Sets of numbers. Absolute value and distance Review of the fundamental trigonometric concepts and their basic properties and relations. Definition and properties of open and closed sets and intervals. Determination of the interior, the boundary and the closure of simple sets on the n-dimensional Euclidean space. Session 5. Group work on conics Session 6. Sequences Session 7. Indeterminations and computing limits Definition and convergence criterion. Geometric, telescopic and alternating seiries. Absolutely convergent series. Series with positive terms. Convergence criteria: comparison, quotient and root.

Specific Objectives

Introduce the sets of numbers on which the subject will be developed. Review the concepts of absolute value and proximity To facilitate the use of the trigonometric identities in the applications. To introduce the basic trigonometric functions. The student should be able to determine the interior, the adherence and the boundary of a set and distinguish between different types of intervals. Formalize the concept of approximation

Dedication

Session 10. Concepts and basic operations with functions. Session 11. Trigonometric and other basic functions Session 12. Limit of a function at a point. Definition of continuity Session 13. Computing limits Session 14. Solving problems on quadrics (work in group) Session 15. Weierstrass and Bolzano's theorems. The bisection method Session 16. Continuity problems and application of the bisection method

Dedication

Session 18. Derivative concept. Algebraic properties Session 19. Computing derivatives. Tangent and normal lines. Rolle and Mean Value theorems. L'Hopital Rule. High order derivatives. Taylor polynomial Session 21. Aplication of differentiable functions theorems. Study of nonlinear equations. Session 22. Problem solving on local approximation of functions (work in group) Session 23. Extreme values of one variable functions Session 24. Computing maximum and minimum values

Dedication

Session 26. Riemann Integral definiton Session 27. Computations of integrals Session 28. Barrow's Rule and change of variable Session 29. Problem solving on integral computation Session 31. Aplications:

Dedication