Overall objectives:

O1 - Introduction to the study of difference equations, nonlinear differential equations and stochastic differential equations.
O2 - Give examples of the application of Mathematics to other sciences such as Physics, Biology, Chemistry, Economics and different branches of engineering. Give examples of problems which appear to be apparently different, but share a similar mathematical structure.
O3 - Develop the ability of abstraction in relating problems of different areas. Increase the ability to examine, solve and interpret results of problems obtained using mathematical models.
O4 - Consolidate and broaden concepts that were acquired during the undergraduate and master's degree.

Syllabus:

P1 - Difference equations: Difference calculus, First order linear difference equations, Higher order difference equations. Theoretical examples and application to other sciences.
P2 - Nonlinear differential equations: nonlinear models, Linear differential equations (complements), Nonlinear differential equations. Theoretical examples and application to other sciences.
P3 - Stochastic differential equations: Stochastic processes, Stochastic integrals, Stochastic differential equations. Theoretical examples and application to other sciences.

Literature/Sources:

Oksendal, B. , 2005 , Stochastic Differential Equations: An Introduction with Applications , Springer
Björk, T. , 1998 , Arbitrage Theory in Continuous Time , Oxford University Press
Kelley W. G. & Peterson A. C. , 2001 , Difference Equations , Academic Press
Verhulst, F. , 1996 , Nonlinear Differential Equations and Dynamical Systems , Springer
Glendinning, P. , 1999 , Stability, instability abd chaos: an introduction to the theory of nonlinear differential equations , Cambridge University Press
Saber, E. , 2005 , An Introduction to Difference Equations , Springer

Assesssment methods and criteria:

Classification Type: Quantitativa (0-20)

Evaluation Methodology:
Teaching: Use of the whiteboard for presentation, explanation of subject material and problem solving. Use of the computer and projector to help visualize and better understand the concepts. The use of slides to introduce concepts may be used promptly (in this case the exposed material should be provided to students, in detail, through a Booklet or other supporting documents). Evaluation: Two tests (one in the middle and one at the end of the semester), both with a weight of 35%, and a practical work (in report or article format) to be delivered at the end of the semester (with a weight of 30%). The work is to motivate students to do research and obtain results on their own initiative (always counting on the support / guidance of the teacher). The work also has the purpose of creating good writing habits (which is not possible with an evaluation using tests only).