92966 - General Mathematics

Learning outcomes

At the end of the course, the student knows the basic principles of mathematics. In particular, the student has a good knowledge of linear algebra and derivatives that are the basic tools for the first economic, financial, and business applications.

Course contents

Real functions of a real variable. Definition of a function. Elementary functions and their graphs (linear, quadratic, polynomial, rational, irrational, power, exponential, logarithmic, absolute value). Even and odd functions. Convexity. Composite functions and inverse functions.

Limits and continuity. Infinitesimals and infinities and their comparison. Bolzano’s theorem on intermediate values, the zero theorem, Weierstrass’ theorem.

Differentiation of functions of one variable: tangent and derivative, rules of differentiation, chain rule, higher-order derivatives. Implicit differentiation and economic examples, differentiation of the inverse function, linear and quadratic approximations, Taylor formula, elasticity; continuity and differentiability, Lagrange’s theorem (mean value theorem), L’Hôpital’s rule.

Optimization of functions of one variable: local and global extrema, stationary points and first-order condition, tests for extrema, extrema for concave and convex functions, second derivative and convexity, inflection points, graph analysis of a function.

Integration: Riemann integral and its geometric interpretation; antiderivatives and indefinite integrals, fundamental theorems of integral calculus. Rules and methods of integration: basic integrals, integration of rational functions, integration by parts, substitution. Improper integrals.

Linear algebra: vector spaces, bases and dimension; matrices and their properties, matrix operations, rank and determinant; systems of equations, existence of solutions, cases of unique and infinite solutions, Gaussian elimination, matrix inverse and Cramer’s rule; eigenvalues and eigenvectors.

Readings/Bibliography

Recommended texts (theory):

• M. Abate, Metodi matematici per l'economia e il management, McGraw Hill;
• A. Guerraggio, Matematica, Pearson editore (solo per la parte di funzioni in una variabile);
• R. Fioresi, M. Morigi, Introduzione all'algebra lineare, Zanichelli editore (solo per la parte di algebra lineare);

Recommended texts (exercises):

•  A. Cambini, L. Carosi, L. Martein, Funzioni di una variabile. Esercizi svolti, Giappichelli editore;
• A. Cambini, L. Carosi, L. Martein, Elementi di algebra lineare e funzioni di più variabili. Esercizi svolti, Giappichelli editore;

Any additional teaching and supplementary material will be uploaded to the course page on the Virtuale platform. Access is granted through one’s institutional account.

Teaching methods

Lectures will be delivered using a projector and an electronic whiteboard. Exercise sessions will be conducted by the instructor or a teaching assistant. Online software tools will be used for educational purposes.

Exercises will be assigned periodically.

The teaching materials presented during lectures will be made available in electronic format on the course page on Virtuale.

Office hours will be held via Microsoft Teams. For the scheduled day and time of office hours, please refer to the instructor's webpage. To attend office hours, students are required to notify the instructor of their intention to participate at least 24 hours in advance.

Students are strongly encouraged to consult the course page on Virtuale, where, in particular, the course regulations are published and are expected to be known by all participants.

Assessment methods

The final assessment consists of a written examination covering the entire course syllabus. During the exam, students may consult their own notes. Computers, tablets, smartphones, or any other electronic or “smart” devices are not permitted, with the exception of non-graphing calculators.

Students are strongly encouraged to consult the course page on Virtuale, where the examination regulations are published and are expected to be known by all participants.

Grading Scale and Assessment Criteria

• < 18: insufficient preparation;
• 18–23: satisfactory preparation, but limited to a restricted portion of the topics covered in the course syllabus;
• 24–27: adequate preparation, although with some gaps in the topics covered in the course syllabus;
• 28–30: thorough mastery of all topics covered in the course syllabus;
• 30 cum laude (30L): outstanding knowledge of all topics covered in the course syllabus.

As regards assessment, the use of AI is prohibited. Any use of AI constitutes a violation of academic integrity.

Teaching tools

Graphics tablet, projector.

Office hours

See the website of Lorenzo Cerboni-Baiardi