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.

CHAPTER 1: Functions and Limits - Real Numbers - Functions - Limits - Continuity - Limits and Infinity CHAPTER 2: Differentiation - The derivative and the tangent line - Basic differentiation rules - The chain rule - Implicit differentiation - Rates of change CHAPTER 3: Rolle-s and mean-value theorems - Extrema - Rolle-s and mean-value theorems - Consequences of Rolle-s theorem - L-Hôpital-s rule - Taylor Polynomial CHAPTER 4: Applications of differentiation - Curve sketching - Optimization problems - Introduction to Differential Equations CHAPTER 5: Indefinite Integrals - Antiderivatives and indefinite integration - Basic integration rules - Special methods of integrations CHAPTER 6: Definite Integrals - Area - Riemann sums and definite integrals - The Fundamental Theorem of Calculus - Improper integrals CHAPTER 7: Logarithmic, exponential and other transcendental functions - The natural logarithmic function - Inverse functions - Exponential functions - Inverse trigonometric functions - Hyperbolic functions CHAPTER 8: Applications of Integration - Area between two curves - Volumes of solids of revolution - Arc length and surfaces of revolution - Applications to Physics CHAPTER 9: Sequences and series - Sequences - Series and convergence - Convergence tests CHAPTER 10: Power and Taylor series - Power series - Representation of functions by power series - Taylor and Maclaurin series - Application of power series to differential equations

The methodology will be the usual one for classes in the classroom, writing on the blackboard, with the occasional help of some resources on-line to illustrate some graphic or computational aspects of the course. Also, the classroom notes will be uploaded in Aula Global at the end of each chapter, along with the problem sheets that will be solved and discussed in the small groups.