Calculus I

Along T classes is presented a theoretical explanation of the whole subject; in class TP and PL are solved exercises to apply the knowledge acquired. Evaluation: Students can opt for a distributed evaluation or a final exam, in wich a minimum grade of 9.5.must be obtained. In distributed evaluation a 50% atendance is mandatory. In this evaluation the PL, worth 4 points, will be distributed by 2 tests of 2 points each; a minimum of 0.75 in each one is mandatory. The remaining 16 points will be gained by T and TP evaluation, through 3 tests worth 16 points each; minimums of 6 in the first and 7 in the last 2, are required. The sum of the 2 components average need to be at least 9.5 points, otherwise the student will have to take a final exam with the whole subject. Taking this exam in the regular season, and not having the minimums required in only 1 of the 3 components, the student can take just that part on the exam.

Promote the learning of the mathematical basic concepts to allow the student to acquire reasoning skills and competence to understand and use mathematics as a helping tool on the numerous disciplines of the course. After acquiring the concepts taught in this curricular unit, the student must have acquired skills of abstraction and demonstration, in order to be able to identify, analyze and solve problems, knowing to argue the solution he suggested. In particular, it is intend that the student clearly assimilate and interpret the concepts of derivate and integral, so that they can apply them in solving problems related to electromechanical engineering.

Theory of Errors: Error Absolute and Relative Error, truncation errors, Taylor polynomial. Solving Nonlinear Equations: Bisection Method, Newton’s Method Elementary functions: Exponential logarithmic, hyperbolic, inverse Trigonometric Differential Calculus: Limits and Continuity, Differentiability of a function, Derivation rules, Differential function. Primitives Real Function of Real Variable: Definition and properties, Primitivation immediate Methods Primitives: Primitives by decomposition, by parts , primitivation of rational functions and primitivation by substitution. Integral Calculus: Integral defined: Definitions and properties, fundamental theorem of calculus; Fundamental results, applications of definite integral. Improper integrals: integrals at intervals not limited and integrals of functions not limited.

NAO