Mathematical Analysis II - a.y. 2016/2017
Period (Year/Semester): I/II
Required/expected prior knowledge: Mathematical Analysis I.
Roberta Schiattarella - Classe A-E Fuorigrotta
Pietro Baldi - Classe F-R Fuorigrotta
Francesco Chiacchio - Classe S-Z Fuorigrotta
Francesco della Pietra - Classe A-I San Giovanni a Teduccio
Barbara Brandolini - Classe J-Z San Giovanni a Teduccio
Provide the basic concepts, in view of the applications, of the infinitesimal, differential and integral calculus for real functions of a real variable; to acquire adequate logical formalization capacities and deliberate operational skills.
Tables of contents:
Sequences and series of functions in the real field.Scalar functions and vector-valued functions of several real variables. Differential calculus for real functions of multiple variables: differentiable functions and main theorems of differential calculus, Taylor's formula. Relative and absolute extrema. Multiple integrals. Regular curves and surfaces, tangent lines and tangent planes. Length of a curve and area of a surface. Contour integrals. Differential forms and integrals of differential forms. Gradient vector fields, irrotational vector fields. Divergence theorem and Stokes theorem in the plane and in the space. Implicit functions and Dini Theorem. Differential equations and Cauchy problem, existence and uniqueness theorems. Differential equations of separable type, linear differential equations.
Lectures and exercises.
Textbooks and learning aids:
See the website: www.docenti.unina.it
Assessment will be written (open questions and numerical exercises) and oral.