This course develops the basic theory of differential and integral calculus of real functions of a real variable and its main applications. Among them, the rates of change, optimization problems in a real variable, the drawing of graphs of functions, integration techniques, area under a curve and calculation of volumes of surfaces of revolution. Broadly speaking, the course begins with an introduction to the concept of function, the types of basic functions, the domain and range of a function. and its graph. Then, the concepts of limit and continuity are presented, leading us to the definition of derivative as a limit and its interpretations. both geometric and physical. We work with the properties of derivatives and their calculation for algebraic and transcendent functions, as well as the plotting curves and solving optimization problems. It continues with the indefinite integral (antiderivative), as an inverse operation to the differentiation, the integral is presented indefinite set of algebraic and transcendent functions, as well as the main integration techniques. The definite integral is studied, the fundamental theorems of calculus and some applications in which definite integration, supported by indefinite integration methods. Finally, with this course you will be able to solve mathematical problems that appear on a daily basis in engineering, showing a correct and systematic understanding of the key concepts and knowing how to interpret the results obtained.