Linear Algebra (First course, first semester) Differential Calculus (First course, first semester) Matrix Algebra (First course, second semester) Mathematical Analysis Principles (Second course, first semester)

The student must acquire the knowledge to solve differential equations as well as the modelization of applied problems through differential equations. A) Learning objectives - Develop models of differential equations - Model and solve first order differential equations - Understand the concept of solution of a differential equation in all its forms - To understand the theorems of existence and uniqueness of solutions - Model and solve second order differential equations - Understand the concept of solution space as well as its existence - Modeling and solving systems of linear differential equations - Stability of solutions for linear systems. Phase diagrams - Phase diagrams for systems of nonlinear differential equations B) Specific skills - Be able to solve systems of linear equations - Be able to model real life problems by means of differential equations and solve them by means of algorithmic procedures - To be able to understand the abstract properties of differential equations C) General skills - Be able to think abstractly, and apply mathematical techniques to obtain information for differential equations. - Be able to communicate orally and in writing using appropriate mathematical language - Be able to model a real problem using differential equations - Be able to interpret the solution of a mathematical problem, its accuracy and limitations - Be able to use mathematical software

K05: Know the fundamental results of linear algebra, linear geometry and discrete mathematics and how to apply them in applied contexts. 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.

1. Introduction. 2. First order equations. Abstract theory. 3. Solving first order equations. 4. Higher order equations. 5. Other methods of resolution. 6. Linear systems. 7. Dynamical systems.

THEORETICAL-PRACTICAL CLASSES. [44 hours with 100% classroom instruction, 1.67 ECTS] The knowledge that students need to acquire will be presented, and exercises will be given to help them develop the necessary skills. TUTORING SESSIONS. [4 hours of tutoring with 100% on-site attendance, 0.15 ECTS] Individualized attendance (individual tutoring) or in-group (group tutoring) for students with a teacher. STUDENT INDIVIDUAL WORK OR GROUP WORK [98 hours with 0 % on-site, 3.72 ECTS] WORKSHOPS AND LABORATORY SESSIONS [8 hours with 100% on site, 0.3 ECTS] FINAL EXAM. [4 hours with 100% on site, 0.15 ECTS] Global assessment of knowledge, skills and capacities acquired throughout the course. METHODOLOGIES THEORY CLASS. Classroom presentations by the teacher with IT and audiovisual support, if necessary, in which the subject's main concepts are developed, while providing material and bibliography to complement student learning. PRACTICAL CLASS. Resolution of practical cases and problem, posed by the teacher, and carried out individually or in a group. TUTORING SESSIONS. Individualized attendance (individual tutoring sessions) or in-group (group tutoring sessions) for students with a teacher as tutor. LABORATORY PRACTICAL SESSIONS. Applied/experimental learning/teaching in workshops and laboratories under the tutor's supervision.