I. To acquire a good knowledge of the theory for series and sequences of functions in R.
II. To develop and acquire the methods in the theory of continuous and regular functions in several real variables.
II. To develop and acquire the methods in the theory of continuous and regular functions in several real variables.
teacher profile teaching materials
Fundamentals of Topology in R^n. Functions of Several Variables, Limits, and Continuity. Open, Closed, Connected, and Compact Sets. Heine-Borel, Weierstrass, and Heine-Cantor Theorems. Functions of Several Variables: Differentiability of C^k Functions. Definition of the P-th Derivative Tensor. Taylor's Formula with Integral Remainder, Lagrange Remainder, and Peano Remainder. Local Maxima and Minima. The Implicit Function Theorem.
Fruizione: 20402076 AM210 - ANALISI MATEMATICA 3 in Matematica L-35 R N0 PROCESI MICHELA, CORSI LIVIA
Programme
Sequences and Series of Functions: Uniform and Total Pointwise Convergence, Limit Passage in the Integral and Derivative, Uniform Convergence Criteria. Power Series and Analytic Functions. Matrix Exponential. Fourier Series: Basic Definitions, Bessel's Inequality, Riemann-Lebesgue Lemma. Pointwise Convergence of the Fourier Series for Piecewise Regular Functions.Fundamentals of Topology in R^n. Functions of Several Variables, Limits, and Continuity. Open, Closed, Connected, and Compact Sets. Heine-Borel, Weierstrass, and Heine-Cantor Theorems. Functions of Several Variables: Differentiability of C^k Functions. Definition of the P-th Derivative Tensor. Taylor's Formula with Integral Remainder, Lagrange Remainder, and Peano Remainder. Local Maxima and Minima. The Implicit Function Theorem.
Prerequisiti
basic calculus. To have passed the exams AM110 and AM120Core Documentation
Analisi Matematica II, Giusti - Analisi Matematica II, Chierchia teacher profile teaching materials
Fundamentals of topology in R^n. Functions of several variables: limits and continuity. Open, closed, connected, and compact sets. Functions of several variables: differentiability, C^k functions, definition of the tensor of p-th order derivatives. Taylor's formula with integral, Lagrange, and Peano remainder terms. Local maxima and minima. Implicit function theorem. Method of Lagrange multipliers.
Invia commenti
Analisi Matematica II, Chierchia
Fruizione: 20402076 AM210 - ANALISI MATEMATICA 3 in Matematica L-35 R N0 PROCESI MICHELA, CORSI LIVIA
Programme
Sequences and series of functions: pointwise, uniform, and total convergence; passing to the limit under the integral and derivative signs; criteria for uniform convergence. Matrix exponential. Fourier series: basic definitions, Bessel's inequality, Riemann-Lebesgue lemma. Pointwise convergence of Fourier series for piecewise smooth functions.Fundamentals of topology in R^n. Functions of several variables: limits and continuity. Open, closed, connected, and compact sets. Functions of several variables: differentiability, C^k functions, definition of the tensor of p-th order derivatives. Taylor's formula with integral, Lagrange, and Peano remainder terms. Local maxima and minima. Implicit function theorem. Method of Lagrange multipliers.
Invia commenti
Prerequisiti
basic calculus, To have passed the exams AM110 and AM120Core Documentation
Analisi Matematica II, GiustiAnalisi Matematica II, Chierchia
Attendance
Attendance is not compulsory but suggestedType of evaluation
The exam consists of a written test (which can be replaced by passing two mid-term tests) covering the course topics, and an oral exam.