Energy Engineering

Differential calculus for functions of several variables: Elements of vector calculus. Internal points, points borders and border points. Open, closed, compact, bounded, connected sets. Real functions of two or more real variable. Level lines. Domains. Limits and continuity. Open and closed sets defined by functions Continues. Theorem of zeros. Derivability, directional derivability and differentiability. theorem of Total differential. Schwarz theorem. Tangent plane and hyperplane. Directional derivative of a differentiable function. Review of quadratic forms, definite, semidefinite and square matrices indefinite and their characterization. Eigenvalue test. Free related details and selling points. Matrix Hessian and study of the nature of critical points with the Hessian matrix. Weierstrass theorem. Taylor's formula with Lagrange remainder and with rest of Peano. Differential curves and shapes Plane and spatial curves. Simple, regular, closed parametric curves. Tangent vector. Reparameterizations. Length of an arc of a curve. Center of gravity of a curve. Curvilinear integrals of functions continue. Orient the curve. Plane linear differential forms. Closed and exact forms. Primitive of a differential form. Connected domains and simply connected. Exactness of a form implies that the form is closed (with proof). Conditions necessary and sufficient for the accuracy of a differential form. Curvilinear integrals of shapes linear differentials. Double integrals Definition of double integral and linearity and additivity properties. Normal x-domains e y-normal. Reduction formula. Change of variable theorem. Polar and elliptical coordinates. Gauss-Green formulas (with proof). Center of gravity of a flat plate. theorem of divergence (with proof). Stokes formula. Integration by parts formula. Formula for the area calculation. Notes on triple integrals. of triple integral and its properties. Integration by wires and by layers. Change of variability theorem. Cylindrical coordinates e spherical. Rotation volumes and Guldino's theorem. Sequences and series of functions Sequences of real functions of one real variable. Convergence punctual and uniform. Properties of the uniform limit. Passage of the limit under the integral sign. Term-to-term differentiability. Series of real functions of one real variable. Punctual convergence, uniform and total. Passage of the series under the integral sign. Term-to-term differentiability. Power series and their properties. Radius of convergence. Pointwise convergence set. Abel's theorem. Trigonometric series and Fourier series. Simple convergence theorems e uniform Fourier series for functions of class C1 - piecewise and periodic. Inequality of Bessel and Parseval's identity.

Elements of mathematical analysis and geometry: infinitesimal, differential and integral calculus for functions of one variable, Taylor's polynomial numerical series. Vector spaces, matrix calculus (product matrix by vector, determinant of a matrix, eigenvalues and eigenvectors), geometry of the plane.

Attendance not compulsory

The evaluation method currently envisaged consists of a written test. In special cases, students may be called to a short oral interview on the assignment before assigning the final mark.