Calculus I Linear Algebra

The aim of this course is to provide students the basic tools of differential and integral calculus of several variables. To achieve this goal students must acquire a range of expertise and capabilities. SPECIFIC LEARNING OBJECTIVES: - To understand the n-dimensional Euclidean space and in more depth n = 2 and 3. - To know the properties of scalar and vector functions of several variables. - To understand the concepts of continuity, differentiability and integrability. - To be able to handle optimization problems using optimization techniques. - To understand how to calculate double, triple, line and surface integrals. - To know and apply the main theorems of vector calculus: Green, Gauss, Stokes. - To understand how to apply the integral to calculate surface areas, volumes and solve some basic problems of Mathematical-Physics. SPECIFIC ABILITIES: - To be able to work with functions of several variables given in terms of a graphical, numerical or analytical description. - To understand the concept of differentiable function and ability to solve problems involving the concept. - To understand the concept of multiple integral, line and surface integral and its practical applications. GENERAL ABILITIES: - To understand the necessity of abstract thinking and formal mathematical proofs. - To acquire communicative skills in mathematics. - To acquire the ability to model real-world situations mathematically, with the aim of solving practical problems. - To improve problem-solving skills.

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 CG3: Knowledge of basic and technological subject areas which enable acquisition of new methods and technologies, as well as endowing the technical engineer with the versatility necessary to adapt to any new situation. RA1: Knowledge and understanding of the general fundamentals of engineering, scientific and mathematical principles, as well as those of their branch or specialty, including some knowledge at the forefront of their field.

1 .- The n-dimensional Euclidean space. Cartesian, polar, cylindrical and spherical coordinates. 2 .- Scalar and vector functions of several variables. Limits, continuity and differentiability. 3 .- Taylor's theorem. Optimization problems with and without constraints. 4 .- Double, triple, line and surface integral. 5 .- Theorems of Green, Gauss, Stokes and its applications .

Lecture sessions: 3 ECTS credits Problem sessions: 3 ECTS credits