By the end of this subject, students will be able to have: 1. Knowledge and understanding of the of the principles of calculus of one variable, underlying their branch of engineering. 2. The ability to apply their knowledge and understanding to identify, formulate and solve problems of the calculus of one variable using established methods. 3. The ability to select and use appropriate tools and methods to solve problems of the calculus of one variable. 4. The ability to combine theory and practice to solve problems of the calculus of one variable. 5. The ability to understanding the methods and procedures of the calculus of one variable, its area of application and their limitations.

RA1.1: Knowledge and understanding of the scientific and mathematical principles underlying their branch of industrial engineering. RA2.1: The ability to apply their knowledge and understanding to identify, formulate and solve engineering problems using established methods. RA5.1: The ability to select and use appropriate equipment, tools and methods. RA5.2: The ability to combine theory and practice to solve engineering problems. 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. CB2: Students are able to apply their knowledge to their work or vocation in a professional manner and possess the competences usually demonstrated through the development and defence of arguments and problem solving within their field of study. CG1: Ability to resolve problems with initiative, creativity decision-making and critical reasoning skills, and to communicate and transmit knowledge, skills and abilities in the Industrial Engineering area. CG11: Capacity to solve mathematic problems arising in engineering. Aptitude for applying knowledge of: linear algebra; geometry; differential geometry; differential and integral calculus; differential equations and partial derivatives: numerical methods; numerical algorithms; statistics and optimization.

1. Real variable functions. 1.1 The real line. 1.2 Elemmentary functions. 1.3 Limits of functions. 1.4 Continuity. 2. Differential calculus in one variable. 2.1 Derivability. 2.2 Extrema of functions. 2.3 Local properties. Graphic representation. 2.4 Taylor's polynomial. 3. Sequences and series 3.1 Sequences of real numbers. 3.2 Series of real numbers. 3.3 Taylor series 4. Integration in one variable. 4.1 Integrable functions, properties of the integral and calculus of primitives. 4.2 The Fundamental Theorem of Calculus. 4.3 Applications: areas, lengths and volumes by sections.

The docent methodology will include: - Master classes, where the knowledge that the students must acquire will be presented. To make easier the development of the class, the students will have written notes and also will have the basic texts of reference that will facilitate their subsequent work. - Resolution of exercises by the student that will serve as self-evaluation and to acquire the necessary skills. - Small groups classes, in which problems proposed to the students are discussed and developed. - Tutorials.