This is a second course of calculus and is related to power series, vector analysis, multiple integrals, line and surface integrals, the integral theorems of vector calculus. In general, there will be much emphasis on the comprehension of the definitions and the principal results. Only few proofs will be treated in full details. There will be several examples and exercises. At the end of the course, the students should be able to do computations on power series, limits, partial and directional derivatives, multiple integrals, line and surface integrals and have a deep knowledge of the main notions.
Course Prerequisites
Students are expected to master the topics presented in the courses Analisi Matematica I, and Geometria e Algebra.
Teaching Methods
Lectures
Assessment Methods
The exam consists of a written test and an oral examination, which is not compulsory, for all the students who passed the written test with a passing mark.
Texts
1) M. Bramanti, C. D. Pagani, S. Salsa. Analisi Matematica 2. Zanichelli, 2009. 2) M. Bramanti. Esercitazioni di Analisi Matematica 2 Esculapio.
Contents
1. Power series; absolute and simple convergence; series with positive terms; special series. Convergence results. Power series; derivation and integration. Taylor expansion. 2. Calculus for functions of several variables. Limits, continuity, partial derivatives, gradient, differentiability, Hessian; stationary points and their classification. Taylor's formula. Calculus for vector functions; Jacobian. 3. Multiple integrals. Two dimensional integrals; change of coordinates, polar coordinates, techniques of integration. Three dimensional integrals: spherical or cylindrical coordinates; evaluating the integral by the slice method or the line method. 4. Line and surface integrals. Parametric equations of a line; tangent line; arc lenght. Parametric equations of a surface; tangent plane; surface area; surface of revolution. Line integrals of scalar fields and of vector fields. Conservative vector fields. The differential operators curl and div. Surface integrals. Green's theorem; Stokes' theorem; divergence theorem.
Course Language
Italian
More information
Students in the categories identified by the project on innovative teaching will have the opportunity to hold receptions also at distance and by appointment at times to be agreed with the teacher, or view the teacher's lecture notes.
