At the end of Mathematics III, students should be able to:
R1. Learn and master the fundamental concepts of Vector Analysis, Laplace and Fourier transforms, and the elementary theory of equations in partial derivatives and be able to.
to use them in practical situations related to the contents of the degree.
More specifically, at the end of the course, the student should be able to:
R2. Know the definitions of scalar and vector field, know how to distinguish clearly between both concepts and manipulate them with ease, in particular, know how to express a scalar or vector field in any coordinate system.
R3. Know the classical differential operators and know how to calculate them in the different coordinate systems.
R4. Parameterise simple curves and manipulate them, as well as calculate integrals of fields along curves directly using the definition in elementary cases or approximating their value by means of an appropriate numerical method in complicated cases.
R5. Know the intuitive idea of surface, handle parameterisations with ease and know how to calculate its fundamental elements: tangent plane and normal vector.
R6. Know the definition of the integral of a field on a surface and know how to calculate it.
R7. Know in detail the statements of Green's theorems, Gaussian divergence and Stokes' theorems and know how to apply them to solve non-trivial problems.
R8. Identify equations in partial derivatives in different scientific/technical contexts and know how to approach different problems of interest in terms of these equations (evolution of the temperature in a bar, transverse oscillations, electric fields generated by charge distributions, etc.).
R9. Know the basic elements of Fourier analysis and its relationship with the method of separation of variables.
R10. Explicitly find the solution to problems associated with equations in partial derivatives by means of the method of separation of variables and the Fourier and Laplace integral transforms.
R11. Know the theoretical foundations of the method of finite differences and know how to use it to obtain approximate solutions of equations in partial derivatives.
R12. Handle the scientific software Maxima to solve numerical and symbolic calculation problems associated with the contents of the subject.
