.it/studenti-con-disabilita-e-dsa/en). The office will propose any necessary accommodations, which must in any case be submitted to the instructor for approval at least 15 days in advance. The instructor will assess their appropriateness in light of the learning objectives of the course.

Teaching tools

Exercise sessions and weekly lecture summaries made available by the instructors on the Virtuale platform.

Office hours

See the website of Cristiano Frattagli