Educational guide 2015_16 E. T. S. de Enxeñaría de Minas

Grao en Enxeñaría dos Recursos Mineiros e Enerxéticos

Contents

Topic	Sub-topic
1. Integral calculation of functions of one variable.	Generalities: The integral of Riemann. Integrable functions. Main theorem of the integral calculation. Theorem of the mean value. Rule of Barrow. Calculation of primitives: integration by parts and change of variable. Improper integrals.
2. Numerical methods of integration in R.	Formulas of Quadrature of polynomial type. Properties. Error of interpolation. Particular cases: Poncelet, Trapece and Simpson. Formulas of quadrature compound.
3. Integral calculation of functions of several variables.	Double and triple integrals in elementary regions. Change of the order of integration. Change of variable. Polar coordinates. Cylindrical and spherical coordinates.
4. Ordinary differential equations.	Generalities on ordinary differential equations. Concept of solution. First order equations. Existence and uniqueness of solution. Autonomous equations. Equations in separate variables. Homogeneous equations. Exact equations. Linear equations. Families of curves: orthogonal trajectories.
5. Ordinary differential equations of upper order.	Differential equations of second order and upper order. Linear equations homogeneous and non-homogeneous. Linear equations with constant coefficients. Method of indeterminate coefficients. Method of variation of parameters. Equation of Cauchy-Euler.
6. Numerical methods for ordinary differential equations.	Methods for problems of initial value: methods of one step, methods multi-step, methods predictor-corrector. Methods for boundary problems: Methods of shot, methods of finite differences.
7. Introduction to the partial derivative equations.	Classification: elliptic, hyperbolic and parabolic equations. Problems with boundary values and problems of initial value. Examples: equation of Laplace, heat equation and wave equation.