30448 - MATHEMATICS - MODULE 1 (THEORY AND METHODS)
Course taught in English
Go to class group/s: 13
- Structures. The set R: real numbers, operations, properties. The set R^n: vectors, operations, properties.
- Functions. Composite function, inverse function. Real functions of one real variable: domain, maxima/minima, convexity, other properties. Real functions of n real variables: domain, maxima/minima, convexity, other properties.
- Sequences of real numbers: definition and properties. Limits of sequences and their computation.
- Number series. Series with non-negative terms, series with terms of indefinite sign.
- Limits and continuity for functions of one or n real variables.
- One-variable differential calculus. Difference quotient, derivative. Differentiability. Differentiation rules. Fermat's and Lagrange's Theorems. Higher-order derivatives. Taylor formula. Convexity and optimization conditions.
- Linear algebra. Subspaces. Linear dependence and independence. Basis and dimension of a subspace. Matrices and their operations. Linear functions and applications: definition, properties, representation. Determinant, rank and inverse matrix. Linear systems: discussion and structure of the solutions, solution. Eigenvalues and eigenvectors.
- Integral calculus. The fundamental theorem of calculus.
The written exam can be taken in one of the two possible ways
- Recommended: it can be split in four partial exams (September, October, November, January). The second and fourth partials are the main ones: each one mainly contains open-answer questions and weighs for one-third of the final mark. The first and third partials are multiple-choice tests and each one weighs for one-sixth of the final mark.
- It can be taken as a single general exam mainly containing open-answer questions and covering the whole syllabus, in one of the four general sessions scheduled in the academic year (the two regular sessions in January and February, or the two make-up sessions in June and August/September). This way is mainly meant for students who have withdrawn from the four partials procedure or could not follow it.
- E. CASTAGNOLI, M. MARINACCI, E. VIGNA, Principles of Mathematics and Economics, Milano, dispense Egea, 2013, (ISBN 978-88-6407-192-3).
- Integrative teaching materials.