Subject 2. Numerical methods for the approximation of integrals. |
Quadrature rules of interpolating polynomial type.
Properties. Interpolation error.
Particular cases: Poncelet, Trapezoidal and Simpson.
Composite quadrature rules. |
Subject 4. Multiple integration. |
The double and triple integrals in elementary regions.
Change in the order of integration.
Theorems for the change of variable.
Applications. |
Subject 6. Ordinary differential equations. |
Generalities on the differential equations: concept of solution, families of curves and orthogonal trajectories.
Differential equations of first order: existence and uniqueness of solution, exact equations, separate variables, homogeneous equations and linear equations.
Differential equations of second order: existence and uniqueness of solution for linear differential equations, application of the Laplace transform, indeterminate coefficients, variation of parameters, equation of Cauchy-Euler. |