A. Learning objectives (PO: a)
A.1. To understand the concept of complex analyticity.
A.2. To be able o compute the Laurent or Taylor series expansions associated to a function which is analytic in part of the complex plane, and to determine the region of convergence of such series.
A.3. To acquire the basic concepts related to the elementary complex functions.
A.4. To compute definite integrals by means of the residue calculus.
A.5. To understand and solve first and second order linear homogeneous and non-homogeneous differential equations.
A.6. To solve second order equations using power series methods.
A.7. To recognisee classical PDEs describing physical processes such as diffusion, wave propagation and electrostatics.
A.8. To solve analytically, using the method of separation of variables, the heat and wave equations (in one space variable).
B. Specific skills (PO: a)
B.1. To understand the concept of complex differentiation and its practical applications.
B.2. To be able to handle functions given in terms of series.
B.3. To understand the concept of concept of complex integration and its practical applications.
B.4. To be able to solve first and second order linear homogeneous and non-homogeneous ODEs.
B.5. To be able to solve second order ODEs using power series methods.
B.5. To be able to model real-world problems using PDEs, and solve them using Fourier techniques.
C. General skills (PO: a)
C.1. To be able to think abstractly, and to use induction and deduction.
C.2. To be able to communicate in oral and written forms using appropriately mathematical language.
C.3. To be able to model a real situation using differential equation techniques.
C.4. To be able to interpret a mathematical solution of a given problem, its accuracy, and its limitations.