Linear Algebra (Course 1- Semester 1) Differential Calculus (Course 1 - Semester 1) Programming (Course 1 - Semester 1) Integral Calculus (Course 1 - Semester 2) Numerical Methods (Course 2 - Semester 1) Ordinary Differential Equations (Course 3 - Semester 1)

K04: now the principles of probability calculus and statistical inference and how to apply them in solving real-life problems K06: Know the fundamental results of the theory of ordinary, partial differential and stochastic differential equations and their applications in mathematical models S03: Apply mathematical language and abstract-rigorous reasoning in the enunciation and demonstration of results in various areas of mathematics. S13: Formulate real-world problems by means of mathematical models for their subsequent analysis and resolution. S14: Apply appropriate analytical or numerical techniques to solve mathematical models associated with real-world problems and interpret the results obtained. C07: Establish the definition of a new mathematical object, in terms of others already known for solving problems in different contexts. KOPT2: Know advanced mathematical models to represent real-world phenomena, assessing their validity in different contexts.

1. Dimensional analysis 2. Ordinary differential equations as models: dynamical systems 3. Calculus of variations 4. Regular and singular perturbation methods 5. Stability and bifurcation 6. Deterministic chaos: properties and characterization 7. Models based on difference equations 8. Agent-based models

AF1.THEORETICAL-PRACTICAL CLASSES. Knowledge and concepts students must acquire. Student receive course notes and will have basic reference texts to facilitatefollowing the classes and carrying out follow up work.Students partake in exercises to resolve practical problems and participatein workshops and an evaluation tests, all geared towards acquiring the necessary capabilities.Subjects with 6 ECTS are44 hours as a general rule/ 100% classroom instruction AF2.TUTORING SESSIONS. Individualized attendance (individual tutoring) or in-group (group tutoring) for students with a teacher.Subjects with 6 credits have 4 hours of tutoring/ 100% on- site attendance. AF3.STUDENT INDIVIDUAL WORK OR GROUP WORK.Subjects with 6 credits have 98 hours/0% on-site. AF8.WORKSHOPS AND LABORATORY SESSIONS. Subjects with 3 credits have 4 hours with 100% on-site instruction. Subjects with 6 credits have 8 hours/100% on-site instruction. MD1.THEORY CLASS. Classroom presentations by the teacher with IT and audiovisual support in which the subject`s main concepts are developed, while providing material and bibliography to complement student learning. MD2.PRACTICAL CLASS. Resolution of practical cases and problem, posed by the teacher, and carried out individually or in a group. MD3.TUTORING SESSIONS. Individualized attendance (individual tutoring sessions) or in-group (group tutoring sessions) for students with teacher as tutor. Subjects with 6 credits have 4 hours of tutoring/100% on-site. MD6.LABORATORY PRACTICAL SESSIONS. Applied/experimental learning/teaching in workshops and laboratories under the tutor's supervision.