27993 - Mathematical Analysis T-2

Course Unit Page

Academic Year 2022/2023

Learning outcomes

At the end of the course the student knows the tools of Mathematical Analysis having seen some applications, with particular regard to the functions of several variables and to differential equations.

Course contents

Basics of linear algebra and analytic geometry of space. The field of complex numbers. Conjugate, modulo, argument of a complex number. Trigonometric representation, De Moivre's formula. N-th roots. Complex exponential function; exponential equations in C. Functions of several real variables with scalar or vector values. Continuity, differentiability, partial derivatives. Gradient, Jacobian matrix, Hessian matrix. Taylor's formula for real functions of several real variables. Extremants for real functions of several real variables. Fermat's theorem. Constrained Extremants: Lagrange's Multiplier Theorem. Ordinary differential equations. Cauchy problem; existence and uniqueness theorem. Solution methods for first order linear differential equations, with separable variables, linear with constant coefficients. Multiple integrals. Reduction theorem; change of variables. Notes on curves in R ^ n, curvilinear integrals and their applications. Continuous, conservative, closed vector fields. Necessary conditions and sufficient conditions for a field to be conservative.


Barozzi-Dore-Obrecht, "Elementi di Analisi Matematica" vol. 2. Zanichelli, Bologna

Paolo Negrini, "Equazioni differenziali", Pitagora, Bologna

Teaching methods

Frontal lessons

Assessment methods

Written exam and subsequent oral exam; admission to the oral exam is subject to the achievement of a score of not less than 15/30 in the written test.

Office hours

See the website of Paolo Negrini