30400 - MATHEMATICS AND STATISTICS - MODULE 1 (MATHEMATICS)
Course taught in English
Go to class group/s: 25
- Mathematical logics: propositional logic, Truth tables. Statements and proof, Quantifiers.
- 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. Recurring sequences.
- Numerical 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. Derivative. Differentiability. Differentiation rules and theorems. Higher-order derivatives. Taylor formula. Optimization conditions.
- Integral calculus. Fundamental theorem of Calculus. Improper integrals. Numerical quadrature.
- Linear algebra. Subspaces. Linear dependence and independence. Basis and dimension of a subspace. Matrices and their operations. Determinant, rank and inverse matrix. Linear systems: discussion and structure of the solutions, solution.
- N-variable differential calculus. Partial derivatives and gradient. Differentiability. Unconstrained extrema: optimization conditions.
- Introduction to numerical analysis with Matlab (R).
Students can choose whether to take the exam with two partial, or through a final exam.
Graded assignments and homeworks will be handed out during the course.
- S. Cerreia Vioglio, M. Marinacci, E. Vigna, Principles of Mathematics for Economics.
- Other materials will be provided online.