Fundamentals of Mathematics

Goals
Provide the basic mathematical tools for the applications of mathematics to the other sciences (in particular chemistry).

acquired skills
Ability to use basic mathematical tools and to recognize elementary applications in the chemical sciences.

Course content
- Numbers: integers, rationals, reals; ordering. Recalls of plane trigonometry; complex numbers and their roots. Vectors and vectorial operations; straight lines and planes in space.
- Sequences and their limits, monotonicity, comparisons, indecision forms; Napier's constant "e". Series and convergence criteria.
- Functions of a real variable: limits, continuity, asymptotes; composite and inverse. Elementary functions and their graphs: powers and radicals, exponentials and logarithms, trigonometric functions and their inverse.
- Differential calculus in one variable: derivatives, maxima and minima, convexity, analysis of functions; Taylor's formula.
- Integral calculus in one variable: definite integral, primitives (by decomposition, substitution and by parts), relations between definite integral and primitives. Physical and geometrical applications; generalized integrals.
- Multivariable functions: partial derivatives, gradient, Hessian; optimization in two variables. Linear regression line.
- Ordinary differential equations: linear first order and separable; linear second order with constant coefficients. Initial conditions, existence and uniqueness theorem.

Suggested prerequisites
Having passed the self-evaluation test of basic mathematics.

Reference material
- C. Pagani and S. Salsa: MATEMATICA. Ed. Zanichelli.
- Online teaching material related to the MATASS (assisted mathematics) project: http://ariel.ctu.unimi.it/corsi/

Prerequisites
Online teaching material related to the MINIMAT (basic mathematics) project: http://ariel.ctu.unimi.it/corsi/

Assessment method
Written (consisting of theory questions - aimed at verifying the comprehension of the main topics - and simple exercises).

Language of instruction
Italian