Complementi di matematica per chimici e biologi

Period of duration of course
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Course info
Number of course hours
80
Number of hours of lecturers of reference
40
Number of hours of supplementary teaching
40
CFU 6
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Type of exam

Written and oral exam

Lecturer

View lecturer details

Lecturer

Gian Maria Dall'Ara

Prerequisites

First year students in Biology and Chemistry

Programme

Basics of Mathematics

Logic and sets; natural, integer, rational and real numbers.

Analysis

Sequences and Series

Limit and convergence; Cauchy sequences.

Metric and Topological Spaces

Open and closed sets; neighborhoods.

Limits and Continuity

Limits of real functions; lim sup and lim inf; continuity and Weiestrass theorem.

Differential Canculus

Rolle, Cauchy, Lagrange and De L'Hopital theorems; Taylor formula and series.

Integration

Riemann integral; fundamental theorem of calculus.

Functions of Many Variables

Continuity; partial derivatives; gradient; differential and differentiability; critical points and Hessian.

Educational aims

  • Become familiar with the abstract language of mathematics (hypothesis, thesis, proof);
  • Knowledge of basic tools of differential and integral calculus;
  • Knowledge of basic tools of linear algebra and geometry.

Bibliographical references

Notes given by the teacher.

Mariano Giaquinta, Giuseppe Modica, Analisi matematica, Volume 1: Funzioni di una variabile. Pitagora, 1998.

Carlo Domenico Pagani, Sandro Salsa, Analisi matematica 1, Second edition. Zanichelli, 2015