Physics | University of Parma

Professor
Academic discipline: Analisi matematica (MAT/05)
Field: Discipline matematiche e informatiche
Type of training activity: Basic

48 hours
of face-to-face activities

6 credits

hub: -

course unit
in - - -

lectures timetable unavailable

exam calls

Integrated course unit module: MATHEMATICS 2

Learning objectives

Furnish the basic mathematical instruments to treat elementary physical or mathematical problems inherents real or vector valued functions of many real variables.

Prerequisites

Knowledge of basic elements of Mathematical Analysis of real valued functions of one real variable.

Course unit content

Differential calculus for real and vector valued functions of many real variables. Optimizazion. Line integrals. Riemann integration. Surface integrals.

Full programme

REAL VALUED FUNCTIONS OF MANY REAL VARIABLES. Limits. Continuity. Partial Derivatives. Differentiability. Hessian matrix. Taylor formula. Vector valued functions. Jacobian matrix. Implicit functions.

OPTIMIZAZION. Weierstrass theorem (en). Stationary points. Quadratic forms. Sufficient conditions of min/max. Optimizazion with constraints. Lagrange theorem.

LINE INTEGRALS. Regular curves. Line integrals of first and second type.

RIEMANN INTEGRATION OF MANY VARIABLES FUNCTIONS. Measurable sets. Integration techniques.

SURFACE INTEGRALS. Gauss-Green Lemma.

Bibliography

C. Canuto - A. Tabacco, Analisi matematica I, Springer Italia C. Canuto - A. Tabacco, Analisi matematica II, Springer Italia
Any other text of Mathematical Analysis inherents to real or vector valued functions of many real variables.

Teaching methods

Frontal lessons

Assessment methods and criteria

The examination combines write text and oral discussion

Other information

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MATHEMATICS 2 PART 2 cod. 1004037