Examination procedure
<p>written and oral</p><p><br></p><p><br></p>
Examination procedure notes
<p>There will be an ongoing written test and a final one, followed by the final oral exam</p><p><br></p>
Prerequisites
The course is held in the first year and does not require prerequisites other than the usual high school education
Syllabus
Linear Algebra
- vector spaces, linear dependence (bases, dimension…), linear transformations
- matrices, vectors and correspondence with the intrinsic concepts of point 1); change of basis
- determinants (basics)
- eigenvalues and eigenvectors, algebraic and geometric multiplicity
- inner product, orthogonalization, unitary matrices, orthogonal projectors
- diagonalization and Jordan form
- Schur form and the spectral theorem
Mathematical Analysis
First part: calculus in one and more variables from a practical point of view:
- limits, derivatives and integrals in one variable
- partial derivatives and their use, for example, for maxima and minima in multiple variables, even constrained ones
- Differential equations, practical solution methods
- curves, curve integrals, potentials.
Second part: theory elements from the textbook:
- elements of topology of Euclidean space and metric spaces
- spaces of functions and convergences
- elements of theory of differential calculus in multiple variables
- elements of theory of differential equations
Bibliographical references
teacher's notes and lists of exercises, for the first part, chapters 5, 6, 7, 8 (in part; and with some of the proposed exercises) of the book "complements of Mathematics" (L. Ambrosio, C. Mantegazza, F. Ricci) for the second part