- Docente: Enrico Obrecht
- Credits: 9
- SSD: MAT/05
- Language: Italian
- Moduli: Enrico Obrecht (Modulo 1) Giovanni Dore (Modulo 2)
- Teaching Mode: Traditional lectures (Modulo 1) Traditional lectures (Modulo 2)
- Campus: Bologna
- Corso: First cycle degree programme (L) in Electronics and Telecommunications Engineering (cod. 0923)
Course contents
THE EUCLIDEAN SPACE R^n. LIMITS, CONTINUITY AND DIFFERENTIAL
CALCULUS FOR FUNCTIONS OF SEVERAL 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, C^(1) functions.
Jacobian matrix. The chain rule. Partial derivatives of higher
order. Taylor's formula of the second order for functions of
several variables. Local extrema for real functions of several
variables. MULTIPLE INTEGRALS. Definition of the double integral
for functions defined 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 the change of variables theorem for a double integral. Triple
integrals: extensions of definitions and theorems from double to
triple integrals. CURVE AND SURFACE INTEGRALS. Smooth and piecewise
smooth curves, length of a curve, integral of a function over a
curve. The integral of a vector field over a curve.
Conservative vector fields and their potentials. The Green-Gauss
theorem. Regular surfaces in R^3, area of a surface, integral of a
function over a surface. Orientable surfaces. The flux of a vector
field through an oriented surface. The divergence theorem and the
Stokes theorem. SERIES OF FUNCTIONS AND INTEGRALS DEPENDING
ON A PARAMETER. Pointwise and uniform convergence of a series of
functions. Exchange of limit operations. Power series. Fourier
series. Integrals depending on a parameter. Exchange of limit
operations. Examples of integrals depending on a parameter: the
integral transforms. DIFFERENTIAL EQUATIONS. The Cauchy problem for
differential equations and systems. Theorems on existence,
uniqueness and continuation of solutions. Some boundary value
problems for linear second order differential equations.
Office hours
See the website of Enrico Obrecht
See the website of Giovanni Dore