Calculus I

This course is essentially formative and tries to coordinate with the fundamental theoretical developments needed in the following courses in the curriculum. At this level is promoted intuitive understanding of the concepts and calculation capacity. In Theoretical-Practical lessons the expository and questioning method is used during the explanation of the theoretical subjects and exercises are solved in groups and individually.
Assessment: a Final Exam, rated for 20 points, is performed ; The approval requires that the mark is greater than or equal to 9,5 points.

Objectives: To understand, manipulate and apply the concepts of integration of real functions. Provide a base set of mathematical knowledge required for the proper functioning of other engineering courses. Develop scientific and mathematical reasoning and ability to apply mathematical concepts.

Generic skills: Development of critical thinking, ability to coordinate and exposure, attitudes of reflection and research, for the acquisition of basic knowledge and develop a solid foundation of training, allowing the use of correct techniques and then the rigorous formulation of engineering problems.

Specific skills: Describe the main results in the basic training of mathematical analysis, identify the techniques to solve problems. Being able to expose the solution of problems in a clear and simple way. Explain the concepts and solve problems in an appropriate manner; Solve, autonomously, practical problems, using the subjects dealt with in classes as well as others with whom they relate.

1. Pre-calculus and calculus introduction: Trigonometric functions, exponential and logarithmic functions, limits and continuity.
2. Complements of differential calculus: Derivative of a function; Differentiation rules, theorems of Rolle, Lagrange and Cauchy.
3. Techniques of integration: Definition and properties; Techniques of integration (decomposition, parts, rational functions, substitution).
4. Applications of integration: Riemann integral, definitions and properties, fundamental theorem of calculus; Applications of the definite integral (Calculation of areas of plane regions, Calculation of volumes of solids of revolution, Calculation of arc length); indefinite integral, improper integrals.

NAO