Complements of Mathematics for Chemistry and Biology
Prerequisiti
The course is held in the first year and does not require prerequisites other than the usual high school education
Programma
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
Obiettivi formativi
The course lays the foundations of linear algebra and mathematical analysis in one or more variables, with much attention to practical aspects but also to the development of the mentality of the foundations and theoretical and abstract reasoning.
Riferimenti bibliografici
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