By the end of this content area, students will be able to have: 1. Knowledge and understanding of the mathematical principles of Real Calculus in one variable underlying their branch of engineering. 2. The ability to apply their knowledge and understanding of Real Calculus to identify, formulate and solve mathematical problems using established methods. 3. The ability to select and use appropriate tools and methods of Real Calculus: limits, differentiation, integrals, sequences and series, to solve mathematical problems. 4. The ability to combine theory and practice to solve mathematical problems that require Real Calculus. 5. The ability to understand mathematical methods and procedures of Real Calculus, their area of application and their limitations.

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. CB3. Students have the ability to gather and interpret relevant data (usually within their field of study) in order to make judgements which include reflection on relevant social, scientific or ethical issues. CB4. Students should be able to communicate information, ideas, problems and solutions to both specialist and non-specialist audiences. CB5. Students will have developed the learning skills necessary to undertake further study with a high degree of autonomy. CG1. Analyze, formulate and solve problems with initiative, decision-making, creativity,critical reasoning skills and ability to efficiently communicate and transmit knowledge, skills and abilities in the Energy Engineering field CG10. Being able to work in a multi-lingual and multidisciplinary environment CE1 Módulo FB. Ability to solve the mathematic problems arising in engineering. Aptitude for applying knowledge on: linear algebra; geometry; differential geometry; differential and integral calculus; differential equations and partial derivatives in differential equations; numerical methods; numerical algorithms; statistics and optimization. CT1. Ability to communicate knowledge orally as well as in writing to a specialized and non-specialized public. CT2. Ability to establish good interpersonal communication and to work in multidisciplinary and international teams. CT3. Ability to organize and plan work, making appropriate decisions based on available information, gathering and interpreting relevant data to make sound judgement within the study area. CT4. Motivation and ability to commit to lifelong autonomous learning to enable graduates to adapt to any new situation. By the end of this content area, students will be able to have: RA1.1 knowledge and understanding of the mathematical principles underlying their branch of engineering; RA2.1 the ability to apply their knowledge and understanding to identify, formulate and solve mathematical problems using established methods; RA5.1 the ability to select and use appropriate tools and methods to solve mathematical problems; RA5.2 the ability to combine theory and practice to solve mathematical problems;

1. Real numbers 1.1 Sets of numbers, real line. Sequences and series. 1.2 Functions: basic concepts and definitions. Most common elementary functions. 2. Limits 2.1 Limits of functions: Definition and fundamental theorems. 2.2 Continuity of functions: Properties and fundamental theorems. 3. Differential Calculus in one variable. 3.1 Differentiation of functions: Definitions. Meaning of the derivative. Differentiation Rules. Derivatives of elementary functions. 3.2 Fundamental Theorems of differentiation. L'Hopital's Rule. Extrema of functions. 3.3 Local study of functions: growth, convexity, asymptotes, graphs of functions. 3.4 Taylor Polynomial: Definition, fundamental theorems and most common Taylor expansions. Finding limits via Taylor expansions. 4. Integration in one variable. 4.1 Computing primitives. Immediate integrals, integration by parts, change of variables. 4.2 Definite integral. Fundamental Theorem of Calculus and its applications. 4.3 Applications of the definite integral: calculating areas and volumes of revolution.

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. - Office hours