Calculus I; Linear Algebra

The student will be able to formulate, solve and understand mathematically several problems related to the Aerospace Engineering. To do so it is necessary to be familiar with the n-dimensional Euclidean space, making a special emphasis in dimensions 2 and 3, visualizing the more important subsets. He/she must be able to manage (scalar and vector) functions of several variables, as well as their continuity, differentiability, and integrability properties. The student must solve optimization problems with and without restrictions and will apply the main theorems of integration of scalar and vector functions to compute, in particular, lengths, areas and volumes, and moments of continuum distributions.

CB1: Students have demonstrated possession and understanding of knowledge in an area of study that builds on the foundation of general secondary education, and is usually at a level that, while relying on advanced textbooks, also includes some aspects that involve knowledge from the cutting edge of their field of study. CE.FB1: Ability to solve mathematical problems that may arise in engineering. Ability to apply knowledge of: linear algebra; geometry; differential geometry; differential and integral calculus; differential and partial differential equations; numerical methods; numerical algorithms; statistics and optimisation. RA1: Have basic knowledge and understanding of mathematics, basic sciences, and engineering within the aerospace field, including: behaviour of structures; thermodynamic cycles and fluid mechanics; the air navigation system, air traffic, and coordination with other means of transport; aerodynamic forces; flight dynamics; materials for aerospace use; manufacturing processes; airport infrastructures and buildings. In addition to a specific knowledge and understanding of the specific aircraft and aero-engine technologies in each of the subjects included in this degree.

1. The Euclidean space Rn and its sets. 2. Scalar and vector functions of n real variables. 3. Limits, continuity and differentiability. 4. Higher order derivatives and local behavior of functions. 5. Differential operators and geometric properties. 6. Optimization with and without constraints. 7. Multiple integration. Techniques and changes of variables. 8. Line and surface integrals. 9. Integral theorems of vector calculus in R2 and R3.

The learning methodology will include: - Attendance to master classes, in which core knowledge will be presented that the students must acquire. The recommended bibliography will facilitate the students' work. - Resolution of exercises by the student that will serve as a self-evaluation method and to acquire the necessary skills. - Exercise classes, in which problems proposed to the students are discussed. - Partial exams. - Final Exam. - Tutorial sessions. - The instructors may propose additional homework and activities.