PORTALE DELLA DIDATTICA

### Mathematical analysis II

02KXULI

A.A. 2018/19

Course Language

Inglese

Course degree

1st degree and Bachelor-level of the Bologna process in Ingegneria Dell'Autoveicolo (Automotive Engineering) - Torino

Course structure
Teaching Hours
Lezioni 50
Esercitazioni in aula 30
Teachers
Teacher Status SSD h.Les h.Ex h.Lab h.Tut Years teaching
Como Giacomo Professore Ordinario ING-INF/04 50 0 0 0 2
Teaching assistant
Context
SSD CFU Activities Area context
MAT/05 6 A - Di base Matematica, informatica e statistica
2018/19
This course first completes the theory of functions of one variable which was developed in the Mathematical Analysis course, by introducing the student to basic concepts of numerical series, power series, Fourier series, and Laplace transform. The course then introduces basic topics in the mathematical analysis of functions of several variables including differential calculus in several variables, the theory of multiple integration, line, and surface integration.
This course first completes the theory of functions of one variable which was developed in the Mathematical Analysis course, by introducing the student to basic concepts of numerical series, power series, Fourier series, and Laplace transform. The course then introduces basic topics in the mathematical analysis of functions of several variables including differential calculus in several variables, the theory of multiple integration, line, and surface integration.
Expected acquired knowledge: - Definition, properties, and convergence criteria for numerical series. - Definition, properties, and convergence criteria for sequences and series of functions, power series, and Fourier series. - Definition and main properties of Laplace transform. - Properties and analysis of functions of several variables. - Definition and properties of double, triple, line, and surface integrals. - Conservative vector field; Green, Gauss, and Stokes theorems. Expected acquired ablities: - to classify the asymptotic behaviour (e.g., converge or the lack thereof) of numerical series, sequences of functions, and series of functions using the criteria introduced in class; - to infer the set and type of convergence of sequences and series of functions; - to compute the power series approximation of a function and the Fourier series approximation of a periodic function; - to compute the Laplace transform of simple functions and compare their properties; - to analyze a function of several variables; find and classify its critical points; - to compute double, triple, line, and surface integrals; - to reproduce, discuss, and explain theoretical results presented in class and apply them to solve simple problems.
Expected acquired knowledge: - Definition, properties, and convergence criteria for numerical series. - Definition, properties, and convergence criteria for sequences and series of functions, power series, and Fourier series. - Definition and main properties of Laplace transform. - Properties and analysis of functions of several variables. - Definition and properties of double, triple, line, and surface integrals. - Conservative vector field; Green, Gauss, and Stokes theorems. Expected acquired ablities: - to classify the asymptotic behaviour (e.g., converge or the lack thereof) of numerical series, sequences of functions, and series of functions using the criteria introduced in class; - to infer the set and type of convergence of sequences and series of functions; - to compute the power series approximation of a function and the Fourier series approximation of a periodic function; - to compute the Laplace transform of simple functions and compare their properties; - to analyze a function of several variables; find and classify its critical points; - to compute double, triple, line, and surface integrals; - to reproduce, discuss, and explain theoretical results presented in class and apply them to solve simple problems.
The topics covered in the Mathematical Analysis I and Linear Algebra and Geometry courses. In particular, notions and properties of limits, numerical sequences, differential and integral calculus for functions of one variable, differential equations, linear algebra, geometry of curves.
The topics covered in the Mathematical Analysis I and Linear Algebra and Geometry courses. In particular, notions and properties of limits, numerical sequences, differential and integral calculus for functions of one variable, differential equations, linear algebra, geometry of curves.
- Laplace transform. - Numerical series: definition and convergence criteria. Power series and Taylor series. Fourier series. - Review on vectors and elementary notions of topology of R^n. Functions of several variables, vector fields. Limits and continuity. Partial and directional derivatives, Jacobian matrix. Differentiability, gradient, and tangent plane. Second derivatives, Hessian matrix. Taylor polynomial. Critical points, unconstrained maxima and minima. - Double and triple integrals, center of mass. Length of a curve and area of the region under the graph of a function. Line and surface integrals (for graphs of functions only). Circulation and flux of a vector field. - Conservative vector fields. Green, Gauss, and Stokes theorems.
- Laplace transform. - Numerical series: definition and convergence criteria. Power series and Taylor series. Fourier series. - Review on vectors and elementary notions of topology of R^n. Functions of several variables, vector fields. Limits and continuity. Partial and directional derivatives, Jacobian matrix. Differentiability, gradient, and tangent plane. Second derivatives, Hessian matrix. Taylor polynomial. Critical points, unconstrained maxima and minima. - Double and triple integrals, center of mass. Length of a curve and area of the region under the graph of a function. Line and surface integrals (for graphs of functions only). Circulation and flux of a vector field. - Conservative vector fields. Green, Gauss, and Stokes theorems.