- Docente: Annalisa Baldi
- Credits: 6
- Language: Italian
- Teaching Mode: Traditional lectures
- Campus: Bologna
- Corso: First cycle degree programme (L) in Engineering Management (cod. 0925)
Learning outcomes
Course contents
COMPLEX NUMBERS
Definition and operations on complex numbers. Algebraic
form. Trigonometric form . The exponential form of a complex
number. Roots of a complex number, algebraic equations in C.
IMPROPER INTEGRALS AND NUMERICAL SERIES.
Definition of an improper integral, absolute convergence of an
improper integral, comparison criterium. Real and complex numerical
series, convergence and absolute convergence of a series, criteria
of absolute convergence, Leibniz criterium, integral criterium.
FUNCTIONS OF SEVERAL REAL VARIABLES
Real and vector functions of several real variables: generalities.
Definition of a continuous function and of the limit of a function.
The Weierstrass theorem and the intermediate value theorem for
functions of several variables. Partial derivatives.
Differentiability and tangent plane. C^(1) functions. Jacobian
matrix. The chain rule. Partial derivatives of higher order. The
Hessian matrix. Taylor's formula of the second order for functions
of several variables. Local extrema for real functions of several
variables.
DIFFERENTIAL EQUATIONS.
Introduction to ordinary differential equations and the Cauchy
problem. Linear differential equations: general integral for
homogeneous and non homogeneous equations. Explicit solvability of
first order equations and of second order equations with constant
coefficients and Cauchy problems for first and second order linear
equations. Equations with separable variables.
MULTIPLE INTEGRALS
Definition of the double integral for continuous functions on a
compact rectangle. Properties of the double integral. Extensions to
more general domains. Reduction theorems for double integrals on
rectangular and normal domains. The theorem on the change of
variables in a double integral. Triple integrals: (rough)
extensions of definitions and theorems on double integrals to
triple integrals.
Readings/Bibliography
M. Bertsch, R. Dal Passo, L. Giacomelli - Elementi di Analisi
Matematica, ed. McGraw Hill (2007).
Potrà essere utile integrare il testo con un libro di esercizi, a
scelta dello studente.
Teaching methods
Lectures by the course instructor. Exercises solved and discussed
by the instructor.
Assessment methods
The evaluation of the course is based on both a written and an oral examination.
Teaching tools
Textbook; exercises and online material available at the
address:
http://www.dm.unibo.it/~baldi/
and here.
Links to further information
http://www.dm.unibo.it/~baldi/
Office hours
See the website of Annalisa Baldi